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School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Executive Summary The Smart Move Challenge was designed for students to challenge themselves with the objective to obtain the most points possible around an obstacle course. In order to achieve this, the Lego Mindstorm Education NXT was used. Students wer
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
102 Study Guide - Exam I I. Immigration A. What were the origins of New Immigrants versus Old Immigrants? New- southern and eastern europe , Ireland, Germany Old- English, Spanish, 17th century immigrants B. What were their motivations for coming to Ameri
School: UMBC
Course: Calculus
vl MATHlsl Mrs. Bonny Tighe EXAM IIA Part I 50 points Name Section Fn rc126/07 I . Usethe position function .s(t)= -cos2 t + er + 400 meters,andfind the velocrty and acceleration time at t= 1sec. 2. Uset}le Limit Definition for a derivative t of
School: UMBC
CHAPTER 7 SECTION 1: RANDOM VARIABLES AND DISCRETE PROBAB ILITY DISTRIBUTIONS TRUE/FALSE 1. The time required to drive from New York to New Mexico is a discrete random variable. ANS: F PTS: 1 NAT: Analytic; Probability Distributions REF: SECTION 7.1 2. A
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Krystal Sweetenburg DUE May 18, 2010 PHIL 100: Class Paper (FINAL) The study of ethics, in philosophy, focuses on understanding what makes an action either just or unjust and why one should strive to commit only just actions. If one addresses the question
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
TABLE OF CONTENTS EXECUTIVE SUMMARY.i INTRODUCTION.2 SPECIFICATIONS. 2 CUSTOMERS.2 DESIGN, TIMELINE. 2 HOW THE DEVICE WORKS.
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Executive Summary The Smart Move Challenge was designed for students to challenge themselves with the objective to obtain the most points possible around an obstacle course. In order to achieve this, the Lego Mindstorm Education NXT was used. Students wer
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Derek Kolokythas The effects of Microsoft SharePoint are that it allows colleagues and coworkers to view and share documents within a corporation or business. It is has great qualities that allows them to work together without being at the same place at t
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Mayen Akpan 3/7/12 IS 310 Research Paper Senseye Eye Control for Mobile Devices It is a known and evident fact that technology is progressing at a rapid pace within our society, swimming with transformational impacts and numerous innovations that are brew
School: UMBC
Course: Calculus
MATH 151 PRACTICE FOR SECTION 5.5 1. Evaluate each integral. 1 dx _ a) 1 x2 c) ex 1 e 2 x dx = _ e) g) 2 1 x ( x 2 3 dx _ 3 b) 7 x 6 dx = _ d) 5 x cos x dx _ f ) tan d _ ex dx h) 1 e x 2 5) x dx _ csc 2 x dx i) cot x sin j) sec( 1 x ) tan 1 x dx x2
School: UMBC
Implicit Functions Implicit Differentiation Logarithmic Differentiation Lecture 14: Implicit Differentiation Implicit Functions Functions Defined Implicitly Example 49 A Function Defined Implicitly Example 50 Two Functions Defined Implicitly by
School: UMBC
Course: Calculus
vl MATHlsl Mrs. Bonny Tighe EXAM IIA Part I 50 points Name Section Fn rc126/07 I . Usethe position function .s(t)= -cos2 t + er + 400 meters,andfind the velocrty and acceleration time at t= 1sec. 2. Uset}le Limit Definition for a derivative t of
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Exam 2B Multiple Choice Identify the choice that best completes the statement or answers the question. _ 1. A(n) _ is the lowest-level command that software can direct a processor to perform. a. instruction c. cycle b. operand d. process 2. The _ of a dis
School: UMBC
Course: Applied Finite Mathematics
( po i nt s ) 14 i F nd t he t so l u i on ge n e ' l l i ne tha t of re a 5' yst du ced by em ec ro w i ng t h e pu t t h e l o n fo au g n t ed me H JJ 0 q x B - 2 0 0 = A T L S = / rs " o t nt? t m o n sis t e n t ? I n c o n s is e in t s) I s t he l
School: UMBC
Course: Applied Finite Mathematics
(L 1) F'" d t h e g e t l c > a l s o l 11t i o n t o t h e f o l i o ;w i n g 1i n G a u s s J o r c l a n Lcducl i or 1 b y ha n d: tj ( 1b ) U se y o (l c ) 0s t h e u r er a ge n n s ;s te n ( 1d ) t 4z + z s o lu t i o n in p a r t sy s t e m Co l
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Systems Architecture, 6e Ch. 5 Solutions-11 Chapter 5 Solutions Vocabulary Exercises 1. Dynamic RAM requires frequent _ to maintain its data content. refresh cycles 2. The _ rate is the speed at which data can be moved to or from a storage device over a c
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Systems Architecture, 6e Ch. 2 Solutions-1 Chapter 2 Solutions Vocabulary Exercises 1. A(n) _ generally supports more simultaneous users than a(n) _. Both are designed to support more than one user. mainframe, minicomputer 2. register 3. The term _ refers
School: UMBC
Course: Applied Finite Mathematics
Ho w y d i l fe r e n t m a n se f le t t e r s o qu e n c e s b e fo can r m ed u sin g t h e le t t e r s fr o each o f t h e fo l l o w i n g ds? w o r 1 \ Cp 7 : Y o u ha f 10 d i s t i n g a n d 1 b l u e 1n a r b l e b le s , m ar o ba g ve a * wm e
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2009 LAB SIX COUNTERS In this lab, you will use the flip-flops and combinational logic gates which you have made previously to implement a special counter. The counter will count from 0 to 14 in twos and both upwards and downwards. Th
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2011 LAB # 4 MINI 4-BIT ALU IMPLEMENTATION For this lab you will need to build a device which performs binary arithmetic and logical operations. Your device should accept two 4-bit operands as input. You will need other inputs in orde
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2011 LAB # 3 Multiplexers and Decoders The goal of this lab is to create structural Verilog code for all the devices listed below: 8 to 1 Multiplexer 1 to 8 De-multiplexer 3 to 8 Decoder 8 to 3 Priority Encoder (do this at the end !)
