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MATH 160  Boise State Study Resources

Curve Sketching Worksheet 2 Key
School: Boise State
Worksheet 2 Curve Sketching Curve Sketching 1. Determine the domain of the function. 2. Find the x and y intercepts of the function. 3. Determine the behavior of the function for large absolute values of x . 4. Find all horizontal and vertical asymp

C674
School: Boise State
9. PRESENT VALUE OF AN INVESTMENT Suppose an invest ment is expected to generate income at the rate of R(t) = 200,000 dollars/year for the next 5 yr. Find the present value of this investment if the prevailing interest rate is 8%/year com pounded c

Opto
School: Boise State
To maximize the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable? f'tAXIMIZING PROFITS The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for man~i'ufactUring

Test 3 Sample_1
School: Boise State
Sample Test This test will cover 4.45.6, excepting 4.6 (Related Rates, which we skipped) This is probably longer than the actual test will be. Part I 1. Find y' for y =e x 3. 2 2. Find f x =ln 3x 1 Find f'(x) 4. dy for dx x 2 y 2=25 x 2 y 2e xy= 20 Find

Limit Of A Function
School: Boise State
Course: Survey Of Calculus
S ECTION 2.2 THE LIMIT OF A FUNCTION each quantity, if it exists. If it does not exist, explain why. (a) lim t t (b) lim t t (c) lim t t (b) lim f x x l 3 xl4 4. For the function f whose graph is given, state the value of each quantity, if it exists. If

Extra Trig Practice
School: Boise State
Course: Survey Of Calculus
Extra Practice: Trigonometry 1. Evaluate the following (exactly, without a calculator): (a) sin(3/4) (c) tan(2/3) (e) csc(29/6) (b) cos(5/4) (d) sec(7/6) (f) tan(/4) 2. What is the amplitude, period and frequency for f (x) = 1 + 2 cos(3x) 3. What is the p

Review For Exam 2
School: Boise State
Course: Survey To Calculus
Review for Exam 2 Covers: section 3.6, 3.7 & 4.1 4.5 Math 160, Fall 12 Section 3.6: Be able to calculate x , y , y / x , dx, and dy for a given function and xvalues Section 3.7: Be able to find marginal cost, marginal revenue, and marginal profit funct

Review For Exam 11
School: Boise State
Course: Survey To Calculus
Review for Exam 1 Covers: section 1.1, 1.2, 2.1, 2.3 & 3.1 3.5 Math 160002, Fall 12 Section 1.1: Be able to solve a linear equation Be able to solve a linear inequality Section 1.2: Be able to graph a linear function Be able to find the slope of a li

Test 4_1
School: Boise State
Test #4 Integrals Chapters 67 Takehome test Part I: evaluating integrals Evaluate the integrals. Show all work. Give answers either as exact answers, or rounded to the nearest hundredth. 1. x 2 1 x dx 3. 1 x x 3 dx 5. 6 x x 3 dx 6 1 2. e 3 t dt 4. 0 x

Test 4
School: Boise State
Name: _ Math 160 Test #4: Integration For the problems marked Calculatorfree, no calculators may be used. You must show all work for these problems so that I can see, step by step, how it is done. Part I: Antiderivatives Find the antiderivative or inte

Test 4 Takehome
School: Boise State
Name: _ Test #4: Integrals Takehome portion Calculators Allowed. Show the setup for the integrals, but you can use the calculator to evaluate it. 1. A computer running a Microsoft operating system will experience its first Blue Screen Of Death 4t (BSOD)

Test 4 Takehome Sols
School: Boise State
Name: _ Test #4: Integrals Takehome portion Calculators Allowed. Show the setup for the integrals, but you can use the calculator to evaluate it. 1. A computer running a Microsoft operating system will experience its first Blue Screen Of Death 4t (BSOD)

Test 2 Sols
School: Boise State
Name: _ Test #2 Limits, Continuity & Derivatives Find the derivative of the following functions: f ' x =10 x 1 x3 3 4 g ' x = 4 =3 x x 2. g x = 1. f x = x 10 9 4. h x =25 5. f t = ln t h ' x =0 f ' t =1 / t 7. f x =3 x x 10. f x = x ln x x y ' =e x 6. f

