Calculus BC AP/Dual Fall Semester Review Sheet REVISED 1 Name Date. 3) Explain why f(x) = x 2 7x 8 is a guarantee zero in between [ 3, 0] g) lim x

Size: px
Start display at page:

Download "Calculus BC AP/Dual Fall Semester Review Sheet REVISED 1 Name Date. 3) Explain why f(x) = x 2 7x 8 is a guarantee zero in between [ 3, 0] g) lim x"

Transcription

1 Calculus BC AP/Dual Fall Semester Review Sheet REVISED Name Date Eam Date and Time: Read and answer all questions accordingly. All work and problems must be done on your own paper and work must be shown. No work = No Credit = NO EXCEPTIONS. It is worth.5 quiz grades. Note: There are two parts of the eam. The NON CALC test has questions (5%) and FRQ s (5%). Chapter Limits ) Find the limit of the following: a) lim b) lim 9 d) lim 5 5 e) lim g) lim h) lim cos ) Solve. If it does not eist, state DNE. c) f) i) a) lim f b) lim f c) lim f lim lim lim sin 5 9 d) f e) f ) Eplain why f() = 7 8 is a guarantee zero in between [, ] ) Define the Intermediate Value Theorem. 5) State the definition of continuity of a function f at which = c. Given: g lim f ) Find the limits as they eist. lim 5 a) lim f 5 g b) lim g c) lim f g h d) lim f limh 7) Given the following function, find k so that the function is k, continuous at =. f k, Chapter Differentiation ) Find the equation of the tangent line to the graph, f() = 5 + at the point (, ). ) Using the difference quotient, find f (). Show all work. 5, f,, (a) Is f continuous at =? Use the definition of continuity to eplain answer. (b) Is f differentiable at =? Eplain. (c) Sketch a graph of f. ) Given: ) Given the f graph, graph f (). Show all work.

2 Calculus BC AP/Dual Fall Semester Review Sheet REVISED ) Find dy d if (a) y + y = (b) y + y = 8 (c) e y cos = + sin(y) ) The radius of a circle is increasing at a rate of cm/sec. Find the rate of change of the area of the circle when the radius is 5 cm. 5) Find dy of the following: d / / (a) f (b) f (d) y (e) y (g) 7 (h) (c) e (f) y y e 5 (i) sin 5 (j) sin 5 ) Suppose that f(5) =, f (5) =, g(5) =, and g (5) =. Find the following values. a) (fg) (5) = b) ( f g ) (5) = c) ( g f ) (5) = 7) f () f ' () g() g '() = 5 = 5 7, solve (b) If h g, solve (a) If h f g h '5 h ' 8) If F() = f(g()), where f( ) =, f ( ) =, f () = 5, g() =, and g () = 7, find F (). ) A 5 ft ladder is leaning against a wall. The bottom of the ladder begins to slide away from the wall at a rate of ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is 9 feet away from the wall? ) Water is dripping through the top of a conical shaped cup at the rate of.5 cubic inches per minute. If the cup s original size is inches high with a diameter of inches across the top, how fast is the height of water decreasing when the water is two inches deep in the cone? ) If a tank holds 5 gallons of water, which drains from the bottom of the tank in 5 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as V 5 t t 5. 5 Find the rate at which water is draining from the tank after the following amounts of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.) (a) 5 min (b) 5 minutes (c) At what time is the water flowing out the fastest? (d) At what time is the water flowing out the slowest? 9) Solve for f (): (a) 8 (b) sec (c) y = cos sin

3 Calculus BC AP/Dual Fall Semester Review Sheet REVISED Chapter Applications of Differentiation ) Given f() = +, identify all absolute etrema on the interval [, ]. ) Find the absolute maimum and absolute minimum values of f on the given interval, f(t) = cos t + sin(t) at I [, π ] (a) Find the velocity of the object when t = 5 (b) Find the acceleration at time t (c) Establish when the particle is at rest (d) When is the particle slowing down? ) A particle starts by moving to the right along a horizontal line; the graph of its position function is shown. ) Define the Etreme Value Theorem and Mean Value Theorem and identify the difference of the two theorems. ) What is the number for c which satisfies the conditions of the Mean Value Theorem of differentiable calculus for f() = on [, ]. 5) Find the relative etrema of f() = + using the First Derivative Test. ) Use the second derivative test to determine the relative etrema for f() = 8. 7) Determine the f() =, determine the following: (a) and y intercepts (b) horizontal and vertical asymptotes (c) intervals of increasing and decreasing 8) Determine the open intervals in which the graph f() = is concave up or down. 9) Find the relative etrema of f() = 9 on the I[, ]. ) Let s(t) = t t + be the position function of a particle moving along the ais. (a) When is the particle moving to the right? (b) When is the particle moving to the left? (c) When is the particle standing still? ) A particle is moving along a horizontal line according to the equation, s(t) = t 7 t + 5t where [, ). Determine the interval of time when the particle is moving to the right. ) Find the shortest distance from f() = to the point (, ½). ) Find two positive numbers whose product is 9 and whose sum is a minimum. 5) Find the dimensions of a rectangle with perimeter 9 m whose area is as large as possible. ) The top and bottom margins of a poster are each 9 cm and the side margins are each cm. If the area of printed material on the poster is fied at 8 cm, find the dimensions of the poster with the smallest area.

