Calculus 1st Semester Final Review
|
|
- Hollie Armstrong
- 5 years ago
- Views:
Transcription
1 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+ 9 Find all vertical asymptotes of the graph of + f ( ) + 7 Find the limit: lim + Find the limit: lim f ( ) if f ( ) + 4,, Find the vertical asymptote(s) of f ( ) + 6 At each point indicated on the graph, determine whether the value of the derivative is positive, negative, zero, or if the function has no derivative 4 Find the limit: lim + 5 Find the limit: lim 6 Let f ( ) a lim f ( ) 0 b lim f ( ) 0 + c lim f ( ) 0 + +, 0 Find each limit (if it eists), > 0 7 Find the values of for which f ( ) is 4 discontinuous and label these discontinuities as removable or nonremovable 8 Let f() 5 and g() 4 a Find f(g()) b Find all values of for which f(g()) is discontinuous 4 Use the definition of a derivative to calculate the derivative of f() + 5 Find an equation of the tangent line to the graph of f() + when 6 Find the values of for all points on the graph of f() at which the slope of the tangent line is 4 7 Find all points at which the graph of f() has horizontal tangent lines 8 The position function for an object is given by s(t) 6t + 40t, where s is measured in feet and t is measured in seconds Find the velocity of the object when t seconds 9 Differentiate: y ( ) 0 Calculate d y d if y
2 Find the derivative of y + Find the derivative of y ( + + 5) 6 Find dy d for y + ( ) 6 Determine whether the Mean Value Theorem applies to f() on the interval [, ] If the Mean Value Theorem can be applied, find all value(s) of c in the interval such that f ( c) f ( ) f ( ) If the Mean Value Theorem does not apply, state why 4 The position equation for the movement of a particle is given by s (t + ) where s is measured in feet and t is measured in seconds Find the acceleration of this particle at second 7 Find the open intervals on which f ( ) decreasing is increasing or 5 Find dy if y d + y 6 Use implicit differentiation to find dy d for + y + y 5 7 Find the slope of the curve y 4 y at the point, 8 Find the open intervals on which f() is increasing or decreasing 9 Use the graph to identify the open intervals on which the function is increasing or decreasing 8 The radius of a circle is increasing at the rate of 5 inches per minute At what rate is the area increasing when the radius is 0 inches? 9 Air is being pumped into a spherical balloon at a rate of 8 cubic feet per minute At what rate is the radius changing when the radius is feet? 4 V πr 0 A point moves along the curve y + 0 so that the y value is decreasing at a rate of units per second Find the instantaneous rate of change of with respect to time at the point on the curve where 5 Find all critical numbers for the function: f ( ) + Find all critical numbers for the function: f() 4 4 Find the minimum and maimum values of f() + on the interval [0, ] 4 Consider f ( ) ( ) a Sketch the graph of f() b Calculate f() and f(4) c State why Rolle s Theorem does not apply to f on the interval [, 4] 5 Decide whether Rolle s Theorem can be applied to f() on the interval [, ] If Rolle s Theorem can be applied, find all value(s), c, in the interval such that f ( c) 0 If Rolle s Theorem cannot be applied, state why 40 Find all relative etrema of y ( + 4) 4 Find the relative minimum and relative maimum for f() + 4 Use the first derivative test to find the -values that give relative etrema for f() Let f ( ) Show that f has no critical numbers 44 A differentiable function f has only one critical number: Identify the relative etrema of f at (, f( )) if f ( 4) and f ( ) 45 Find the intervals on which the graph of the function f() is concave upward or downward Then find all points of inflection for the function 46 Find all points of inflection of the graph of the function f() ( 4) 47 Find all points of inflection of the graph of the function f() Let f() + Use the Second Derivative Test to determine which critical numbers, if any, give relative etrema
3 49 The graph of a polynomial function, f, is given On the same coordinate aes sketch f and f Find the horizontal asymptote for f ( ) 5 Find the limit: lim 4 5 An open bo is to be made from a square piece of material, inches on each side, by cutting equal squares from each corner and turning up the sides Find the volume of the largest bo that can be made in this manner 5 Use the techniques learned in this chapter to sketch the graph of f() A rancher has 00 feet of fencing to enclose a pasture bordered on one side by a river The river side of the pasture needs no fence Find the dimensions of the pasture that will produce a pasture with a maimum area 55 A manufacturer determines that employees on a certain production line will produce y units per month where y To obtain maimum monthly production, how many employees should be assigned to the production line? 56 The volume of a cube is claimed to be 7 cubic inches, correct to within 007 in Use differentials to estimate the propagated error in the measurement of the side of the cube