Test 4 In Class Sols
School: Boise State
Name: _ Test #4 Integrals Inclass portion No Calculators 1. The easiest thing to do here would be to split it up. The first part needs usubstitution, but not the second part. 4 4 4 t t 0 2 t 21 2 1 dt =0 2 t 21 2 dt 0 1 dt 2 u = 2 t 1 ; du =4 t dt 1 9 u

Test 3
School: Boise State
Name: _ Test #3: Applications of Derivatives Math 160 This is a calculus test. I need to see calculus in order to give credit. Show all work. If I don't see calculus work, I won't give credit. 1. f is continuous and a < b < c < . < k < l < m x a b c d e f

Test 3 Spring 2011
School: Boise State
Name: _ Test #3 Applications of Derivatives Math 160 Calculators are permitted, but show all work. 1. Solve either of the problems below. A. A boat is tied to a dock as shown in the picture below. A winch on the dock is connected to the boat, and when the

Test 3 Sols
School: Boise State
Name: _ Test #3 Part I (40 points) Find the derivative: 1. Find f ' x for f x =e x x 25 3 f ' x =e x 6 x x 2 5 2 y ' for x 2 y 2=1 xy 2 y y ' = 2 = x xy 2. Find dy for dx dy 2 x e y = dx xe y 1 y 3. Find 2 x e y = x 2 Find the limit 2 4. lim x 1 x x ln x

Test 3 Sols1
School: Boise State
Name: _ Test #3 Applications of Derivatives Math 160 Calculators are permitted, but show all work. 1. Solve either of the problems below. A. A boat is tied to a dock as shown in the picture below. A winch on the dock is connected to the boat, and when the

Test 2
School: Boise State
Name: _ Test #2 Limits, Continuity & Derivatives Find the derivative of the following functions: 1 x3 1. f x = x 10 2. g x = 4. h x =25 5. f t = ln t 6. f x =12 x 7. f x =3 x 8. V x = 2 9. r s =log 5 s 10. f x = x ln x x 11. y = 3. y =e x 5 x 3 x 2 2 x 1

Test 4 In Class
School: Boise State
Name: _ Test #4 Integrals Inclass portion No Calculators 1. 4 0 t 1 dt 2 t 1 2 2 Find the average value of this function over the interval [0, 4] dy =x2 y dx 2. Find the general solution to the equation Find the particular solution to the equation that

Rates And Changes
School: Boise State
Course: Survey Of Calculus
The slope of a line is given by: y x The slope at (1,1) can be approximated by the slope of the secant through (4,16). 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 y 16 1 15 = = =5 x 4 1 3 We could get a better approximation if we move the point closer to (1,1)

Exam 2 Review
School: Boise State
Course: Survey Of Calculus
Exam 2 Review: 2.83.6 This portion of the course covered the bulk of the formulas for dierentiation, together with a few denitions and techniques. Remember that we also left 2.8 for this exam. From 2.8, we should be able to plot the derivative given a gr

Exam 1 Review
School: Boise State
Course: Survey Of Calculus
Exam 1 Review Questions 8. Show that there must be at least one real solution to: x5 = x2 + 4 Please also review the old quizzes, and be sure that you understand the homework problems. General notes: (1) Always give an algebraic reason for your answer (gr

Exam 3 Review
School: Boise State
Course: Survey Of Calculus
Math 125: Exam 3 Review Since were using calculators, to keep the playing eld level between all students, I will ask that you refrain from using certain features of your calculator, including graphing. Here is the statement that will appear on the exam an

Exam 1 Summary
School: Boise State
Course: Survey Of Calculus
Summary: To Exam 1 (Up through 2.7) General Background: Chapter 1 and Appendices There is a lot of algebra and trigonometry in Chapter 1, and Appendices A, B, C and D, so this is not an exhaustive list of everything you need to know, but there are some th