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2009 LAB TWO NAND/NOR LOGIC IMPLEMENTATION F = (A'B + A'C' + BC)' The goal of this lab assignment is to implement the above function using structural Verilog. You are to implement this function three times as follows: (a.) Implement t
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2011 LAB # 1 Introduction to Verilog The goal of this lab assignment is to implement the following schematic using structural Verilog. In order to verify your code is working correctly, you will need to also build a test bench routine
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
102 Study Guide - Exam I I. Immigration A. What were the origins of New Immigrants versus Old Immigrants? New- southern and eastern europe , Ireland, Germany Old- English, Spanish, 17th century immigrants B. What were their motivations for coming to Ameri
School: UMBC
Course: Applied Finite Mathematics
ur Ji n ex a m w Yo * , t es t p e n C a lc u St u d e n ts st u . x p ec :e n t is n p h as is em a o n ge t he t a o f c la s s , J a n u a r y 23 r d i n M P 10 1 t he m a t e r i a l c o v e r e d a f t e r t he s e c o on it h y o u w la it da y fi n
School: UMBC
Course: Introduction To Linear Algebra
Math 221-03 (Intro to Linear Algebra) Fall Semester 2012 TuTh 10 11:15am Math & Psychology 103 Instructor: Dr. Kalman M. Nanes Oce: Math/Psych 439, phone 4104552439 Oce hours: F 1 3pm in MP439, F 3 6pm in the CASTLE (UC115D), or by appointment. e-mail: kn
School: UMBC
MATH 151 CALCULUS I 4 credits Spring, 2013 COURSE INFORMATION: LECTURE: Sections 01/02/03/04/05 MWF 10:00-10:50 ACIV 003 (old LH4) DISCUSSIONS: 02 on Mon and Wed from 11:00-11:50 in UC 115D TA Edna Cheng 03 on Mon and Wed from 1:00-1:50 in ACIV 015 TA Edn
School: UMBC
Course: Calculus And Analytic Geometry I
Syllabus for MATH 151 Calculus I Summer 2009 Course information: Lecture: Mon/Wed/Thu, 6:00pm8:05pm (SOND 108) Discussion: Mon/Wed, 5:00pm5:50pm (SOND 108) Course website: http:/www.math.umbc.edu/~aa5/teaching/math151 Instructor: Alen Agheksanterian
School: UMBC
Course: Introduction To Partial Differential Equations I
Math 404 Introduction to Partial Differential Equations I Spring Semester, 2006 Monday-Wednesday 5:30-6:45pm M/P 008 Instructor: Jonathan Bell M/P 405 Office hours: right after class, or by appointment (see me, or contact Mr. Mashbaum, or drop by t
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Executive Summary The Smart Move Challenge was designed for students to challenge themselves with the objective to obtain the most points possible around an obstacle course. In order to achieve this, the Lego Mindstorm Education NXT was used. Students wer
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
102 Study Guide - Exam I I. Immigration A. What were the origins of New Immigrants versus Old Immigrants? New- southern and eastern europe , Ireland, Germany Old- English, Spanish, 17th century immigrants B. What were their motivations for coming to Ameri
School: UMBC
Course: Calculus
vl MATHlsl Mrs. Bonny Tighe EXAM IIA Part I 50 points Name Section Fn rc126/07 I . Usethe position function .s(t)= -cos2 t + er + 400 meters,andfind the velocrty and acceleration time at t= 1sec. 2. Uset}le Limit Definition for a derivative t of
School: UMBC
CHAPTER 12 SECTION 1: INFERENCE ABOUT A POPULATION TRUE/FALSE 1. In order to determine the p-value associated with hypothesis testing about the population mean , it is necessary to know the value of the test statistic. ANS: T PTS: 1 NAT: Analytic; Hypothe
School: UMBC
CHAPTER 7 SECTION 1: RANDOM VARIABLES AND DISCRETE PROBAB ILITY DISTRIBUTIONS TRUE/FALSE 1. The time required to drive from New York to New Mexico is a discrete random variable. ANS: F PTS: 1 NAT: Analytic; Probability Distributions REF: SECTION 7.1 2. A
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Exam 2B Multiple Choice Identify the choice that best completes the statement or answers the question. _ 1. A(n) _ is the lowest-level command that software can direct a processor to perform. a. instruction c. cycle b. operand d. process 2. The _ of a dis
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Systems Architecture, 6e Ch. 5 Solutions-11 Chapter 5 Solutions Vocabulary Exercises 1. Dynamic RAM requires frequent _ to maintain its data content. refresh cycles 2. The _ rate is the speed at which data can be moved to or from a storage device over a c
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Systems Architecture, 6e Ch. 2 Solutions-1 Chapter 2 Solutions Vocabulary Exercises 1. A(n) _ generally supports more simultaneous users than a(n) _. Both are designed to support more than one user. mainframe, minicomputer 2. register 3. The term _ refers
School: UMBC
Course: Calculus
2.6 LIMITS AT INFINITY DEFINITION for Limits at Infinity Let f be a function defined on some open interval (a, ) . Then lim f ( x) L means that for every 0 there is a N 0 such x that if x N then Prove: f ( x) L 1 0 x x 2 lim 1) Find a number such that i
School: UMBC
Course: Calculus
2.5 CONTINUITY OF A FUNCTION AT A POINT The function f (x ) is continuous at point a if: 1. f (a ) exists 2. lim f ( x) exists and x a 3. lim f ( x) f (a ) x a Find discontinuous points and state why the point is discontinuous. State the intervals of cont
School: UMBC
Course: Calculus
2.8 Derivatives as functions DEFINITION: A function f is differentiable at a if f ' (a ) exists. f ' (a ) exists if 1- f is continuous at a, 2- there is no vertical tangent line at a 3 the slope of f as x approaches a from both sides is the same (no corne
School: UMBC
Course: Calculus
2.7 Derivatives and Rates of Change DEFINITION: The tangent line to the curve y f (x) at the point P (a, f (a) is the line through P with slope f ( x) f (a) f ( x h) f ( x) m lim m lim or x a h 0 h x a DERIVATIVE OF A FUNCTION f ' ( x) lim f ( x) f (a ) O
School: UMBC
Course: Calculus
3.1 DIFFERENTIATION RULES d ( f ( x) g ( x) dx f ' ( x) g ( x) d (a ) 0 dx d ( x n ) nx n 1 dx d (e x ) e x dx d (af ( x) a f ' ( x) dx d (a x ) dx a x ln a HIGHER ORDER DERIVATIVES f ' ( x), f ' ' ( x), f ' ' ' ( x), ., f ( n ) ( x) dy dx d2y , dx d3y 2
School: UMBC
Course: Calculus
3.11 DEFINITION OF THE HYPERBOLIC TRIGONOMETRIC FUNCTIONS e x e x sinh x 2 tanh x e x e x cosh x 2 sinh x cosh x DERIVATIVES OF HYPERBOLIC FUNCTIONS d d cosh x sinh x sinh x cosh x dx dx d tanh x sec h 2 x dx Find the numerical value of each expression
School: UMBC
Course: Calculus
Differentiate f(x) - . (cfw_o^n sinx-cscx tanx + 4' g*) GasX cfw_'(x) s@) -2e*(cos x+3^til fcr. x c-otrJ * (.;k -c\ct 4*-y rv ") t (co.r.+a o.J 2 '5' f (t) = Soc /, uu'f>) -, fird f" cfw_'/o) (?.J, e* .W,@"lri' *,n/, = Find the 95th derivative for f (t) -
School: UMBC
Course: Calculus
3.10 Linear Approximation (Using the tangent line to a function at a point a to approximate function values near point a) Of f(x) at x = a L( x ) f ( a ) f ' ( a )( x a ) Find the linear approximation of the function f ( x) x 5 2 x 3 3 x 5 at a = 1 and us
School: UMBC
Course: Calculus
3.2 DIFFERENTIATION of PRODUCTS and QUOTIENTS Find a) c) b) d) e) f) Find the second derivative for If f is a differentiable function, find an expression for the derivative of each of the following functions. Suppose that
School: UMBC