4 Calculus BC AP/Dual Fall Semester Review Sheet REVISED 7) A rancher has feet of fencing with which to enclose two adjacent rectangular corrals. What dimensions should be used so that the enclosed area will be a maimum? Chapter Integration ) Solve for these indefinite integrals. (a) d (b) cos ) Find y = f() if f ", f ', and ) Given d f. f d for the functions below, use the left, right, and trapezoidal Riemann sum with subintervals. f().5.8 ) If f() =,, evaluate the Riemann sum with n =, taking the sample points to be right endpoints. Then, determine if the graph is an underestimation or an overestimation. 5) Sketch the region whose is area is given by the definite integral and then use a geometric formula to evaluate the integral of 7 9 d ) The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. A) g d 8 B) g d C) g d y 9 9 7) Given f d and f d, solve for 9, and 7 f d 9 g d 8) Evaluate: (a) d (b) (d) sin cos f d, 5 d (c) d (e) d 9) Use the Fundamental Theorem of Calculus to solve: 5 (a) d (b) csc d (c) (d) d (e) d (f) 5cos 5 d d 5 d ) Use the Mean Value Theorem of Integration to identify c of f() = 9, [, ] ) Find the average value of f() = on [, ] ) Solve (a) d sin t dt d d and (b) sin t dt d ) Accumulation/Riemann s Sum: Let y(t) represent the population of Sugar Mill over a -year period, where y is differentiable function of t. The table shows the population recorded every two years. t (years) y (people)

5 Calculus BC AP/Dual Fall Semester Review Sheet REVISED 5 (a) Use the data from the table to find an approimation for y (7) and eplain the meaning of y (7) in terms of the population of Sugar Mill. Show the computations that lead to the answer. (b) Use the data from the table to approimate the average population of Sugar Mill over the time interval, < t < by using a LEFT Riemann s Sum with five equal intervals. Show all work. (c) A model for the population of another town, Pine Grove, over the same -year period is given by the function t 5 P t where t is measured in years and P(t) is measured in people. Use the model to find the value of (d) Use the model given in part (c) to find the value of P '7. P(t)dt. Eplain the meaning of this integral epression in terms of the population of Pine Grove. Chapter 5: Logarithms ) Write the following epression as a log of a single quantity, ln ln( + ). ) Find the derivative: (a) y y ln 7 log ln 7 (b) (d) 7 7 f t t 5 t (e) ) Find (f ) = 5 if f() = 5 ) Given f 5, g are inverses, solve for f ' 7,, g '. f and (c) 5 y e f ', and f and 5) Solve for g ' : 8 f() f () / 5 5 ) Solve d 9) d d cos arcsin 7 7) tan d ) ) 5 Chapter - Differential Equations ) Solve for the differential equation: dy dy (a) cos (b) d d y (c) y' 8 (d) dy y d 8) ) Write the function y = f(t) passing through the point (, ) dy with the given first derivative of t dt ) The number of bacteria in a culture is increasing according to the law of eponential growth. There are 5 bacteria in the culture after hours and 55 bacteria after hours. (calc) e (a) Find the initial population. (b) Write an eponential growth model for the bacteria population. Let t represent time in hours. (c) Use the model to determine the number of bacteria after 8 hours. (d) After how many hours will the bacteria count be,? d d

6 Calculus BC AP/Dual Fall Semester Review Sheet REVISED ) At time t =, bacterium weighs grams. Three hours later, the culture weighs 5 grams. The maimum weight of the culture is grams. (calc.) (a) Write a logistic equation that models the weight of the bacterial culture. (b) When will the culture's weight reach grams? (c) At what time is the culture's weight increasing most rapidly? 5) In a town of population, twenty thousand residents heard a radio announcement about a local political scandal. The rate of growth of the spread of information was jointly proportional to the amount of people who had not heard it. If 5% heard the scandal after one hour, how long until 8% of the population has heard the rumor? (calc) ) Consider the differential equation dy d = y ( + ) Let y = f() be the particular solution to the differential equation with initial condition f() =. Use Euler s method, starting at = with two steps of equal size, to approimate f ( ). ) AB- Free Response Questions ) AB/BC-

7 Calculus BC AP/Dual Fall Semester Review Sheet REVISED 7 ) AB/BC5- At time t =, boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal temperature of the potato is 9 degrees Celsius C at time t, and the internal temperature of the potato is greater than 7 C for all times t. The internal temperature of the potato at time t minutes can be modeled by the function H that satisfies the differential equation dh dt H 7, where H 9. H t is measured in degrees Celsius and (a) Write an equation for the line tangent to the graph of H at t =. Use this equation to approimate the internal temperature of the potato at time t =. d H (b) Use to determine whether your answer in part (a) is an dt underestimate or an overestimate of the internal temperature of the potato at time t =. (c) For t, an alternate model for the internal temperature of the potato at time t minutes is the function G that satisfies the dg differential equation G 7 /, where G(t) is measured dt in degrees Celsius and G. Find an epression for G(t). 9 Based on this model, what is the internal temperature of the potato at time t =? ) AB5- The function g is defined and differentiable on the closed interval [ 7,5]and satisfies g() = 5. The graph of y = g (), the derivative of g, consists of a semicircle and three-line segments, as shown in the figure above. (a) Find the -coordinate of each point of inflection of the graph of y = g()on the interval 7 < < 5. Eplain your reasoning. (b) The function h is defined by h() = g(). Find the coordinate of each critical point of h, where 7 < < 5, and classify each critical point as the location of a relative minimum, relative maimum, or neither a minimum nor a maimum. Eplain your reasoning. 5) List ways you will do to help you study for the midterm eam.

ANOTHER FIVE QUESTIONS:

ANOTHER FIVE QUESTIONS: No peaking!!!!! See if you can do the following: f 5 tan 6 sin 7 cos 8 sin 9 cos 5 e e ln ln @ @ Epress sin Power Series Epansion: d as a Power Series: Estimate sin Estimate MACLAURIN SERIES ANOTHER FIVE

More information

x f(x)

x f(x) CALCULATOR SECTION. For y y 8 find d point (, ) on the curve. A. D. dy at the 7 E. 6. Suppose silver is being etracted from a.t mine at a rate given by A'( t) e, A(t) is measured in tons of silver and

More information

Technical Calculus I Homework. Instructions

Technical Calculus I Homework. Instructions Technical Calculus I Homework Instructions 1. Each assignment is to be done on one or more pieces of regular-sized notebook paper. 2. Your name and the assignment number should appear at the top of the

More information

x f(x)

x f(x) CALCULATOR SECTION. For y + y = 8 find d point (, ) on the curve. A. B. C. D. dy at the 7 E. 6. Suppose silver is being etracted from a.t mine at a rate given by A'( t) = e, A(t) is measured in tons of

More information

AP Calculus (BC) Summer Assignment (104 points)

AP Calculus (BC) Summer Assignment (104 points) AP Calculus (BC) Summer Assignment (0 points) This packet is a review of some Precalculus topics and some Calculus topics. It is to be done NEATLY and on a SEPARATE sheet of paper. Use your discretion

More information

(i) find the points where f(x) is discontinuous, and classify each point of discontinuity.