Definite Integrals
School: Boise State
Course: Survey Of Calculus
3 1 V = t2 +1 8 When we find the area under a curve by adding rectangles, the answer is called a Rieman sum. 2 1 The width of a rectangle is called a subinterval. 0 1 2 subinterval 3 4 The entire interval is called the partition. partition Subintervals do

Derivatives Of Trig Functions
School: Boise State
Course: Survey Of Calculus
Consider the function y = sin ( ) slope We could make a graph of the slope: 2 0 Now we connect the dots! 2 The resulting curve is a cosine curve. 1 0 1 0 1 d sin ( x ) = cos x dx We can do the same thing for y = cos ( ) slope 2 0 The resulting curve is

Parametric Equations
School: Boise State
Course: Survey Of Calculus
There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations for the x and y coordinates in terms of a third variable (usually t or ). x = f (t ) y = g (t ) These are called parametric equations.

Take Home Final1
School: Boise State
Name: _ Math 160 Final Exam Takehome portion Calculators are permitted. Please show all necessary steps, including setting up integrals. Part I (Test 2) 1. Use the definition of the derivative (i.e., the four step process) to find the derivative of the f

Final
School: Boise State
Name: _ Math 160 Final Exam Business Calculus Part I 1. Limits and Continuity cfw_ x 2 5 x 6 g x = x 2 2 x 3 a x 3 x =3 What value of x makes g continuous at x = a? Using this value for a, is g continuous everywhere? (i.e., are there any other discontinui

Probapp1
School: Boise State
ems for Section 8.6 . . 1. Consider the fishing data given in Example 1 on page 463. Show that the area under the density function in Figure 8.44 is 1. Why is this to be expected? 2. Find the mean daily catch for the fishing data in Figure 8.44, page

Phyapp1
School: Boise State
Problems for Section 8.3 I. A water tank is in the fonn of a right circular cylinder with height 20 ft and radius 6 ft. If tIJ tank is half full of water, find the work required to pump all of it over the top rim. (Note I cubic foot of water weighs 6

Geoapp2
School: Boise State
8.2 APPLICAnONS TO GEOMETRY 435 14. Rotate the bellshaped curve y = exz/2 shown in Figure 8.21 around the yaxis, forming a hillshaped solid of revolution. By slicing horizontally, find the volume of this hill. y 1 Y = exzJ2 x Figure 8.21 15. The

Ecoapp2
School: Boise State
.  ~ ~  7. (a) If you deposit money continuously at a constant rate of $1000 per year into a bank account that earns 5% interest, how many years will it take for the balance to reach $10,000? (b) How many years would it take if the account had $

C676
School: Boise State
a. Compute the coefficient of inequality for each Lorentz curve. b. Which profession has a more equitable income distribution? 23. LORENTZ CURVES A certain country's income distribution is described by the function 14 1 f(x) = , X2 +  x 15 15 a. S

Historical Activities For The Calculus Classroom
School: Boise State
1 Historical Activities for the Calculus Classroom Gabriela R. Sanchis1 Department of Mathematical Sciences Elizabethtown College sanchisgr@etown.edu Introduction The history of the calculus is a fascinating story, inspired by the search for soluti

3.9relatedrates
School: Boise State
BC Calculus Lesson 3.9 Related Rates 3.9(1) If xy = 10 and dx dy = 20 , find when x = 5 . dt dt 3.9(2) (Dedicated to Mr. Ray a math teacher who once actually had the ladder fall. He broke his arm but had a great problem for his classes.) A man

Ti83
School: Boise State
Supplement On Using The TI83 Mark S. Korlie Department of Mathematical Sciences, Montclair State University Upper Montclair, New Jersey 1 Getting Started and Editing Tips Turning on the calculator and turning it off: Press ON to turn the calcula

WorldOilProd
School: Boise State
Table 2: Petroleum Production and Consumpti on in the United States, 19932003 (in thousands of barrels per day) 1993 Production (total)* Production (Crude Oil only) Consumpti on * includes crude oil, natural gas plant liquids, other liquids, and refi