4 Calculus st Semester Final Review Reference: [66] [] The limit does not eist Reference: [] [5] y 6 Reference: [78] [] 0 Reference: [74] [] 5 Reference: [79] [4] Reference: [746] [5] Reference: [80] [6] a b c The limit does not eist Reference: [80] [7], removable;, nonremovable Reference: [8] [8] 5 a 4 b, Reference: [86] [9] 7 Reference: [98] [0] Reference: [9] [] 7 Reference: [95] [] Reference: [05] [] a no derivative b negative c zero d positive e zero Reference: [6], [6] Reference: [8] [7] (, ), (, ) Reference: [40] [8] 64 ft/sec Reference: [] [9] [0] 6 + ( ) Reference: [5] [] ( ) Reference: [] + ( + ) / Reference: [] [] ( + )( + + 5) 5 Reference: [] ( 7 + ) [] + Reference: [4] [4] 4 ft/sec Reference: [4] y [5] ( + y) + Reference: [40] y [6] + y Reference: [0] [4]
5 Reference: [49] [7] Reference: [55] [8] 00π in /min Reference: [54] 7 ft/min [9] 9π Reference: [59] [0] 5 units/sec Reference: [6], [] Reference: [64] [] 0, Reference: [67] [] Minimum at (, 0); Maimum at (, 4) Reference: [7] a Reference: [84] [8] Increasing (, 0) and (, ); decreasing (0, ) Reference: [80] [9] Decreasing (, ) and (, ) Reference: [86] [40], 54 Reference: [87], relative maimum [4] Relative maimum: (, 0); relative minimum: (, 7) Reference: [8] [4] Relative maimum at Reference: [87] [4] f ( ) 0 for all ( ) f ( ) is undefined at, a vertical asymptote Reference: [88] [44] Relative maimum Reference: [94] [45] Concave upward: (, 0), (, ) Concave downward: (0, ) Points of inflection: (0, ) and (, 4) Reference: [94] [46] (4, 0), (, ) Reference: [98] [47] (, 4) [4] b f() f(4) c f is not continuous on [, 4] Reference: [77] [5] Rolle s Theorem applies; c 0,, and Reference: [9] [48] 0, relative maimum;, relative minimum Reference: [74] [6] The Mean Value Theorem applies; c 5 Reference: [8] [7] Increasing (, 0); decreasing (0, )
6 Reference: [9] [49] Reference: [0] [50] y Reference: [07] [5] Reference: [7] [5] 8 () 8 cubic inches Reference: [8] [5] Reference: [8] [54] 75 feet by 50 feet Reference: [8] [55] 4 Reference: [4] [56] ±000 in
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 informationFinal 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 informationCollege Calculus Final Review
College Calculus Final Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the following limit. (Hint: Use the graph to calculate the limit.)
More informationAP Calculus AB Semester 1 Practice Final
Class: Date: AP Calculus AB Semester 1 Practice Final Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the limit (if it exists). lim x x + 4 x a. 6
More informationAP 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 informationCalculus 437 Semester 1 Review Chapters 1, 2, and 3 January 2016
Name: Class: Date: Calculus 437 Semester 1 Review Chapters 1, 2, and 3 January 2016 Short Answer 1. Decide whether the following problem can be solved using precalculus, or whether calculus is required.
More information1. 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 informationMATH 2053 Calculus I Review for the Final Exam
MATH 05 Calculus I Review for the Final Exam (x+ x) 9 x 9 1. Find the limit: lim x 0. x. Find the limit: lim x + x x (x ).. Find lim x (x 5) = L, find such that f(x) L < 0.01 whenever 0 < x
More informationMath 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( ) 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 information3.1 ANALYSIS OF FUNCTIONS I INCREASE, DECREASE, AND CONCAVITY
MATH00 (Calculus).1 ANALYSIS OF FUNCTIONS I INCREASE, DECREASE, AND CONCAVITY Name Group No. KEYWORD: increasing, decreasing, constant, concave up, concave down, and inflection point Eample 1. Match the
More information+ 2 on the interval [-1,3]
Section.1 Etrema on an Interval 1. Understand the definition of etrema of a function on an interval.. Understand the definition of relative etrema of a function on an open interval.. Find etrema on a closed
More informationMathematics 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 informationDate Period For each problem, find all points of absolute minima and maxima on the given interval.