(i) find the points where f(x) is discontinuous, and classify each point of discontinuity. Math Final Eam - Practice Problems. A function f is graphed below. f() 5 4 8 7 5 4 4 5 7 8 4 5 (a) Find f(0), f( ), f(), and f(4) Find the domain and range of f (c) Find the intervals where f () is positive

More information

AP Calculus (BC) Summer Assignment (169 points)

AP Calculus (BC) Summer Assignment (169 points) AP Calculus (BC) Summer Assignment (69 points) This packet is a review of some Precalculus topics and some Calculus topics. It is to be done NEATLY and on a SEPARATE sheet of paper. Use your discretion

More information

AP CALCULUS BC - FIRST SEMESTER EXAM REVIEW: Complete this review for five extra percentage points on the semester exam.

AP CALCULUS BC - FIRST SEMESTER EXAM REVIEW: Complete this review for five extra percentage points on the semester exam. AP CALCULUS BC - FIRST SEMESTER EXAM REVIEW: Complete this review for five etra percentage points on the semester eam. *Even though the eam will have a calculator active portion with 0 of the 8 questions,

More information

A.P. Calculus BC Summer Assignment 2018 I am so excited you are taking Calculus BC! For your summer assignment, I would like you to complete the

A.P. Calculus BC Summer Assignment 2018 I am so excited you are taking Calculus BC! For your summer assignment, I would like you to complete the A.P. Calculus BC Summer Assignment 2018 I am so excited you are taking Calculus BC! For your summer assignment, I would like you to complete the attached packet of problems, and turn it in on Monday, August

More information

( + ) 3. AP Calculus BC Chapter 6 AP Exam Problems. Antiderivatives. + + x + C. 2. If the second derivative of f is given by f ( x) = 2x cosx

( + ) 3. AP Calculus BC Chapter 6 AP Exam Problems. Antiderivatives. + + x + C. 2. If the second derivative of f is given by f ( x) = 2x cosx Chapter 6 AP Eam Problems Antiderivatives. ( ) + d = ( + ) + 5 + + 5 ( + ) 6 ( + ). If the second derivative of f is given by f ( ) = cos, which of the following could be f( )? + cos + cos + + cos + sin

More information

In #1-5, find the indicated limits. For each one, if it does not exist, tell why not. Show all necessary work.

In #1-5, find the indicated limits. For each one, if it does not exist, tell why not. Show all necessary work. Calculus I Eam File Fall 7 Test # In #-5, find the indicated limits. For each one, if it does not eist, tell why not. Show all necessary work. lim sin.) lim.) 3.) lim 3 3-5 4 cos 4.) lim 5.) lim sin 6.)

More information

2008 CALCULUS AB SECTION I, Part A Time 55 minutes Number of Questions 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION

2008 CALCULUS AB SECTION I, Part A Time 55 minutes Number of Questions 28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION 8 CALCULUS AB SECTION I, Part A Time 55 minutes Number of Questions 8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions: Solve each of the following problems. After eamining the form

More information

BE SURE TO READ THE DIRECTIONS PAGE & MAKE YOUR NOTECARDS FIRST!! Part I: Unlimited and Continuous! (21 points)

BE SURE TO READ THE DIRECTIONS PAGE & MAKE YOUR NOTECARDS FIRST!! Part I: Unlimited and Continuous! (21 points) BE SURE TO READ THE DIRECTIONS PAGE & MAKE YOUR NOTECARDS FIRST!! Part I: United and Continuous! ( points) For #- below, find the its, if they eist.(#- are pt each) ) 7 ) 9 9 ) 5 ) 8 For #5-7, eplain why

More information

AP Calculus Review Assignment Answer Sheet 1. Name: Date: Per. Harton Spring Break Packet 2015

AP Calculus Review Assignment Answer Sheet 1. Name: Date: Per. Harton Spring Break Packet 2015 AP Calculus Review Assignment Answer Sheet 1 Name: Date: Per. Harton Spring Break Packet 015 This is an AP Calc Review packet. As we get closer to the eam, it is time to start reviewing old concepts. Use

More information

Math 1431 Final Exam Review. 1. Find the following limits (if they exist): lim. lim. lim. lim. sin. lim. cos. lim. lim. lim. n n.

Math 1431 Final Exam Review. 1. Find the following limits (if they exist): lim. lim. lim. lim. sin. lim. cos. lim. lim. lim. n n. . Find the following its (if they eist: sin 7 a. 0 9 5 b. 0 tan( 8 c. 4 d. e. f. sin h0 h h cos h0 h h Math 4 Final Eam Review g. h. i. j. k. cos 0 n nn e 0 n arctan( 0 4 l. 0 sin(4 m. cot 0 = n. = o.

More information

AP Calculus AB/BC ilearnmath.net

AP Calculus AB/BC ilearnmath.net CALCULUS AB AP CHAPTER 1 TEST Don t write on the test materials. Put all answers on a separate sheet of paper. Numbers 1-8: Calculator, 5 minutes. Choose the letter that best completes the statement or

More information

y=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions

y=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions. Which of the following integrals correctly corresponds to the area of the shaded region in the figure to the right? (A) (B) (C) (D) (E)

More information

AP CALCULUS BC SUMMER ASSIGNMENT

AP CALCULUS BC SUMMER ASSIGNMENT AP CALCULUS BC SUMMER ASSIGNMENT Work these problems on notebook paper. All work must be shown. Use your graphing calculator only on problems -55, 80-8, and 7. Find the - and y-intercepts and the domain

More information

Find the following limits. For each one, if it does not exist, tell why not. Show all necessary work.

Find the following limits. For each one, if it does not exist, tell why not. Show all necessary work. Calculus I Eam File Spring 008 Test #1 Find the following its. For each one, if it does not eist, tell why not. Show all necessary work. 1.) 4.) + 4 0 1.) 0 tan 5.) 1 1 1 1 cos 0 sin 3.) 4 16 3 1 6.) For

More information

Multiple Choice. Circle the best answer. No work needed. No partial credit available. is continuous.