Course: Calculus
2.4 Precise Definition of a Limit Let f be a function defined on some open interval that contains the number a, except possibly at a itself. Then we say that the limit of f(x) as x approaches a lim f ( x) L if for every is L, and we write x a number 0 the
School: UMBC
Course: Calculus
2.3 LIMIT LAWS lim f ( x) g ( x) lim f ( x) lim g ( x) x a x a x a lim f ( x) g ( x) lim f ( x) lim g ( x) x a x a x a lim f ( x) g ( x) lim f ( x) lim g ( x) x a x a x a lim cf ( x) c lim f ( x) x a x a lim f ( x) lim f ( x) x a x a lim c c n x a n l
School: UMBC
Course: Calculus
2.1 TANGENTS AND VELOCITIES 1. If a rock is thrown upward on the planet Mars with a velocity of 15 m/s, its height in meters t seconds later is given by y = 15t 1.86t2. (a) The average velocity over the given time intervals is given. (i) [1, 2] 9.42 m/s (
School: UMBC
Course: Calculus
QUIZ 1A MATH 151 Mrs. Bonny Tighe 2.1 2.3 25 points NAME _ TA_ Monday 9/8/2014 1. The graphs of f and g are given. Use them to evaluate each limit, if it exists 3g ( x ) _ a) lim f g ( x ) _ b) lim 2 f 3g ( x ) _ c) xlim x 1 x 2 1 f ( x) 2. Use the
School: UMBC
Course: Calculus
QUIZ 1 MATH 151 Mrs. Bonny Tighe 2.1 2.3 25 points NAME _ TA_ Monday 9/8/14 1. The graphs of f and g are given. Use them to evaluate each limit, if it exists. g ( x) _ a) lim f g ( x) _ b) xlim f g ( x ) _ c) lim 2 x 4 x 3 f ( x ) 2. Use the given gra
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 2A 2.4 2.5 25 points NAME _ TA_ Wed 9/15/2014 1. a) What must be true for a function to be continuous at a point? b) What must be true for a function to be continuous on an interval [a, b]? 2. a) Find a number such that if |
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 2 2.4 2.5 25 points NAME _ TA_ Wed 9/15/2014 1. a) What must be true for a function to be continuous at a point? b) What must be true for a function to be continuous on an interval [a, b]? 2. a) Find a number such that if |
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 3 25 points 2.6-2.8 NAME_ TA_ Mon 9/22/2014 Use the definition of a derivative only on this quiz, no formulas. 1. Find the following limits, if possible. x a) lim e _ x 2 x 2 3 _ lim c) x 4 3 x x 3 3 _ e) lim 4 x x
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 3A 25 points 2.6-2.8 NAME_ TA_ Mon 9/22/2014 Use the definition of a derivative only on this quiz, no formulas. 1. Find the following limits, if possible. x a) lim e _ x b) lim(ln(sin x ) _ x 0 2 x 2 3 _ lim c) 2 x 4 x
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 4A NAME _ 3.4 25 points TA_ Monday 10/6/2014 1. Find dy/dx a) b) c) d) e) 2. a) Suppose that F(x) = f [g(x)] and , Find =_. b) If 3. Find the 97th derivative for each of the functions using patterns. a) g(x) = b)
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 4 NAME _ 3.4 25 points TA_ Monday 10/6/2014 1. Find dy/dx a) b) c) d) e) 2. a) Suppose that F(x) = f [g(x)] and , Find =_. b) If 3. Find the 97th derivative for each of the functions using patterns. a) g(x) = b)
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 5 3.5, 3.6,3.9 25 points NAME _ TA_ Mon 10/13/2014 1. Find the equation of the tangent line to the curve at the point (1, ln5) 2. Find for at the point where x = 1. 3. Use logarithmic differentiation to find the derivative o
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 5A 3.5, 3.6,3.9 25 points NAME _ TA_ Mon 10/13/2014 1. Find dy/dx a) b) c) 2. Find for at the point where x = 1. 3. Find the equation of the tangent line to the curve at the point (1, ln4) 4. Use logarithmic differentiation
School: UMBC
Course: Calculus
3.3 DERIVATIVES OF TRIG FUNCTIONS MEMORIZE sin x 1 x 0 x lim 1 cos x 0 x 0 x lim x 1 x 0 sin x lim cos x 1 0 x 0 x lim Find the following limits: lim sin 3 x x 0 x lim lim 1 cos x x 0 sin x lim sin 5 x x 0 sin 2 x lim lim tan 2 x x 0 x tan 4 x x 0 sin 5 x
School: UMBC
Course: Calculus
3.4 THE CHAIN RULE If y f g ( x ) then dy dx f ' g ( x ) g ' ( x ) Find dy/dx y (3x 2)5 y sin(cos x ) y e x y cos(7 x ) y sin( x 2 ) cos 2 x 3 y 4 x 7 y 5tan x y 2 x 3 3x (2 x 3) 4 y x 5 (3x 3 ) y (e5 x 1)6 ( x3 tan x)6 y = 34 x y sec(sin(cos x ) Suppose
School: UMBC
Course: Calculus
3.5 IMPLICIT DIFFERENTIATION Where y f (x ) Find dy/dx Implicitly and Explicitly Explicit x 2 y 2 9 Example: Given: Implicit f ( x ) 2 x 3 f ( x ) 5 and f (1) 2, find f ' (1) y 9 x2 Find dy/dx: sin( y ) xy tan xy 5 x x 3 y 3 2 x 2 cos x e xy x e y y 2 9
School: UMBC
Course: Calculus
Definition: The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of the approximating rectangles. A lim Rn lim x f ( x1 ) x f ( x 2 ) x f ( x n ) n n n * b Or A lim x f ( xi ) f ( x )dx n
School: UMBC
Course: Calculus
THEFUNDAMENTAL THEOREMOFCALCULUS Suppose f is continuous on [a, b] x PART 1. If g ( x) f (t )dt , then g ' ( x) f ( x) a x Or d f (t )dt f ( x) dx a b PART 2. f ( x)dx F (b) F (a) a antiderivative of f, that is F ' f where F is any Use the definition of t
School: UMBC
Course: Calculus
5.4 Indefinite Integrals and Net Change Theorem f ( x) dx F ( x) means F ' ( x) f ( x) The Integral of a rate of change is the net change b F ' ( x)dx F (b) F (a) a b TOTAL DISTANCE TRAVELED v(t ) dt a b DISPLACEMENT v (t ) dt a The change in velocity fr
School: UMBC
Course: Calculus
5.5 THE SUBSTITUTION RULE (U-substitution) If u g (x) is a differentiable function whose range is the interval I and f is continuous on I , then f g ( x)g ' ( x)dx f (u )du sin 4 x dx e3 x dx sec 2 2 x dx 5 2 x dx sec 5x tan 5x dx sin 4 x dx ( x 3 4 2
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 7A 4.4 25 points NAME _ TA _Mon 11/3/2014 1. Find the limit. Use LHospitals Rule where appropriate. sin x _ x 0 x 2 a ) lim c ) lim(3x 9 x 2 2 x 1) _ x e x 3x 2 _ x x3 b) lim d ) lim ( x ) ( ln x ) _ x o x 2x 5 e) lim
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM I NAME _ 2.1-3.3 100 points TA_ Mon 9/29/2014 1. (20 points) Find the following limits, if possible. 2 x 2 3 1 3 a) lim b) xlim tan ( x ) _ 4 5 x _ x c) lim x 2 2 x _ 2 x 2 d) tan( 4t ) lim _ t 0 sin( 7t ) 2 e) li
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM IA NAME _ 2.1-3.3 100 points TA_ Mon 9/29/2014 1. (10 points) State and use the definition of the derivative to find f (x) for 1 f ( x) 3x 1 2. (10 points) Short Answer a) What must be true for a function to be differentiab
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM II 3.4-4.3 100 points NAME _ TA_ Mon 10/27/2014 1. (10 points) a) Use the properties of logarithms to find dy/dx. cosh(4 x ) y ln x 5 (tan x)(5 ln x ) b) Use logarithmic differentiation to find the derivative of the funct
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM IIA NAME _ 3.4-4.3 100 points TA_ Mon 10/27/2014 1. (10 points) A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM III 100 points 4.4-5.4 NAME _ TA_Mon12/2/2014 1. (15 points) Find the limits. Use LHospitals rule where appropriate a) xlim( x )(ln x ) 0 2 x 3 b) lim x 2x 4 x 2. (10 points) A poster is to have an area of 500 square inc
School: UMBC
Course: Calculus
MATH EXAM 151 Mrs. Bonny Tighe A III NAME 100 points TA 4.4-5.4 1. (15 points) Find the limits. Use L'Hospital's rule where appropriate r $d- f'"M\ ryr #.jL 't" j 1lcfw_?il' lim(x)(lnx) a) x-+0* #"@ i 1, MonlLl2l2013 f J -_'l-oe* I ? i"'t ) -?u I ial\' .