Calculus C o_0b1k5k gkbult_ai nsoo\fwtvwhairkew ULNLuCC._ ` naylflu [rhisg^h^tlsi traesgevrpvfe_dl. Final Eam Review Day 1 Name ID: 1 Date Period For each problem, find all points of absolute minima and
More informationAP 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 informationMath 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 informationAP 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 informationIt 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 informationIf C(x) is the total cost (in dollars) of producing x items of a product, then
Supplemental Review Problems for Unit Test : 1 Marginal Analysis (Sec 7) Be prepared to calculate total revenue given the price - demand function; to calculate total profit given total revenue and total
More information( ) 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 informationFind 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 informationsin 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 informationx π. Determine all open interval(s) on which f is decreasing
Calculus Maimus Increasing, Decreasing, and st Derivative Test Show all work. No calculator unless otherwise stated. Multiple Choice = /5 + _ /5 over. Determine the increasing and decreasing open intervals
More informationx 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 informationWork the following on notebook paper. You may use your calculator to find
CALCULUS WORKSHEET ON 3.1 Work the following on notebook paper. You may use your calculator to find f values. 1. For each of the labeled points, state whether the function whose graph is shown has an absolute
More information1. 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 informationIn #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 informationBE 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 informationMA 123 Calculus I Midterm II Practice Exam Answer Key
MA 1 Midterm II Practice Eam Note: Be aware that there may be more than one method to solving any one question. Keep in mind that the beauty in math is that you can often obtain the same answer from more
More information4.1 & 4.2 Student Notes Using the First and Second Derivatives. for all x in D, where D is the domain of f. The number f()
4.1 & 4. Student Notes Using the First and Second Derivatives Definition A function f has an absolute maximum (or global maximum) at c if f ( c) f ( x) for all x in D, where D is the domain of f. The number
More informationMAT 1339-S14 Class 4
MAT 9-S4 Class 4 July 4, 204 Contents Curve Sketching. Concavity and the Second Derivative Test.................4 Simple Rational Functions........................ 2.5 Putting It All Together.........................
More informationf on the same coordinate axes.
Calculus AB 0 Unit : Station Review # TARGETS T, T, T, T8, T9 T: A particle P moves along on a number line. The following graph shows the position of P as a function of t time S( cm) (0,0) (9, ) (, ) t
More information1. The cost (in dollars) of producing x units of a certain commodity is C(x) = x x 2.
APPM 1350 Review #2 Summer 2014 1. The cost (in dollars) of producing units of a certain commodity is C() 5000 + 10 + 0.05 2. (a) Find the average rate of change of C with respect to when the production
More informationx 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 informationSection Derivatives and Rates of Change
Section. - Derivatives and Rates of Change Recall : The average rate of change can be viewed as the slope of the secant line between two points on a curve. In Section.1, we numerically estimated the slope
More information1. 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 informationNO CALCULATOR 1. Find the interval or intervals on which the function whose graph is shown is increasing:
AP Calculus AB PRACTICE MIDTERM EXAM Read each choice carefully and find the best answer. Your midterm exam will be made up of 8 of these questions. I reserve the right to change numbers and answers on
More informationTechnical 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 informationName Date Period. AP Calculus AB/BC Practice TEST: Curve Sketch, Optimization, & Related Rates. 1. If f is the function whose graph is given at right
Name Date Period AP Calculus AB/BC Practice TEST: Curve Sketch, Optimization, & Related Rates. If f is the function whose graph is given at right Which of the following properties does f NOT have? (A)
More informationReview Exercises for Chapter 3. Review Exercises for Chapter r v 0 2. v ft sec. x 1 2 x dx f x x 99.4.