How Gauss Determined The Orbit Of Ceres
School: Boise State
How Gauss Determined The Orbit of Ceres by Jonathan Tennenbaum and Bruce Director PREFACE The following presentation of Carl Gauss's determination of the orbit of the asteroid Ceres, was commissioned by Lyndon H. LaRouche, Jr., in October 1997, as p

Archimedes Of Syracuse
School: Boise State
Archimedes of Syracuse1 Archimedes of Syracuse (287  212 BCE), the most famous and probably the best mathematician of antiquity, made so many discoveries in mathematics and physics that it is difficult to point to any of them as his greatest. He wa

A History Of The Calculus
School: Boise State
A history of the calculus Analysis index History Topics Index The main ideas which underpin the calculus developed over a very long period of time indeed. The first steps were taken by Greek mathematicians. http:/wwwhistory.mcs.standrews.ac.uk/his

A Brief Survey Of The Calculus Of Variations
School: Boise State
A Brief Survey of the History of the Calculus of Variations and its Applications James Ferguson jcf@uvic.ca University of Victoria Abstract In this paper, we trace the development of the theory of the calculus of variations. From its roots in the wo

A Brief Introduction To Infinitesimal Calculus
School: Boise State
Lecture2.nb 1 A Brief Introduction to Infinitesimal Calculus Section 2: Keisler's Axioms The following presentation of Keisler's foundations for Robinson's Theory of Infinitesimals is explained in more detail in either of the (free .pdf) files: Fou

TransitionToCalculus
School: Boise State
October 25, 2000 The Transition to Calculus 1 Introduction 1 By the end of the 16th century the European algebraists had achieved about as much as possible following the Islamic Tradition. They were expert at algebraic manipulation, could solve cu

The History Of Infinity
School: Boise State
The History of Infinity1 What is it? Where did it come from? How do we use it? Who are the inventors? 1 The Beginning As there is no record of earlier civilizations regarding, conceptualizing, or discussing infinity, we will begin the story of inf

Supply And Demand
School: Boise State
SUPPLY AND DEMAND Law of Demand: Other things equal, price and the quantity demanded are inversely related. Every term is important 1. "Other things equal" means that other factors that affect demand do NOT change. We assume by this clause that inco

The NewtonLeibniz Controversy Over The Invention Of The Calculus
School: Boise State
The NewtonLeibniz controversy over the invention of the calculus S.Subramanya Sastry 1 Introduction Perhaps one the most infamous controversies in the history of science is the one between Newton and Leibniz over the invention of the innitesimal calculus

Limit Quiz Key
School: Boise State
Limits 1. lim x 3 lim x x 2 x 2 2 3 3 8 3 3 3 2. lim 5 x 2 lim x 2 4 2 40 5 5 x 4 x 4 3. lim x 4 lim x 4 lim lim 4 4 3 5 2 5 2 5 x lim 2 5 2 1 x 1 x 1 x 1 1 x x 1 4. lim 2x 3 x 2 7 x 3 lim lim 2x 3

Final Takehome(1)1
School: Boise State
Name: _ Final Exam Take home portion. Please show all work. This is a calculus test, so I need to see calculus work. If you use a calculator to evaluate an integral, you need to show it set up. 1. Nonbuoyant bulls and cows need to be pastured separately

160 Test 2 Derivatives Revised
School: Boise State
Name: _ Math 160 Test #2: Limits, Continuity and Derivatives Find the derivative of the function: 1. f ( x) = 6 x 10 2. h(t ) = ln(t ) 3. m(k ) = 5ke k 4. r (t ) = 10 t + t 10 5. p ( s) = log 2 ( s) 6. g ( x) = 3 9. Q(r ) = r 2 + 2r 5r 2 7. s (t ) = 1 t3

Implicit Extra Credit
School: Boise State
Extra Credit The Folium of Descartes is a famous curve that looks something like this: It is the graph described by the equation x 3 y 3= 3 xy . You can see that there is a point on this graph where the tangent line is horizontal, and a point where it is

MATH 160hw
School: Boise State
MATH 160 Homework problems Section 1.1: Section 1.2: Section 1.3: Section 2.1: Section 2.2: Section 2.3: Section 2.4: Section 2.5: Section 3.1: Section 3.2: Section 3.3: Section 3.4: Section 3.5: Section 3.6: Section 3.7: Section 4.1: Section 4.2: S