School: UMBC
Course: Calculus
5.2 The Definite Integral DEFINITION OF A DEFINITE INTEGRAL The AREA under the curve f (x) on the interval [a, b] b a and ( xi )* a x i Where x n n THEN A lim n n c cn i 1 i 1 b x f ( xi* ) f ( x) dx a n(n 1) n2 n i 2 or 2 2 i 1 n n(n 1)(2n 1) n3 n2 n
School: UMBC
Course: Calculus
5.1 AREAS AND DISTANCES n * A f ( xi ) x i 1 n b a x n A lim f ( xi )*x lim f ( x1 )x f ( x2 )x f ( xn )x n i 1 n Approximate the area under the curve f ( x) x 2 2 x 1 on [0,2] using 4 approximating rectangles (n=4) a) Using Right-hand endpoints b) Us
School: UMBC
Course: Calculus
3.6 DERIVATIVE OF LOGARITHMS d (ln x) 1 dx x d (log a x) d (ln u ( x) 1 dx x ln a u ' ( x) dx u ( x) Definition e lim(1 x) 1 x x 0 LOGARITHMIC DIFFERENTIATION Type I Using properties of logs to simplify before differentiating. Type II Taking the log of bo
School: UMBC
Course: Calculus
3.9 RELATED RATES 1-Rate(s) are given Draw a diagram Give variables to all parts of the picture that are moving do not put any numbers that are not constant on this diagram 2-A related rate needs to be found Get an equation relating the variables in the g
School: UMBC
Course: Calculus
4.1 MAXIMUM AND MINIMUM VALUES THE EXTREME VALUE THEOREM If f is continuous on a closed interval [a, b], then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in [a, b] Definition: Let c be a number in th
School: UMBC
Course: Calculus
4.2 THE MEAN VALUE THEOREM ROLLES THEOREM Let f be a function that satisfies the following three hypotheses: 1. f is continuous on the closed interval [a,b] 2. f is differentiable on the open interval (a,b) 3. f(a)=f(b) Then there is a number c in (a,b) s
School: UMBC
Course: Calculus
4.3 Derivatives and graphs INCREASING/DECREASING TEST a) If f ' ( x) 0 on an interval, then f is increasing on that interval b) If f ' ( x ) 0 on an interval, then f is decreasing on that interval The First Derivative Test Suppose that c is a critical num
School: UMBC
Course: Calculus
4.4 LHospitals Rule Suppose f and g are differentiable and g ' ( x) 0 on an open interval I that contains a (except possibly at a) Suppose that lim f ( x) 0 x a and Or that lim f ( x) and Then lim g ( x) 0 x a f ( x) f ' ( x) lim lim x a g ( x ) x a g '
School: UMBC
Course: Calculus
4.5 CURVE SKETCHING SECTION 1 Find Domain 2 Find Intercepts 3 Find Asymptotes 4 Find Critical Numbers and Intervals of Increasing and Decreasing using the First Derivative Test 5- Find Inflection Points and Intervals of Concave Up and Concave Down Using t
School: UMBC
Course: Calculus
4.7 B OPTIMIZATION a) I have a sheet of material 5 m by 5 m to construct an open-topped box. I want to cut squares out of each corner and fold up the sides to form the box. What dimensions will maximize this box? b) A farmer wants to enclose three adjacen
School: UMBC
Course: Calculus
OPTIMIZATION (Maximum or Minimum) OBJECTIVE CONSTRAINT What you are trying to optimize Diagram Givens Get into one variable Using constraint Differentiate Find the zeros Ex: A piece of paper 8 by 11 is to be made into an open top box by cutting squares ou
School: UMBC
Course: Calculus
4.8 NEWTONS METHOD (Approximating zeros of functions) f ( xn ) xn 1 xn f ' ( xn ) Use Newtons Method to find an approximate root. Use xo = 1 for the initial approximation and find up x 5 5 x 2 4 x 1 0 to the x2. Use Newtons Method to find an approximate
School: UMBC
Course: Calculus
4.9 ANTIDIFFERENTIATION If If If If If If If If If If If If If x n 1 f ' ( x) x n , then f ( x) C n 1 f ' ( x) a, then f ( x) ax C 1 f ' ( x) , then f ( x) ln x C x f ' ( x) sin x, then f ( x) cos x C f ' ( x) cos x, then f ( x) sin x C f ' ( x) sec 2 x,
School: UMBC
CHAPTER 7 SECTION 1: RANDOM VARIABLES AND DISCRETE PROBAB ILITY DISTRIBUTIONS TRUE/FALSE 1. The time required to drive from New York to New Mexico is a discrete random variable. ANS: F PTS: 1 NAT: Analytic; Probability Distributions REF: SECTION 7.1 2. A
School: UMBC
CHAPTER 10 SECTION 2: INTRODUCTION TO ESTIMATION TRUE/FALSE 47. In order to construct a confidence interval estimate of the population mean, the value of the population mean is needed. ANS: F PTS: 1 NAT: Analytic; Interval Estimation REF: SECTION 10.2 48.
