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MATH 160  Boise State Study Resources

Domain And Functions Quiz
School: Boise State
Course: Survey To Calculus
I V U  X +a F a J] th 16 0 S e c ti o n s W W 11 U :e 2 0 14 Q In  0 0 1/ 0 0 2 str u c ti o n s : C .e a r l y sh o w e Je c t r o n i c d e v i c e s m a y v a lues ar e sh o w n in a ll w o rk n o t b e u sed to re c e iv e d u r in g th e le f t m a

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

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

Natural Log Homework
School: Boise State
Course: Survey To Calculus
 b; 3 \ e Y P 4 (x\ i _ ) +  = . 1 L < * t V\ ? e 8  , 7 5 7 b K T . _ t e _ : e y f e _ [v\ Zl f 9 + 13 ) y \ [ lz Le ) l s( 18 3x 2 ll . ) _ e 1r 1  . , e t (k x , 2+ " ) :2 = z+ v z m  e .  j x ? + l  = ) 1 4 1 ) 2 . 2 e e 1  1) Q, . )  s G

Slope Quiz
School: Boise State
Course: Survey To Calculus
M a lh 1 6 0 Fa ll 2 0 14 L j 1 S ec t i o n s 0 0 1/ 0 0 2 / Qu i z In st r u c t i o n s : C l e ar l y s h o w a <l w o r k t o r e c e i v e f u l l c r e d i t e l e c t r o n i c d ev i c e s m a y n o t b e u s ed d u r i n g th e e x am : Po in t

Functions Quiz
School: Boise State
Course: Survey To Calculus
U V L J ; \ L 1 U 1 1 U V 1 1 U V A 2 Qu i z r c t i o n s : C 1e a r l y s h o w t all w o rk to receiv e f u ll c red i . Ca l c u l at o r s bu t 3 2 6 m ay b e u sed This t e st c o v e r s se c t i o n s 2 d u rin g th e ex am r o n i c d ev i c e s

Derivatives Quiz
School: Boise State
Course: Survey To Calculus
N am e : , ' llc a IW t h 16 0 S e c t i o n s 0 0 1 / 0 0 2 pp e t I 1 2 0 14 Qu i z al l w o rk to r e c e iv e fu l l c red it n st r u c t i o n s : C l e ar l y sh o w \e c t r o n 3 i c d e v i c e s m a y n o t b e u se d d u D n g t h e ex a m pt

Optimization
School: Boise State
Course: Survey To Calculus
1  o t s \ u c  i Opwl i Mon n e e n o7 uM  w w w 1 3e + A )(   _ ( y . p v  Or 3 t e lr l + c r v k  >l 1 lv\ 6 v P CV t_ ) Yv Tt _ > z en P(1 9 . , + y Ev .  = . B m  \ \ z > ) 1 1 + 2 5 n 0 _ _ . . . . . oz K w i f 7 5 0 0 o + 5 0 0 F @

Lines And Functions
School: Boise State
Course: Survey To Calculus
; i 0 >uw ^  1 I ( I T * 1 1n t l i J _ Per per di uL ( L , I L W i nbn t f dn m I LTE ( . cfw_l e l ) 09 5/ [ 1 4 a re w q  0c ; r [ r l 3 " . T3 ) _ \ \n e _ 9p o l e n d cp o rw 1 _  T h ( 3 I) 1 h v , p n  y + t  D j 1 1 = 3x  tz J h Xt z 0

Initial Concentrations Quiz
School: Boise State
Course: Survey To Calculus
M a th Fa u 16 0 r nl S e c t i o n s 0 0 1/ 0 0 2 2 0 14 Qu i z In s tr u c t i o n s : C le a r ly sh o w e le c tr o n ic d e v ic e s m a y v a lu e s a r e sh o w n ( 15 p t s ) 1 . in to r e c e iv e fu l l c r e d it a ll w o rk n o t b e u se d d

Area Between Two Curves
School: Boise State
Course: Survey To Calculus
L z Ar i e  L = cA T+ t . p\ . l Qv t ) t . . l h 2 = . _ r z (  , T + t z) Z . L J H) 1  . . _ _ 3 3 2 843 )  1l  ( e   u A a ) = ) z+ I ) 8 Y p  ) 2 + 8 1 y : \ x = z ; c w th )  1 Lx ) 31 : 4 y 2x l 0 .  Y 1? X . _  1 Zl c 3 Scanned by Cam

Product And Quotient Rule
School: Boise State
Course: Survey To Calculus
Th t e u c\ ( x\ p( Vt L i v s = k (x  h ) ? y ) p( y  =  2 XL y : u c k) ( ZK )(v \  z E ir . ( t x 2 _ x e 2 K ? . 1 W . ie , : c ce h d N + s  :r/ t y 1 . v  A e v f u a " t o . 4 ,v + a ) 3  ) V 1  QL * i e n  r v ) a = x ( 1 / : 7 7 UW  ! z

Rates Homework
School: Boise State
Course: Survey To Calculus
: Q m c _ _ c N = _ 9 00 0 _ _ _ J _ h . _ CU r _ n u5 = r _ t . 1 10 . . L  P ) 0 t r oco Zl  2 ( l+ 0 0 o o o o S 1 77 8 l D (n 3. 53 z r n o e + w + 12 L N : . 00 0 t o t o + + D Ot Y . . , zo t to z \ o to o o 7 5 , t t 00 D + 1o t 1 t TO . D

Modeling And Limits
School: Boise State
Course: Survey To Calculus
 W \ f (+) C0 /t W m A A \s . 12 3 m eK )  . 3 3 4 r t + u :  on z x _ K K 1  a z s o n c h ? 5 1T ? & o ( z ar o 0 + po t . T t* t 2  ( O + + a s t 2 a) _ r v + im  5 13 f l * , e >i on 33 7  s + l t 8 3 s ec o M r ) N . N n r z tu t . L t o _ ,

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

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

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

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 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

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 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

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

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

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

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

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 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

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

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.

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)

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)

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