Multiple Choice. Circle the best answer. No work needed. No partial credit available. is continuous. Multiple Choice. Circle the best answer. No work needed. No partial credit available. + +. Evaluate lim + (a (b (c (d 0 (e None of the above.. Evaluate lim (a (b (c (d 0 (e + + None of the above.. Find

More information

AP Calculus BC Summer Assignment 2018

AP Calculus BC Summer Assignment 2018 AP Calculus BC Summer Assignment 018 Name: When you come back to school, I will epect you to have attempted every problem. These skills are all different tools that we will pull out of our toolbo at different

More information

1. Find A and B so that f x Axe Bx. has a local minimum of 6 when. x 2.

1. Find A and B so that f x Axe Bx. has a local minimum of 6 when. x 2. . Find A and B so that f Ae B has a local minimum of 6 when.. The graph below is the graph of f, the derivative of f; The domain of the derivative is 5 6. Note there is a cusp when =, a horizontal tangent

More information

lim 2 x lim lim sin 3 (9) l)

lim 2 x lim lim sin 3 (9) l) MAC FINAL EXAM REVIEW. Find each of the following its if it eists, a) ( 5). (7) b). c). ( 5 ) d). () (/) e) (/) f) (-) sin g) () h) 5 5 5. DNE i) (/) j) (-/) 7 8 k) m) ( ) (9) l) n) sin sin( ) 7 o) DNE

More information

y=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions

y=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions. Which of the following integrals correctly corresponds to the area of the shaded region in the figure to the right? (A) (B) (C) (D) (E)

More information

AP Calculus BC Chapter 4 (A) 12 (B) 40 (C) 46 (D) 55 (E) 66

AP Calculus BC Chapter 4 (A) 12 (B) 40 (C) 46 (D) 55 (E) 66 AP Calculus BC Chapter 4 REVIEW 4.1 4.4 Name Date Period NO CALCULATOR IS ALLOWED FOR THIS PORTION OF THE REVIEW. 1. 4 d dt (3t 2 + 2t 1) dt = 2 (A) 12 (B) 4 (C) 46 (D) 55 (E) 66 2. The velocity of a particle

More information

AP Calculus BC. Free-Response Questions

AP Calculus BC. Free-Response Questions 017 AP Calculus BC Free-Response Questions 017 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. 017 AP CALCULUS

More information

CALCULUS AB SECTION II, Part A

CALCULUS AB SECTION II, Part A CALCULUS AB SECTION II, Part A Time 45 minutes Number of problems 3 A graphing calculator is required for some problems or parts of problems. pt 1. The rate at which raw sewage enters a treatment tank

More information

cos 5x dx e dt dx 20. CALCULUS AB WORKSHEET ON SECOND FUNDAMENTAL THEOREM AND REVIEW Work the following on notebook paper. No calculator.

cos 5x dx e dt dx 20. CALCULUS AB WORKSHEET ON SECOND FUNDAMENTAL THEOREM AND REVIEW Work the following on notebook paper. No calculator. WORKSHEET ON SECOND FUNDAMENTAL THEOREM AND REVIEW Work the following on notebook paper. No calculator. Find the derivative. Do not leave negative eponents or comple fractions in our answers. 4. 8 4 f

More information

Math 75B Practice Problems for Midterm II Solutions Ch. 16, 17, 12 (E), , 2.8 (S)

Math 75B Practice Problems for Midterm II Solutions Ch. 16, 17, 12 (E), , 2.8 (S) Math 75B Practice Problems for Midterm II Solutions Ch. 6, 7, 2 (E),.-.5, 2.8 (S) DISCLAIMER. This collection of practice problems is not guaranteed to be identical, in length or content, to the actual

More information

Limits. Final Exam Study Guide. Calculus I. 1. Basic Limits I: Evaluate each limit exactly. (a) lim. (c) lim. 2t 15 3 (g) lim. (e) lim. (f) lim.

Limits. Final Exam Study Guide. Calculus I. 1. Basic Limits I: Evaluate each limit exactly. (a) lim. (c) lim. 2t 15 3 (g) lim. (e) lim. (f) lim. Limits 1. Basic Limits I: Evaluate each limit eactly. 3 ( +5 8) (c) lim(sin(α) 5cos(α)) α π 6 (e) lim t t 15 3 (g) lim t 0 t (4t 3 8t +1) t 1 (tan(θ) cot(θ)+1) θ π 4 (f) lim 16 ( 5 (h) lim t 0 3 t ). Basic

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine from the graph whether the function has an absolute etreme values on the interval

More information

sin x (B) sin x 1 (C) sin x + 1

sin x (B) sin x 1 (C) sin x + 1 ANSWER KEY Packet # AP Calculus AB Eam Multiple Choice Questions Answers are on the last page. NO CALCULATOR MAY BE USED IN THIS PART OF THE EXAMINATION. On the AP Eam, you will have minutes to answer

More information

AP Calculus AB Free-Response Scoring Guidelines

AP Calculus AB Free-Response Scoring Guidelines Question pt The rate at which raw sewage enters a treatment tank is given by Et 85 75cos 9 gallons per hour for t 4 hours. Treated sewage is removed from the tank at the constant rate of 645 gallons per

More information

Math 2413 Final Exam Review 1. Evaluate, giving exact values when possible.