School: UMBC
Course: Calculus And Analytic Geometry II
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Anxious Apprihension 1. High levels of diffuse negative emotion 2. A sense of uncontrollability and 3. A shift in attention to a primary self-focus or a state of self-preoccupation Worry Acognitive activity that is associated with anxiety Relatively uncon
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Chapter One Examples and Definitions of Abnormal Behavior Psychopathology is the pathology of the mind Abnormal psychology is the application of psychological science to the study of mental disorders Recognizing the presence of a disorder Psychosis, is a
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMSC201 Final Exam Review Fall 2009 Picture ID required for the Final Exam These questions are sample questions. The questions below may be modified by being reworded (i.e. true statements may be made false), by changing variable names, constants, etc. if
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
United States has the largest import factor than export, The most patents and ideas are created in United States. South America excels at exporting food Primary Activities Natural resources Secondary Activates Manufactured resources Tertiary Activities Se
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Review for the Final Exam The final exam will be cumulative and will be entirely multiple choice. Review for Material Covered on Midterm 1 Production Possibility Frontiers The production possibility frontier shows the combinations of goods that can be pro
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
SharePoint Technology, created by the technical master Microsoft, is the new intranet software of the business world. Since 2007, SharePoint has helped various business owners across the globe to organize web content, create and edit documents, and mainta
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
HIST 102: 29 March *N.B.-The major theme to take away from the 1920s is the culture clash between traditional values and modern values* (For example-the new woman, the new negro, new morality, new view of marriage, *religion*) Religion in the 1920s -Chang
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Krystal Sweetenburg DUE May 18, 2010 PHIL 100: Class Paper (FINAL) The study of ethics, in philosophy, focuses on understanding what makes an action either just or unjust and why one should strive to commit only just actions. If one addresses the question
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
TABLE OF CONTENTS EXECUTIVE SUMMARY.i INTRODUCTION.2 SPECIFICATIONS. 2 CUSTOMERS.2 DESIGN, TIMELINE. 2 HOW THE DEVICE WORKS.
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Executive Summary The Smart Move Challenge was designed for students to challenge themselves with the objective to obtain the most points possible around an obstacle course. In order to achieve this, the Lego Mindstorm Education NXT was used. Students wer
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Derek Kolokythas The effects of Microsoft SharePoint are that it allows colleagues and coworkers to view and share documents within a corporation or business. It is has great qualities that allows them to work together without being at the same place at t
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Mayen Akpan 3/7/12 IS 310 Research Paper Senseye Eye Control for Mobile Devices It is a known and evident fact that technology is progressing at a rapid pace within our society, swimming with transformational impacts and numerous innovations that are brew
School: UMBC
Course: Calculus
MATH 151 PRACTICE FOR SECTION 5.5 1. Evaluate each integral. 1 dx _ a) 1 x2 c) ex 1 e 2 x dx = _ e) g) 2 1 x ( x 2 3 dx _ 3 b) 7 x 6 dx = _ d) 5 x cos x dx _ f ) tan d _ ex dx h) 1 e x 2 5) x dx _ csc 2 x dx i) cot x sin j) sec( 1 x ) tan 1 x dx x2
School: UMBC
Implicit Functions Implicit Differentiation Logarithmic Differentiation Lecture 14: Implicit Differentiation Implicit Functions Functions Defined Implicitly Example 49 A Function Defined Implicitly Example 50 Two Functions Defined Implicitly by
School: UMBC
Course: Calculus
vl MATHlsl Mrs. Bonny Tighe EXAM IIA Part I 50 points Name Section Fn rc126/07 I . Usethe position function .s(t)= -cos2 t + er + 400 meters,andfind the velocrty and acceleration time at t= 1sec. 2. Uset}le Limit Definition for a derivative t of
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Exam 2B Multiple Choice Identify the choice that best completes the statement or answers the question. _ 1. A(n) _ is the lowest-level command that software can direct a processor to perform. a. instruction c. cycle b. operand d. process 2. The _ of a dis
School: UMBC
Course: Applied Finite Mathematics
( po i nt s ) 14 i F nd t he t so l u i on ge n e ' l l i ne tha t of re a 5' yst du ced by em ec ro w i ng t h e pu t t h e l o n fo au g n t ed me H JJ 0 q x B - 2 0 0 = A T L S = / rs " o t nt? t m o n sis t e n t ? I n c o n s is e in t s) I s t he l
School: UMBC
Course: Applied Finite Mathematics
(L 1) F'" d t h e g e t l c > a l s o l 11t i o n t o t h e f o l i o ;w i n g 1i n G a u s s J o r c l a n Lcducl i or 1 b y ha n d: tj ( 1b ) U se y o (l c ) 0s t h e u r er a ge n n s ;s te n ( 1d ) t 4z + z s o lu t i o n in p a r t sy s t e m Co l
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM IIIA 4.4- 5.3 100 points Name _ TA_ Mon 12/2/2014 1. (10 points) Find the limit. Use LHospitals Rule where appropriate. a ) lim ( x ) tan 1 _ x x x 3x 2 b) lim _ x 3x 1 2. (10 points) Find the dimensions of the rectangl
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 10A 25 points 5.1 5.2 NAME _ TA_ Monday 11/24/14 1. (15 points) Approximate the area under the curve f ( x ) ln x, 1 x 2 using n = 4 rectangles. Approximate the area using the following: . Sketch the graph. SET UP, DO NOT EV
School: UMBC
Course: Calculus
MATH 152 Mrs. Bonny Tighe QUIZ 9A 25 points 4.5-4.7 NAME _ TA_ Mon 11/11/2014 1. Find the dimensions of the rectangle with largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola y 27 x 2 . 2. Fin
School: UMBC
Course: Calculus
MATH 152 Mrs. Bonny Tighe QUIZ 9A 25 points 4.7 NAME _ TA_ Mon 11/11/2014 1. Find the critical numbers, intervals of increasing and decreasing, inflection points, intervals of concave up and concave down and local maximums and minimums using the first and
School: UMBC
Course: Calculus
MATH 152 Mrs. Bonny Tighe QUIZ 9 25 points 4.7 NAME _ TA_ Mon 11/11/2014 1. Find the critical numbers, intervals of increasing and decreasing, inflection points, intervals of concave up and concave down and local maximums and minimums using the first and
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 7 4.4 25 points NAME _ TA _ Mon 11/3/2014 1. Find the limit. Use LHospitals Rule where appropriate. x2 _ x 0 1 cos x a ) lim c ) lim( x 2 3x 1 x ) _ x x e x 4 _ x x3 b) lim d ) lim x ln x _ x o x 3x 2 e) lim _ x 3x 1 g
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 7A 4.4 25 points NAME _ TA _Mon 11/3/2014 1. Find the limit. Use LHospitals Rule where appropriate. sin x _ x 0 x 2 a ) lim c ) lim(3x 9 x 2 2 x 1) _ x e x 3x 2 _ x x3 b) lim d ) lim ( x ) ( ln x ) _ x o x 2x 5 e) lim
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 6 25 points 3.10,3.11 NAME _ TA _ Mon 10/20/2014 1. Find the linear approximation of the function f ( x ) sin x at a 3 and use it to approximate the number x 59 0 2. Compute y and dy for the given values of x and x dx f ( x)
School: UMBC
Course: Calculus
MATH EXAM 151 Mrs. Bonny Tighe A III NAME 100 points TA 4.4-5.4 1. (15 points) Find the limits. Use L'Hospital's rule where appropriate r $d- f'"M\ ryr #.jL 't" j 1lcfw_?il' lim(x)(lnx) a) x-+0* #"@ i 1, MonlLl2l2013 f J -_'l-oe* I ? i"'t ) -?u I ial\' .