Quotient Rule Worksheet
School: Boise State
Derivatives  Quotient Rule Worksheet 11. f ( x ) = 1 x 2 x 1 2x + 1 x 2x  4 f' ( x) = 12. f ( x ) = f' ( x) = 13. f ( x ) = df = dy 14. y = x2 + 1 x2  1 d ( y) = dx 15. y = x x +1 2 dy = dx x2 + 2 16. y = 2 x + x +1 x2 + 1 x y' = 17

Regression Problems 2
School: Boise State
Example: Below is a table of asteroid names, their average distances from the sun (in millions of miles), and their orbital periods (the time it takes them, in years, to revolve around the sun). Question 1: About how long would it take an asteroid th

Optimization Problems A
School: Boise State
Optimization Problems 1. MAXIMIZING PROFITS The estimated monthly profit ( in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 camera is P ( x ) =  0.04 X 2 + 240 x  10,000 To maximize its pr

Application Problems
School: Boise State
Economic Applications 1. Draw a graph, with time in years on the horizontal axis, of what an income stream might look like for a company that sells sunscreen in the Northeast. 2. A company that owes your company money offers to begin repaying the deb

Optimization Worksheet Key
School: Boise State
Optimization Worksheet 1. FLIGHT OF A ROCKET The altitude ( in feet ) attained by a model rocket t sec Into flight is given by the function 1 3 t + 4t 2 + 20t + 2 3 Find the maximum altitude attained by the rocket. h( t ) = 1 3 t + 4t 2 + 20t + 2 3 h

Optimization Problems B
School: Boise State
Optimization Problems 1. A blue boat is 30 nautical miles due east of point A and traveling due west at 12 nautical miles per hour. A green boat is 20 nautical miles due north of point A and traveling due south at 15 nautical miles per hour. How long

Curve Sketching Worksheet 1 Key
School: Boise State
Worksheet 1 Curve Sketching Sketch the graph of the function using the curvesketching guide. 1. f ( t ) = 2t 3  15t 2 + 36t  20 f ( t ) = 2t 3  15t 2 + 36t  20 Domain y intercept ( , ) 3 2 f ( 0 ) = 2 ( 0 )  15 ( 0 ) + 36 ( 0 )  20 t = 20

Curve Sketching Worksheet
School: Boise State
Curve Sketching Worksheet Sketch the graph of the function using the curvesketching guide. Curve Sketching 1. Determine the domain of the function. 2. Find the x and y intercepts of the function. 3. Determine the behavior of the function for large

Antiderivative Worksheet
School: Boise State
Antiderivative Worksheet Find the most general antiderivative of the function 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Key 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

Related Rates Worksheet Key
School: Boise State
Related Rates Worksheet Key ft 3 1. A tank of water in the shape of an inverted cone is leaking water at 2 . The base hour radius is 5 ft and the height of the tank is 14 ft. a) At what rate is the depth of the water changing when the depth of the w

Implicit Differentiation Worksheet
School: Boise State
Implicit Derivatives Find dy by implicit differentiation dx 1. x 2 + y 2 = 16 2. x 2  2 y 2 = 16 3. x 2 y 2  xy = 6 4. x 2 + 5 xy + y 2 = 10 5. x+y = x 6. ( 2 x + 3y ) 3 1 = x2 Find an equation of the tangent line to the graph of the fun

A Visual Approach To Calculus Problems
School: Boise State
You might think you need calculus to determine the area between the tire tracks made by this bike, ridden by Jason McIlhaney, BS 2000. Surprisingly, geometry offers another way of solving itwithout formulas. 22 E N G I N E E R I N G & S C I E N C

SylM160F05
School: Boise State
MATH 160 Survey of Calculus 4 semester credits Fall 2005 MATH 160 SURVEY OF CALCULUS (404) (Area III). A survey of the essentials of calculus intended mainly for students in business and social sciences; emphasis on applications to such areas. Bas