Math 2413 Final Exam Review 1. Evaluate, giving exact values when possible. Math 4 Final Eam Review. Evaluate, giving eact values when possible. sin cos cos sin y. Evaluate the epression. loglog 5 5ln e. Solve for. 4 6 e 4. Use the given graph of f to answer the following: y f

More information

Solutions to Math 41 Final Exam December 9, 2013

Solutions to Math 41 Final Exam December 9, 2013 Solutions to Math 4 Final Eam December 9,. points In each part below, use the method of your choice, but show the steps in your computations. a Find f if: f = arctane csc 5 + log 5 points Using the Chain

More information

Math 1000 Final Exam Review Solutions. (x + 3)(x 2) = lim. = lim x 2 = 3 2 = 5. (x + 1) 1 x( x ) = lim. = lim. f f(1 + h) f(1) (1) = lim

Math 1000 Final Exam Review Solutions. (x + 3)(x 2) = lim. = lim x 2 = 3 2 = 5. (x + 1) 1 x( x ) = lim. = lim. f f(1 + h) f(1) (1) = lim Math Final Eam Review Solutions { + 3 if < Consider f() Find the following limits: (a) lim f() + + (b) lim f() + 3 3 (c) lim f() does not eist Find each of the following limits: + 6 (a) lim 3 + 3 (b) lim

More information

Math 231 Final Exam Review

Math 231 Final Exam Review Math Final Eam Review Find the equation of the line tangent to the curve 4y y at the point (, ) Find the slope of the normal line to y ) ( e at the point (,) dy Find d if cos( y) y 4 y 4 Find the eact

More information

Calculus AB Semester 1 Final Review

Calculus AB Semester 1 Final Review Name Period Calculus AB Semester Final Review. Eponential functions: (A) kg. of a radioactive substance decay to kg. after years. Find how much remains after years. (B) Different isotopes of the same element

More information

( ) 7 ( 5x 5 + 3) 9 b) y = x x

( ) 7 ( 5x 5 + 3) 9 b) y = x x New York City College of Technology, CUNY Mathematics Department Fall 0 MAT 75 Final Eam Review Problems Revised by Professor Kostadinov, Fall 0, Fall 0, Fall 00. Evaluate the following its, if they eist:

More information

Key- Math 231 Final Exam Review

Key- Math 231 Final Exam Review Key- Math Final Eam Review Find the equation of the line tangent to the curve y y at the point (, ) y-=(-/)(-) Find the slope of the normal line to y ) ( e at the point (,) dy Find d if cos( y) y y (ysiny+y)/(-siny-y^-^)

More information

June Stone Bridge Math Department. Dear Advanced Placement Calculus BC Student,

June Stone Bridge Math Department. Dear Advanced Placement Calculus BC Student, Stone Bridge Math Department June 06 Dear Advanced Placement Calculus BC Student, Congratulations on your wisdom in taking the BC course. I know you will find it rewarding and a great way to spend your

More information

CALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS. Second Fundamental Theorem of Calculus (Chain Rule Version): f t dt

CALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS. Second Fundamental Theorem of Calculus (Chain Rule Version): f t dt CALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS d d d d t dt 6 cos t dt Second Fundamental Theorem of Calculus: d f tdt d a d d 4 t dt d d a f t dt d d 6 cos t dt Second Fundamental

More information

1985 AP Calculus AB: Section I

1985 AP Calculus AB: Section I 985 AP Calculus AB: Section I 9 Minutes No Calculator Notes: () In this eamination, ln denotes the natural logarithm of (that is, logarithm to the base e). () Unless otherwise specified, the domain of

More information

( ) 9 b) y = x x c) y = (sin x) 7 x d) y = ( x ) cos x

( ) 9 b) y = x x c) y = (sin x) 7 x d) y = ( x ) cos x NYC College of Technology, CUNY Mathematics Department Spring 05 MAT 75 Final Eam Review Problems Revised by Professor Africk Spring 05, Prof. Kostadinov, Fall 0, Fall 0, Fall 0, Fall 0, Fall 00 # Evaluate

More information

1. Determine the limit (if it exists). + lim A) B) C) D) E) Determine the limit (if it exists).

1. Determine the limit (if it exists). + lim A) B) C) D) E) Determine the limit (if it exists). Please do not write on. Calc AB Semester 1 Exam Review 1. Determine the limit (if it exists). 1 1 + lim x 3 6 x 3 x + 3 A).1 B).8 C).157778 D).7778 E).137778. Determine the limit (if it exists). 1 1cos

More information

It s Your Turn Problems I. Functions, Graphs, and Limits 1. Here s the graph of the function f on the interval [ 4,4]

It s Your Turn Problems I. Functions, Graphs, and Limits 1. Here s the graph of the function f on the interval [ 4,4] It s Your Turn Problems I. Functions, Graphs, and Limits. Here s the graph of the function f on the interval [ 4,4] f ( ) =.. It has a vertical asymptote at =, a) What are the critical numbers of f? b)

More information

Ex. Find the derivative. Do not leave negative exponents or complex fractions in your answers.

Ex. Find the derivative. Do not leave negative exponents or complex fractions in your answers. CALCULUS AB THE SECOND FUNDAMENTAL THEOREM OF CALCULUS AND REVIEW E. Find the derivative. Do not leave negative eponents or comple fractions in your answers. 4 (a) y 4 e 5 f sin (b) sec (c) g 5 (d) y 4

More information

1993 AP Calculus AB: Section I

1993 AP Calculus AB: Section I 99 AP Calculus AB: Section I 9 Minutes Scientific Calculator Notes: () The eact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among

More information

CALCULUS I. Practice Problems. Paul Dawkins

CALCULUS I. Practice Problems. Paul Dawkins CALCULUS I Practice Problems Paul Dawkins Table of Contents Preface... iii Outline... iii Review... Introduction... Review : Functions... Review : Inverse Functions... 6 Review : Trig Functions... 6 Review

More information

Mathematics 1161: Midterm Exam 2 Study Guide

Mathematics 1161: Midterm Exam 2 Study Guide Mathematics 1161: Midterm Eam 2 Study Guide 1. Midterm Eam 2 is on October 18 at 6:00-6:55pm in Journalism Building (JR) 300. It will cover Sections 3.8, 3.9, 3.10, 3.11, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6,

More information

Final Exam Review / AP Calculus AB

Final Exam Review / AP Calculus AB Chapter : Final Eam Review / AP Calculus AB Use the graph to find each limit. 1) lim f(), lim f(), and lim π - π + π f 5 4 1 y - - -1 - - -4-5 ) lim f(), - lim f(), and + lim f 8 6 4 y -4 - - -1-1 4 5-4

More information

(a) During what time intervals on [0, 4] is the particle traveling to the left?