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM III 100 points 4.4-5.4 NAME _ TA_Mon12/2/2014 1. (15 points) Find the limits. Use LHospitals rule where appropriate a) xlim( x )(ln x ) 0 2 x 3 b) lim x 2x 4 x 2. (10 points) A poster is to have an area of 500 square inc
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM IIA NAME _ 3.4-4.3 100 points TA_ Mon 10/27/2014 1. (10 points) A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM II 3.4-4.3 100 points NAME _ TA_ Mon 10/27/2014 1. (10 points) a) Use the properties of logarithms to find dy/dx. cosh(4 x ) y ln x 5 (tan x)(5 ln x ) b) Use logarithmic differentiation to find the derivative of the funct
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM IA NAME _ 2.1-3.3 100 points TA_ Mon 9/29/2014 1. (10 points) State and use the definition of the derivative to find f (x) for 1 f ( x) 3x 1 2. (10 points) Short Answer a) What must be true for a function to be differentiab
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe EXAM I NAME _ 2.1-3.3 100 points TA_ Mon 9/29/2014 1. (20 points) Find the following limits, if possible. 2 x 2 3 1 3 a) lim b) xlim tan ( x ) _ 4 5 x _ x c) lim x 2 2 x _ 2 x 2 d) tan( 4t ) lim _ t 0 sin( 7t ) 2 e) li
School: UMBC
Course: Calculus
5.5 THE SUBSTITUTION RULE (U-substitution) If u g (x) is a differentiable function whose range is the interval I and f is continuous on I , then f g ( x)g ' ( x)dx f (u )du sin 4 x dx e3 x dx sec 2 2 x dx 5 2 x dx sec 5x tan 5x dx sin 4 x dx ( x 3 4 2
School: UMBC
Course: Calculus
5.4 Indefinite Integrals and Net Change Theorem f ( x) dx F ( x) means F ' ( x) f ( x) The Integral of a rate of change is the net change b F ' ( x)dx F (b) F (a) a b TOTAL DISTANCE TRAVELED v(t ) dt a b DISPLACEMENT v (t ) dt a The change in velocity fr
School: UMBC
Course: Calculus
THEFUNDAMENTAL THEOREMOFCALCULUS Suppose f is continuous on [a, b] x PART 1. If g ( x) f (t )dt , then g ' ( x) f ( x) a x Or d f (t )dt f ( x) dx a b PART 2. f ( x)dx F (b) F (a) a antiderivative of f, that is F ' f where F is any Use the definition of t
School: UMBC
Course: Calculus
Definition: The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of the approximating rectangles. A lim Rn lim x f ( x1 ) x f ( x 2 ) x f ( x n ) n n n * b Or A lim x f ( xi ) f ( x )dx n
School: UMBC
Course: Calculus
5.2 The Definite Integral DEFINITION OF A DEFINITE INTEGRAL The AREA under the curve f (x) on the interval [a, b] b a and ( xi )* a x i Where x n n THEN A lim n n c cn i 1 i 1 b x f ( xi* ) f ( x) dx a n(n 1) n2 n i 2 or 2 2 i 1 n n(n 1)(2n 1) n3 n2 n
School: UMBC
Course: Calculus
5.1 AREAS AND DISTANCES n * A f ( xi ) x i 1 n b a x n A lim f ( xi )*x lim f ( x1 )x f ( x2 )x f ( xn )x n i 1 n Approximate the area under the curve f ( x) x 2 2 x 1 on [0,2] using 4 approximating rectangles (n=4) a) Using Right-hand endpoints b) Us
School: UMBC
Course: Calculus
4.9 ANTIDIFFERENTIATION If If If If If If If If If If If If If x n 1 f ' ( x) x n , then f ( x) C n 1 f ' ( x) a, then f ( x) ax C 1 f ' ( x) , then f ( x) ln x C x f ' ( x) sin x, then f ( x) cos x C f ' ( x) cos x, then f ( x) sin x C f ' ( x) sec 2 x,
School: UMBC
Course: Calculus
4.8 NEWTONS METHOD (Approximating zeros of functions) f ( xn ) xn 1 xn f ' ( xn ) Use Newtons Method to find an approximate root. Use xo = 1 for the initial approximation and find up x 5 5 x 2 4 x 1 0 to the x2. Use Newtons Method to find an approximate
School: UMBC
Course: Calculus
OPTIMIZATION (Maximum or Minimum) OBJECTIVE CONSTRAINT What you are trying to optimize Diagram Givens Get into one variable Using constraint Differentiate Find the zeros Ex: A piece of paper 8 by 11 is to be made into an open top box by cutting squares ou
School: UMBC
Course: Calculus
4.7 B OPTIMIZATION a) I have a sheet of material 5 m by 5 m to construct an open-topped box. I want to cut squares out of each corner and fold up the sides to form the box. What dimensions will maximize this box? b) A farmer wants to enclose three adjacen
School: UMBC
Course: Calculus
4.5 CURVE SKETCHING SECTION 1 Find Domain 2 Find Intercepts 3 Find Asymptotes 4 Find Critical Numbers and Intervals of Increasing and Decreasing using the First Derivative Test 5- Find Inflection Points and Intervals of Concave Up and Concave Down Using t
School: UMBC
Course: Calculus
4.4 LHospitals Rule Suppose f and g are differentiable and g ' ( x) 0 on an open interval I that contains a (except possibly at a) Suppose that lim f ( x) 0 x a and Or that lim f ( x) and Then lim g ( x) 0 x a f ( x) f ' ( x) lim lim x a g ( x ) x a g '
School: UMBC
Course: Calculus
4.3 Derivatives and graphs INCREASING/DECREASING TEST a) If f ' ( x) 0 on an interval, then f is increasing on that interval b) If f ' ( x ) 0 on an interval, then f is decreasing on that interval The First Derivative Test Suppose that c is a critical num
School: UMBC
Course: Calculus
4.2 THE MEAN VALUE THEOREM ROLLES THEOREM Let f be a function that satisfies the following three hypotheses: 1. f is continuous on the closed interval [a,b] 2. f is differentiable on the open interval (a,b) 3. f(a)=f(b) Then there is a number c in (a,b) s
School: UMBC
Course: Calculus
4.1 MAXIMUM AND MINIMUM VALUES THE EXTREME VALUE THEOREM If f is continuous on a closed interval [a, b], then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in [a, b] Definition: Let c be a number in th
School: UMBC
Course: Calculus
3.9 RELATED RATES 1-Rate(s) are given Draw a diagram Give variables to all parts of the picture that are moving do not put any numbers that are not constant on this diagram 2-A related rate needs to be found Get an equation relating the variables in the g
School: UMBC
Course: Calculus
3.6 DERIVATIVE OF LOGARITHMS d (ln x) 1 dx x d (log a x) d (ln u ( x) 1 dx x ln a u ' ( x) dx u ( x) Definition e lim(1 x) 1 x x 0 LOGARITHMIC DIFFERENTIATION Type I Using properties of logs to simplify before differentiating. Type II Taking the log of bo
School: UMBC
Course: Calculus
3.5 IMPLICIT DIFFERENTIATION Where y f (x ) Find dy/dx Implicitly and Explicitly Explicit x 2 y 2 9 Example: Given: Implicit f ( x ) 2 x 3 f ( x ) 5 and f (1) 2, find f ' (1) y 9 x2 Find dy/dx: sin( y ) xy tan xy 5 x x 3 y 3 2 x 2 cos x e xy x e y y 2 9