Review Eercises for Chapter 6. r v 0 sin. Let f, 00, d 0.6. v 0 00 ftsec changes from 0 to dr 00 cos d 6 0 d 0 r dr 80 00 6 96 feet 80 cos 0 96 feet 8080 f f fd d f 99. 00 0.6 9.97 00 Using a calculator:
More informationMath 1500 Fall 2010 Final Exam Review Solutions
Math 500 Fall 00 Final Eam Review Solutions. Verify that the function f() = 4 + on the interval [, 5] satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers c that
More informationName: Date: Block: Quarter 2 Summative Assessment Revision #1
Name: Date: Block: Multiple Choice Non-Calculator Quarter Summative Assessment Revision #1 1. The graph of y = x x has a relative maximum at (a) (0,0) only (b) (1,) only (c) (,4) only (d) (4, 16) only
More informationSo, t = 1 is a point of inflection of s(). Use s () t to find the velocity at t = Because 0, use 144.
AP Eam Practice Questions for Chapter AP Eam Practice Questions for Chapter f 4 + 6 7 9 f + 7 0 + 6 0 ( + )( ) 0,. The critical numbers of f( ) are and.. Evaluate each point. A: d d C: d d B: D: d d d
More informationlim 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 informationMA Lesson 25 Notes Section 5.3 (2 nd half of textbook)
MA 000 Lesson 5 Notes Section 5. ( nd half of tetbook) Higher Derivatives: In this lesson, we will find a derivative of a derivative. A second derivative is a derivative of the first derivative. A third
More informationMath 1325 Final Exam Review. (Set it up, but do not simplify) lim
. Given f( ), find Math 5 Final Eam Review f h f. h0 h a. If f ( ) 5 (Set it up, but do not simplify) If c. If f ( ) 5 f (Simplify) ( ) 7 f (Set it up, but do not simplify) ( ) 7 (Simplify) d. If f. Given
More informationCALCULUS 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 informationMultiple 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 informationSemester 1 Review. Name. Period
P A (Calculus )dx Semester Review Name Period Directions: Solve the following problems. Show work when necessary. Put the best answer in the blank provided, if appropriate.. Let y = g(x) be a function
More information3 Applications of Derivatives Instantaneous Rates of Change Optimization Related Rates... 13
Contents Limits Derivatives 3. Difference Quotients......................................... 3. Average Rate of Change...................................... 4.3 Derivative Rules...........................................
More informationUnit 3 Applications of Differentiation Lesson 4: The First Derivative Lesson 5: Concavity and The Second Derivative
Warmup 1) The lengths of the sides of a square are decreasing at a constant rate of 4 ft./min. In terms of the perimeter, P, what is the rate of change of the area of the square in square feet per minute?
More informationCLEP 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 informationThe 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 information1993 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 information2008 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 information1. sin 2. Honors Pre-Calculus Final Exam Review 2 nd semester June TRIGONOMETRY Solve for 0 2. without using a calculator: 2. csc 2 3.
Honors Pre-Calculus Name: Final Eam Review nd semester June 05 TRIGONOMETRY Solve for 0 without using a calculator:. sin. csc. tan. cos ) ) ) ) Solve for in degrees giving all solutions. 5. sin 6. cos
More informationf'(x) = x 4 (2)(x - 6)(1) + (x - 6) 2 (4x 3 ) f'(x) = (x - 2) -1/3 = x 2 ; domain of f: (-, ) f'(x) = (x2 + 1)4x! 2x 2 (2x) 4x f'(x) =
85. f() = 4 ( - 6) 2 f'() = 4 (2)( - 6)(1) + ( - 6) 2 (4 3 ) = 2 3 ( - 6)[ + 2( - 6)] = 2 3 ( - 6)(3-12) = 6 3 ( - 4)( - 6) Thus, the critical values are = 0, = 4, and = 6. Now we construct the sign chart
More information(b) x = (d) x = (b) x = e (d) x = e4 2 ln(3) 2 x x. is. (b) 2 x, x 0. (d) x 2, x 0
1. Solve the equation 3 4x+5 = 6 for x. ln(6)/ ln(3) 5 (a) x = 4 ln(3) ln(6)/ ln(3) 5 (c) x = 4 ln(3)/ ln(6) 5 (e) x = 4. Solve the equation e x 1 = 1 for x. (b) x = (d) x = ln(5)/ ln(3) 6 4 ln(6) 5/ ln(3)
More informationCopyright 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter 5 Review 95 (c) f( ) f ( 7) ( 7) 7 6 + ( 6 7) 7 6. 96 Chapter 5 Review Eercises (pp. 60 6). y y ( ) + ( )( ) + ( ) The first derivative has a zero at. 6 Critical point value: y 9 Endpoint values:
More informationLimits. 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 informationAP Calculus BC Chapter 4 AP Exam Problems A) 4 B) 2 C) 1 D) 0 E) 2 A) 9 B) 12 C) 14 D) 21 E) 40
Extreme Values in an Interval AP Calculus BC 1. The absolute maximum value of x = f ( x) x x 1 on the closed interval, 4 occurs at A) 4 B) C) 1 D) 0 E). The maximum acceleration attained on the interval
More informationSolutions 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 informationChapter 2 THE DERIVATIVE
Chapter 2 THE DERIVATIVE 2.1 Two Problems with One Theme Tangent Line (Euclid) A tangent is a line touching a curve at just one point. - Euclid (323 285 BC) Tangent Line (Archimedes) A tangent to a curve
More information1985 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 informationAP 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 informationBARUCH COLLEGE MATH 2207 FALL 2007 MANUAL FOR THE UNIFORM FINAL EXAMINATION. No calculator will be allowed on this part.