(a) During what time intervals on [0, 4] is the particle traveling to the left? Chapter 5. (AB/BC, calculator) A particle travels along the -ais for times 0 t 4. The velocity of the particle is given by 5 () sin. At time t = 0, the particle is units to the right of the origin. t /

More information

lim x c) lim 7. Using the guidelines discussed in class (domain, intercepts, symmetry, asymptotes, and sign analysis to

lim x c) lim 7. Using the guidelines discussed in class (domain, intercepts, symmetry, asymptotes, and sign analysis to Math 7 REVIEW Part I: Problems Using the precise definition of the it, show that [Find the that works for any arbitrarily chosen positive and show that it works] Determine the that will most likely work

More information

The questions listed below are drawn from midterm and final exams from the last few years at OSU. As the text book and structure of the class have

The questions listed below are drawn from midterm and final exams from the last few years at OSU. As the text book and structure of the class have The questions listed below are drawn from midterm and final eams from the last few years at OSU. As the tet book and structure of the class have recently changed, it made more sense to list the questions

More information

K. Function Analysis. ). This is commonly called the first derivative test. f ( x) is concave down for values of k such that f " ( k) < 0.

K. Function Analysis. ). This is commonly called the first derivative test. f ( x) is concave down for values of k such that f  ( k) < 0. K. Function Analysis What you are finding: You have a function f ( ). You want to find intervals where f ( ) is increasing and decreasing, concave up and concave down. You also want to find values of where

More information

Sample Final Exam 4 MATH 1110 CALCULUS I FOR ENGINEERS

Sample Final Exam 4 MATH 1110 CALCULUS I FOR ENGINEERS Dept. of Math. Sciences, UAEU Sample Final Eam Fall 006 Sample Final Eam MATH 0 CALCULUS I FOR ENGINEERS Section I: Multiple Choice Problems [0% of Total Final Mark, distributed equally] No partial credit

More information

Answer Key 1973 BC 1969 BC 24. A 14. A 24. C 25. A 26. C 27. C 28. D 29. C 30. D 31. C 13. C 12. D 12. E 3. A 32. B 27. E 34. C 14. D 25. B 26.

Answer Key 1973 BC 1969 BC 24. A 14. A 24. C 25. A 26. C 27. C 28. D 29. C 30. D 31. C 13. C 12. D 12. E 3. A 32. B 27. E 34. C 14. D 25. B 26. Answer Key 969 BC 97 BC. C. E. B. D 5. E 6. B 7. D 8. C 9. D. A. B. E. C. D 5. B 6. B 7. B 8. E 9. C. A. B. E. D. C 5. A 6. C 7. C 8. D 9. C. D. C. B. A. D 5. A 6. B 7. D 8. A 9. D. E. D. B. E. E 5. E.

More information

Math 180, Final Exam, Spring 2008 Problem 1 Solution. 1. For each of the following limits, determine whether the limit exists and, if so, evaluate it.

Math 180, Final Exam, Spring 2008 Problem 1 Solution. 1. For each of the following limits, determine whether the limit exists and, if so, evaluate it. Math 80, Final Eam, Spring 008 Problem Solution. For each of the following limits, determine whether the limit eists and, if so, evaluate it. + (a) lim 0 (b) lim ( ) 3 (c) lim Solution: (a) Upon substituting

More information

Mat 270 Final Exam Review Sheet Fall 2012 (Final on December 13th, 7:10 PM - 9:00 PM in PSH 153)

Mat 270 Final Exam Review Sheet Fall 2012 (Final on December 13th, 7:10 PM - 9:00 PM in PSH 153) Mat 70 Final Eam Review Sheet Fall 0 (Final on December th, 7:0 PM - 9:00 PM in PSH 5). Find the slope of the secant line to the graph of y f ( ) between the points f ( b) f ( a) ( a, f ( a)), and ( b,

More information

UBC-SFU-UVic-UNBC Calculus Exam Solutions 7 June 2007

UBC-SFU-UVic-UNBC Calculus Exam Solutions 7 June 2007 This eamination has 15 pages including this cover. UBC-SFU-UVic-UNBC Calculus Eam Solutions 7 June 007 Name: School: Signature: Candidate Number: Rules and Instructions 1. Show all your work! Full marks

More information

AP Calculus AB/BC ilearnmath.net 21. Find the solution(s) to the equation log x =0.

AP Calculus AB/BC ilearnmath.net 21. Find the solution(s) to the equation log x =0. . Find the solution(s) to the equation log =. (a) (b) (c) (d) (e) no real solutions. Evaluate ln( 3 e). (a) can t be evaluated (b) 3 e (c) e (d) 3 (e) 3 3. Find the solution(s) to the equation ln( +)=3.

More information

Chapter 27 AB Calculus Practice Test

Chapter 27 AB Calculus Practice Test Chapter 7 AB Calculus Practice Test The Eam AP Calculus AB Eam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time 1 hour and 45 minutes Number

More information

Answers to Some Sample Problems

Answers to Some Sample Problems Answers to Some Sample Problems. Use rules of differentiation to evaluate the derivatives of the following functions of : cos( 3 ) ln(5 7 sin(3)) 3 5 +9 8 3 e 3 h 3 e i sin( 3 )3 +[ ln ] cos( 3 ) [ln(5)

More information

Calculus 1st Semester Final Review

Calculus 1st Semester Final Review Calculus st Semester Final Review Use the graph to find lim f ( ) (if it eists) 0 9 Determine the value of c so that f() is continuous on the entire real line if f ( ), c /, > 0 Find the limit: lim 6+

More information

5.5 Worksheet - Linearization

5.5 Worksheet - Linearization AP Calculus 4.5 Worksheet 5.5 Worksheet - Linearization All work must be shown in this course for full credit. Unsupported answers ma receive NO credit. 1. Consider the function = sin. a) Find the equation

More information

Chapter 5 Review. 1. [No Calculator] Evaluate using the FTOC (the evaluation part) 2. [No Calculator] Evaluate using geometry

Chapter 5 Review. 1. [No Calculator] Evaluate using the FTOC (the evaluation part) 2. [No Calculator] Evaluate using geometry AP Calculus Chapter Review Name: Block:. [No Calculator] Evaluate using the FTOC (the evaluation part) a) 7 8 4 7 d b) 9 4 7 d. [No Calculator] Evaluate using geometry a) d c) 6 8 d. [No Calculator] Evaluate

More information

Chapter (AB/BC, non-calculator) (a) Find the critical numbers of g. (b) For what values of x is g increasing? Justify your answer.