School: UMBC
Course: Calculus
3.4 THE CHAIN RULE If y f g ( x ) then dy dx f ' g ( x ) g ' ( x ) Find dy/dx y (3x 2)5 y sin(cos x ) y e x y cos(7 x ) y sin( x 2 ) cos 2 x 3 y 4 x 7 y 5tan x y 2 x 3 3x (2 x 3) 4 y x 5 (3x 3 ) y (e5 x 1)6 ( x3 tan x)6 y = 34 x y sec(sin(cos x ) Suppose
School: UMBC
Course: Calculus
3.3 DERIVATIVES OF TRIG FUNCTIONS MEMORIZE sin x 1 x 0 x lim 1 cos x 0 x 0 x lim x 1 x 0 sin x lim cos x 1 0 x 0 x lim Find the following limits: lim sin 3 x x 0 x lim lim 1 cos x x 0 sin x lim sin 5 x x 0 sin 2 x lim lim tan 2 x x 0 x tan 4 x x 0 sin 5 x
School: UMBC
Course: Calculus
Differentiate f(x) - . (cfw_o^n sinx-cscx tanx + 4' g*) GasX cfw_'(x) s@) -2e*(cos x+3^til fcr. x c-otrJ * (.;k -c\ct 4*-y rv ") t (co.r.+a o.J 2 '5' f (t) = Soc /, uu'f>) -, fird f" cfw_'/o) (?.J, e* .W,@"lri' *,n/, = Find the 95th derivative for f (t) -
School: UMBC
Course: Calculus
3.2 DIFFERENTIATION of PRODUCTS and QUOTIENTS Find a) c) b) d) e) f) Find the second derivative for If f is a differentiable function, find an expression for the derivative of each of the following functions. Suppose that
School: UMBC
Course: Calculus
3.11 DEFINITION OF THE HYPERBOLIC TRIGONOMETRIC FUNCTIONS e x e x sinh x 2 tanh x e x e x cosh x 2 sinh x cosh x DERIVATIVES OF HYPERBOLIC FUNCTIONS d d cosh x sinh x sinh x cosh x dx dx d tanh x sec h 2 x dx Find the numerical value of each expression
School: UMBC
Course: Calculus
3.10 Linear Approximation (Using the tangent line to a function at a point a to approximate function values near point a) Of f(x) at x = a L( x ) f ( a ) f ' ( a )( x a ) Find the linear approximation of the function f ( x) x 5 2 x 3 3 x 5 at a = 1 and us
School: UMBC
Course: Calculus
3.1 DIFFERENTIATION RULES d ( f ( x) g ( x) dx f ' ( x) g ( x) d (a ) 0 dx d ( x n ) nx n 1 dx d (e x ) e x dx d (af ( x) a f ' ( x) dx d (a x ) dx a x ln a HIGHER ORDER DERIVATIVES f ' ( x), f ' ' ( x), f ' ' ' ( x), ., f ( n ) ( x) dy dx d2y , dx d3y 2
School: UMBC
Course: Calculus
2.8 Derivatives as functions DEFINITION: A function f is differentiable at a if f ' (a ) exists. f ' (a ) exists if 1- f is continuous at a, 2- there is no vertical tangent line at a 3 the slope of f as x approaches a from both sides is the same (no corne
School: UMBC
Course: Calculus
2.7 Derivatives and Rates of Change DEFINITION: The tangent line to the curve y f (x) at the point P (a, f (a) is the line through P with slope f ( x) f (a) f ( x h) f ( x) m lim m lim or x a h 0 h x a DERIVATIVE OF A FUNCTION f ' ( x) lim f ( x) f (a ) O
School: UMBC
Course: Calculus
2.6 LIMITS AT INFINITY DEFINITION for Limits at Infinity Let f be a function defined on some open interval (a, ) . Then lim f ( x) L means that for every 0 there is a N 0 such x that if x N then Prove: f ( x) L 1 0 x x 2 lim 1) Find a number such that i
School: UMBC
Course: Calculus
2.5 CONTINUITY OF A FUNCTION AT A POINT The function f (x ) is continuous at point a if: 1. f (a ) exists 2. lim f ( x) exists and x a 3. lim f ( x) f (a ) x a Find discontinuous points and state why the point is discontinuous. State the intervals of cont
School: UMBC
Course: Calculus
2.4 Precise Definition of a Limit Let f be a function defined on some open interval that contains the number a, except possibly at a itself. Then we say that the limit of f(x) as x approaches a lim f ( x) L if for every is L, and we write x a number 0 the
School: UMBC
Course: Calculus
2.3 LIMIT LAWS lim f ( x) g ( x) lim f ( x) lim g ( x) x a x a x a lim f ( x) g ( x) lim f ( x) lim g ( x) x a x a x a lim f ( x) g ( x) lim f ( x) lim g ( x) x a x a x a lim cf ( x) c lim f ( x) x a x a lim f ( x) lim f ( x) x a x a lim c c n x a n l
School: UMBC
Course: Calculus
2.1 TANGENTS AND VELOCITIES 1. If a rock is thrown upward on the planet Mars with a velocity of 15 m/s, its height in meters t seconds later is given by y = 15t 1.86t2. (a) The average velocity over the given time intervals is given. (i) [1, 2] 9.42 m/s (
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 5A 3.5, 3.6,3.9 25 points NAME _ TA_ Mon 10/13/2014 1. Find dy/dx a) b) c) 2. Find for at the point where x = 1. 3. Find the equation of the tangent line to the curve at the point (1, ln4) 4. Use logarithmic differentiation
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 5 3.5, 3.6,3.9 25 points NAME _ TA_ Mon 10/13/2014 1. Find the equation of the tangent line to the curve at the point (1, ln5) 2. Find for at the point where x = 1. 3. Use logarithmic differentiation to find the derivative o
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 4 NAME _ 3.4 25 points TA_ Monday 10/6/2014 1. Find dy/dx a) b) c) d) e) 2. a) Suppose that F(x) = f [g(x)] and , Find =_. b) If 3. Find the 97th derivative for each of the functions using patterns. a) g(x) = b)
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 4A NAME _ 3.4 25 points TA_ Monday 10/6/2014 1. Find dy/dx a) b) c) d) e) 2. a) Suppose that F(x) = f [g(x)] and , Find =_. b) If 3. Find the 97th derivative for each of the functions using patterns. a) g(x) = b)
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 3A 25 points 2.6-2.8 NAME_ TA_ Mon 9/22/2014 Use the definition of a derivative only on this quiz, no formulas. 1. Find the following limits, if possible. x a) lim e _ x b) lim(ln(sin x ) _ x 0 2 x 2 3 _ lim c) 2 x 4 x
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 3 25 points 2.6-2.8 NAME_ TA_ Mon 9/22/2014 Use the definition of a derivative only on this quiz, no formulas. 1. Find the following limits, if possible. x a) lim e _ x 2 x 2 3 _ lim c) x 4 3 x x 3 3 _ e) lim 4 x x
School: UMBC
Course: Calculus
MATH 151 Mrs. Bonny Tighe QUIZ 2 2.4 2.5 25 points NAME _ TA_ Wed 9/15/2014 1. a) What must be true for a function to be continuous at a point? b) What must be true for a function to be continuous on an interval [a, b]? 2. a) Find a number such that if |
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Systems Architecture, 6e Ch. 5 Solutions-11 Chapter 5 Solutions Vocabulary Exercises 1. Dynamic RAM requires frequent _ to maintain its data content. refresh cycles 2. The _ rate is the speed at which data can be moved to or from a storage device over a c
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Systems Architecture, 6e Ch. 2 Solutions-1 Chapter 2 Solutions Vocabulary Exercises 1. A(n) _ generally supports more simultaneous users than a(n) _. Both are designed to support more than one user. mainframe, minicomputer 2. register 3. The term _ refers
School: UMBC
Course: Applied Finite Mathematics
Ho w y d i l fe r e n t m a n se f le t t e r s o qu e n c e s b e fo can r m ed u sin g t h e le t t e r s fr o each o f t h e fo l l o w i n g ds? w o r 1 \ Cp 7 : Y o u ha f 10 d i s t i n g a n d 1 b l u e 1n a r b l e b le s , m ar o ba g ve a * wm e
School: UMBC
Course: Applied Finite Mathematics
M a : _ 0 a , T 0 b1 n s 9 c\ cl o 2 \ t o n 0 0 Ser v c 5 u n i\ b f t 6 0 b 6 l :0 Fn r o m p r 0 ' qc ) \ b 2 0 00 s ' 5 a 0 O n 0 l o D o . q r3 0 c O \ D So o * . m A . c m m 0 u n C 1 S el v i c e s 0 /A 0 0 ci i s n p
School: UMBC
Course: Applied Finite Mathematics
' x ; o w o w & o w o H * H w G iv D 3 W n a ma ec a n r n M e d 10 0 isin g de m t t u n un y n y , Fo r t he t he rn a n t he t y n y o ts f paper p p er a of its i o .o d its ts i u n un hn !y _ 500, 4 en m a n ma o of gy t he f w o o w o m a c o r r e
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Systems Architecture, 6e Ch. 1 Solutions-1 Chapter 1 Solutions Vocabulary Exercises 1. Students of information systems generally focus on application software. Students of _ generally focus on system software. computer science 2. Configuring hardware and
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Hemorrhage A hemorrhage is simply bleeding and can range to a spurting artery. There are two main types of hemorrhage: o external hemorrhage o from small capillary bleed or visible hemorrhage Internal hemorrhage External hemorrhage is bleeding on the Inte
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
Dylan Poole EHS 476 Homework 1 1. The first component of a comprehensive trauma system is primary, secondary and tertiary injury prevention. Primary injury prevention involves things like educating the public about safety, such as informing them of the da
School: UMBC
Course: Precalculus
Math 150 Suggested HW Problems Fall 2009 Sec 1.7: 1, 5, 9,14,17, 21, 25, 27, 29, 32, 35, 38, 43, 47, 50, 53, 55, 57, 63, 66, 69, 71, 75, 101,103, 105 Sec 1.10: 1, 5, 9, 11, 15, 18, 20, 23, 25, 29, 32, 35, 4152, 55, 63, 65, 67 Sec 2.1: 1-8, 11, 13, 15, 17,
School: UMBC
Course: Precalculus
Math 106 Suggested HW Problems Spring 2008 Chapter 7 Sec 7.1: Sec 7.2: Sec 7.3: 7, 11, 15, 19, 25, 30, 35, 43, 49, 55, 60, 65, 69, 75, 79 7, 11, 17, 23, 23, 31, 35, 45, 51, 55, 67, 75 7, 11, 17, 23 Chapter 4 Sec 4.1: Sec 4.2: Sec 4.3: Sec 4.4: Sec 4
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2009 LAB SIX COUNTERS In this lab, you will use the flip-flops and combinational logic gates which you have made previously to implement a special counter. The counter will count from 0 to 14 in twos and both upwards and downwards. Th
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2011 LAB # 4 MINI 4-BIT ALU IMPLEMENTATION For this lab you will need to build a device which performs binary arithmetic and logical operations. Your device should accept two 4-bit operands as input. You will need other inputs in orde
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2011 LAB # 3 Multiplexers and Decoders The goal of this lab is to create structural Verilog code for all the devices listed below: 8 to 1 Multiplexer 1 to 8 De-multiplexer 3 to 8 Decoder 8 to 3 Priority Encoder (do this at the end !)
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2009 LAB TWO NAND/NOR LOGIC IMPLEMENTATION F = (A'B + A'C' + BC)' The goal of this lab assignment is to implement the above function using structural Verilog. You are to implement this function three times as follows: (a.) Implement t
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
CMPE 212-0101 Spring 2011 LAB # 1 Introduction to Verilog The goal of this lab assignment is to implement the following schematic using structural Verilog. In order to verify your code is working correctly, you will need to also build a test bench routine
School: UMBC
Course: INTRO TO LINEAR ALGEBRA
102 Study Guide - Exam I I. Immigration A. What were the origins of New Immigrants versus Old Immigrants? New- southern and eastern europe , Ireland, Germany Old- English, Spanish, 17th century immigrants B. What were their motivations for coming to Ameri
School: UMBC
Course: Applied Finite Mathematics
ur Ji n ex a m w Yo * , t es t p e n C a lc u St u d e n ts st u . x p ec :e n t is n p h as is em a o n ge t he t a o f c la s s , J a n u a r y 23 r d i n M P 10 1 t he m a t e r i a l c o v e r e d a f t e r t he s e c o on it h y o u w la it da y fi n
School: UMBC
Course: Introduction To Linear Algebra
Math 221-03 (Intro to Linear Algebra) Fall Semester 2012 TuTh 10 11:15am Math & Psychology 103 Instructor: Dr. Kalman M. Nanes Oce: Math/Psych 439, phone 4104552439 Oce hours: F 1 3pm in MP439, F 3 6pm in the CASTLE (UC115D), or by appointment. e-mail: kn
School: UMBC
MATH 151 CALCULUS I 4 credits Spring, 2013 COURSE INFORMATION: LECTURE: Sections 01/02/03/04/05 MWF 10:00-10:50 ACIV 003 (old LH4) DISCUSSIONS: 02 on Mon and Wed from 11:00-11:50 in UC 115D TA Edna Cheng 03 on Mon and Wed from 1:00-1:50 in ACIV 015 TA Edn
School: UMBC
Course: Calculus And Analytic Geometry I
Syllabus for MATH 151 Calculus I Summer 2009 Course information: Lecture: Mon/Wed/Thu, 6:00pm8:05pm (SOND 108) Discussion: Mon/Wed, 5:00pm5:50pm (SOND 108) Course website: http:/www.math.umbc.edu/~aa5/teaching/math151 Instructor: Alen Agheksanterian
School: UMBC
Course: Introduction To Partial Differential Equations I
Math 404 Introduction to Partial Differential Equations I Spring Semester, 2006 Monday-Wednesday 5:30-6:45pm M/P 008 Instructor: Jonathan Bell M/P 405 Office hours: right after class, or by appointment (see me, or contact Mr. Mashbaum, or drop by t