Chapter (AB/BC, non-calculator) (a) Find the critical numbers of g. (b) For what values of x is g increasing? Justify your answer. Chapter 3 1. (AB/BC, non-calculator) Given g ( ) 2 4 3 6 : (a) Find the critical numbers of g. (b) For what values of is g increasing? Justify your answer. (c) Identify the -coordinate of the critical

More information

Solutions Exam 4 (Applications of Differentiation) 1. a. Applying the Quotient Rule we compute the derivative function of f as follows:

Solutions Exam 4 (Applications of Differentiation) 1. a. Applying the Quotient Rule we compute the derivative function of f as follows: MAT 4 Solutions Eam 4 (Applications of Differentiation) a Applying the Quotient Rule we compute the derivative function of f as follows: f () = 43 e 4 e (e ) = 43 4 e = 3 (4 ) e Hence f '( ) 0 for = 0

More information

Math 121 Test 3 - Review 1. Use differentials to approximate the following. Compare your answer to that of a calculator

Math 121 Test 3 - Review 1. Use differentials to approximate the following. Compare your answer to that of a calculator Math Test - Review Use differentials to approximate the following. Compare your answer to that of a calculator.. 99.. 8. 6. Consider the graph of the equation f(x) = x x a. Find f (x) and f (x). b. Find

More information

Chapter 8: Radical Functions

Chapter 8: Radical Functions Chapter 8: Radical Functions Chapter 8 Overview: Types and Traits of Radical Functions Vocabulary:. Radical (Irrational) Function an epression whose general equation contains a root of a variable and possibly

More information

WW Prob Lib1 Math course-section, semester year

WW Prob Lib1 Math course-section, semester year Young-Seon Lee WW Prob Lib Math course-section, semester year WeBWorK assignment due /4/03 at :00 PM..( pt) Give the rational number whose decimal form is: 0 7333333 Answer:.( pt) Solve the following inequality:

More information

Math 180, Exam 2, Spring 2013 Problem 1 Solution

Math 180, Exam 2, Spring 2013 Problem 1 Solution Math 80, Eam, Spring 0 Problem Solution. Find the derivative of each function below. You do not need to simplify your answers. (a) tan ( + cos ) (b) / (logarithmic differentiation may be useful) (c) +

More information

Review: A Cross Section of the Midterm. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Review: A Cross Section of the Midterm. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review: A Cross Section of the Midterm Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit, if it eists. 4 + ) lim - - ) A) - B) -

More information

Math 2250 Final Exam Practice Problem Solutions. f(x) = ln x x. 1 x. lim. lim. x x = lim. = lim 2

Math 2250 Final Exam Practice Problem Solutions. f(x) = ln x x. 1 x. lim. lim. x x = lim. = lim 2 Math 5 Final Eam Practice Problem Solutions. What are the domain and range of the function f() = ln? Answer: is only defined for, and ln is only defined for >. Hence, the domain of the function is >. Notice

More information

AP Calc AB First Semester Review

AP Calc AB First Semester Review AP Calc AB First Semester Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit. 1) lim (7-7) 7 A) -4 B) -56 C) 4 D) 56 1) Determine

More information

1. The following problems are not related: (a) (15 pts, 5 pts ea.) Find the following limits or show that they do not exist: arcsin(x)

1. The following problems are not related: (a) (15 pts, 5 pts ea.) Find the following limits or show that they do not exist: arcsin(x) APPM 5 Final Eam (5 pts) Fall. The following problems are not related: (a) (5 pts, 5 pts ea.) Find the following limits or show that they do not eist: (i) lim e (ii) lim arcsin() (b) (5 pts) Find and classify

More information

Exam Review Sheets Combined

Exam Review Sheets Combined Exam Review Sheets Combined Fall 2008 1 Fall 2007 Exam 1 1. For each part, if the statement is always true, circle the printed capital T. If the statement is sometimes false, circle the printed capital

More information

Math 251 Final Exam Review Fall 2016

Math 251 Final Exam Review Fall 2016 Below are a set of review problems that are, in general, at least as hard as the problems you will see on the final eam. You should know the formula for area of a circle, square, and triangle. All other

More information

Review Sheet for Exam 1 SOLUTIONS

Review Sheet for Exam 1 SOLUTIONS Math b Review Sheet for Eam SOLUTIONS The first Math b midterm will be Tuesday, February 8th, 7 9 p.m. Location: Schwartz Auditorium Room ) The eam will cover: Section 3.6: Inverse Trig Appendi F: Sigma

More information

1993 AP Calculus AB: Section I

1993 AP Calculus AB: Section I 99 AP Calculus AB: Section I 90 Minutes Scientific Calculator Notes: () The eact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among

More information

CLEP Calculus. Time 60 Minutes 45 Questions. For each question below, choose the best answer from the choices given. 2. If f(x) = 3x, then f (x) =

CLEP Calculus. Time 60 Minutes 45 Questions. For each question below, choose the best answer from the choices given. 2. If f(x) = 3x, then f (x) = CLEP Calculus Time 60 Minutes 5 Questions For each question below, choose the best answer from the choices given. 7. lim 5 + 5 is (A) 7 0 (C) 7 0 (D) 7 (E) Noneistent. If f(), then f () (A) (C) (D) (E)

More information

Review sheet Final Exam Math 140 Calculus I Fall 2015 UMass Boston

Review sheet Final Exam Math 140 Calculus I Fall 2015 UMass Boston Review sheet Final Eam Math Calculus I Fall 5 UMass Boston The eam is closed tetbook NO CALCULATORS OR ELECTRONIC DEVICES ARE ALLOWED DURING THE EXAM The final eam will contain problems of types similar

More information

This is only a list of questions use a separate sheet to work out the problems. 1. (1.2 and 1.4) Use the given graph to answer each question.

This is only a list of questions use a separate sheet to work out the problems. 1. (1.2 and 1.4) Use the given graph to answer each question. Mth Calculus Practice Eam Questions NOTE: These questions should not be taken as a complete list o possible problems. The are merel intended to be eamples o the diicult level o the regular eam questions.

More information

AP Calculus BC Final Exam Preparatory Materials December 2016

AP Calculus BC Final Exam Preparatory Materials December 2016 AP Calculus BC Final Eam Preparatory Materials December 06 Your first semester final eam will consist of both multiple choice and free response questions, similar to the AP Eam The following practice problems

More information

Differential Equations

Differential Equations Differential Equations Big Ideas Slope fields draw a slope field, sketch a particular solution Separation of variables separable differential equations General solution Particular solution Growth decay

More information

Math 111 Calculus I - SECTIONS A and B SAMPLE FINAL EXAMINATION Thursday, May 3rd, POSSIBLE POINTS

Math 111 Calculus I - SECTIONS A and B SAMPLE FINAL EXAMINATION Thursday, May 3rd, POSSIBLE POINTS Math Calculus I - SECTIONS A and B SAMPLE FINAL EXAMINATION Thursday, May 3rd, 0 00 POSSIBLE POINTS DISCLAIMER: This sample eam is a study tool designed to assist you in preparing for the final eamination

More information

MATH 1325 Business Calculus Guided Notes

MATH 1325 Business Calculus Guided Notes MATH 135 Business Calculus Guided Notes LSC North Harris By Isabella Fisher Section.1 Functions and Theirs Graphs A is a rule that assigns to each element in one and only one element in. Set A Set B Set

More information

BC Calculus Diagnostic Test

BC Calculus Diagnostic Test BC Calculus Diagnostic Test The Eam AP Calculus BC Eam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a Glance Total Time hour and 5 minutes Number of Questions

More information

1998 AP Calculus AB: Section I, Part A

1998 AP Calculus AB: Section I, Part A 55 Minutes No Calculator Note: Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f () is a real number.. What is the -coordinate of the point

More information

Math 2413 General Review for Calculus Last Updated 02/23/2016

Math 2413 General Review for Calculus Last Updated 02/23/2016 Math 243 General Review for Calculus Last Updated 02/23/206 Find the average velocity of the function over the given interval.. y = 6x 3-5x 2-8, [-8, ] Find the slope of the curve for the given value of

More information

Welcome to Advanced Placement Calculus!! Summer Math

Welcome to Advanced Placement Calculus!! Summer Math Welcome to Advanced Placement Calculus!! Summer Math - 017 As Advanced placement students, your first assignment for the 017-018 school year is to come to class the very first day in top mathematical form.

More information

Math 113 Final Exam Practice Problem Solutions. f(x) = ln x x. lim. lim. x x = lim. = lim 2

Math 113 Final Exam Practice Problem Solutions. f(x) = ln x x. lim. lim. x x = lim. = lim 2 Math 3 Final Eam Practice Problem Solutions. What are the domain and range of the function f() = ln? Answer: is only defined for, and ln is only defined for >. Hence, the domain of the function is >. Notice

More information

Math 170 Calculus I Final Exam Review Solutions

Math 170 Calculus I Final Exam Review Solutions Math 70 Calculus I Final Eam Review Solutions. Find the following its: (a (b (c (d 3 = + = 6 + 5 = 3 + 0 3 4 = sin( (e 0 cos( = (f 0 ln(sin( ln(tan( = ln( (g (h 0 + cot( ln( = sin(π/ = π. Find any values

More information

Math3A Exam #02 Solution Fall 2017

Math3A Exam #02 Solution Fall 2017 Math3A Exam #02 Solution Fall 2017 1. Use the limit definition of the derivative to find f (x) given f ( x) x. 3 2. Use the local linear approximation for f x x at x0 8 to approximate 3 8.1 and write your

More information

1. sin 2. csc 2 3. tan 1 2. Cos 8) Sin 10. sec. Honors Pre-Calculus Final Exam Review 2 nd semester. TRIGONOMETRY Solve for 0 2

1. sin 2. csc 2 3. tan 1 2. Cos 8) Sin 10. sec. Honors Pre-Calculus Final Exam Review 2 nd semester. TRIGONOMETRY Solve for 0 2 Honors Pre-Calculus Final Eam Review nd semester Name: TRIGONOMETRY Solve for 0 without using a calculator: 1 1. sin. csc 3. tan 1 4. cos 1) ) 3) 4) Solve for in degrees giving all solutions. 5. sin 1

More information

AP Calculus BC Summer Review

AP Calculus BC Summer Review AP Calculus BC 07-08 Summer Review Due September, 07 Name: All students entering AP Calculus BC are epected to be proficient in Pre-Calculus skills. To enhance your chances for success in this class, it

More information

AP Calculus Prep Session Handout. Integral Defined Functions

AP Calculus Prep Session Handout. Integral Defined Functions AP Calculus Prep Session Handout A continuous, differentiable function can be epressed as a definite integral if it is difficult or impossible to determine the antiderivative of a function using known

More information

All work must be shown in this course for full credit. Unsupported answers may receive NO credit.

All work must be shown in this course for full credit. Unsupported answers may receive NO credit. AP Calculus.4 Worksheet All work must be shown in this course for full credit. Unsupported answers may receive NO credit.. What is a difference quotient?. How do you find the slope of a curve (aka slope

More information

AP Calculus BC Fall Final Part IIa

AP Calculus BC Fall Final Part IIa AP Calculus BC 18-19 Fall Final Part IIa Calculator Required Name: 1. At time t = 0, there are 120 gallons of oil in a tank. During the time interval 0 t 10 hours, oil flows into the tank at a rate of

More information

Math 117. Study Guide for Exam #1

Math 117. Study Guide for Exam #1 Math 117 Study Guide for Eam #1 Structure of the Eam 0 to 1 problem of finding the derivative of a function by definition (most likely a polynomial) 3 to problems of finding the derivative of functions

More information