BARUCH COLLEGE MATH 07 FALL 007 MANUAL FOR THE UNIFORM FINAL EXAMINATION The final eamination for Math 07 will consist of two parts. Part I: Part II: This part will consist of 5 questions. No calculator
More informationAP 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 informationMath 2413 t2rsu14. Name: 06/06/ Find the derivative of the following function using the limiting process.
Name: 06/06/014 Math 413 trsu14 1. Find the derivative of the following function using the limiting process. f( x) = 4x + 5x. Find the derivative of the following function using the limiting process. f(
More informationCalculus 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
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.
More informationDaily Lessons and Assessments for AP* Calculus AB, A Complete Course Page 119 Mark Sparks 2012
Unit # Understanding the Derivative Homework Packet f ( h) f ( Find lim for each of the functions below. Then, find the equation of the tangent line to h 0 h the graph of f( at the given value of. 1. f
More information1998 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 informationApplications of Derivatives
Applications of Derivatives Extrema on an Interval Objective: Understand the definition of extrema of a function on an interval. Understand the definition of relative extrema of a function on an open interval.
More informationNO CALCULATOR 1. Find the interval or intervals on which the function whose graph is shown is increasing:
AP Calculus AB PRACTICE MIDTERM EXAM Read each choice carefully and find the best answer. Your midterm exam will be made up of 5 of these questions. I reserve the right to change numbers and answers on
More informationMath 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 informationMath Honors Calculus I Final Examination, Fall Semester, 2013
Math 2 - Honors Calculus I Final Eamination, Fall Semester, 2 Time Allowed: 2.5 Hours Total Marks:. (2 Marks) Find the following: ( (a) 2 ) sin 2. (b) + (ln 2)/(+ln ). (c) The 2-th Taylor polynomial centered
More information4.3 - How Derivatives Affect the Shape of a Graph
4.3 - How Derivatives Affect the Shape of a Graph 1. Increasing and Decreasing Functions Definition: A function f is (strictly) increasing on an interval I if for every 1, in I with 1, f 1 f. A function
More informationMath 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 informationMATH 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 informationMath 1431 Final Exam Review
Math 1431 Final Exam Review Comprehensive exam. I recommend you study all past reviews and practice exams as well. Know all rules/formulas. Make a reservation for the final exam. If you miss it, go back
More informationMath 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 informationName: NOTES 4: APPLICATIONS OF DIFFERENTIATION. Date: Period: Mrs. Nguyen s Initial: WARM UP:
NOTES 4: APPLICATIONS OF DIFFERENTIATION Name: Date: Period: Mrs. Nguyen s Initial: WARM UP: Assume that f ( ) and g ( ) are differentiable functions: f ( ) f '( ) g ( ) g'( ) - 3 1-5 8-1 -9 7 4 1 0 5
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1325 Test 3 Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the location and value of each relative etremum for the function. 1)
More informationChapter 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?
NOTES 4: APPLICATIONS OF DIFFERENTIATION Name: Date: Period: WARM UP: Assume that f( ) and g ( ) are differentiable functions: f( ) f '( ) g ( ) g'( ) - 3 1-5 8-1 -9 7 4 1 0 5 9 9-3 1 3-3 6-5 3 8? 1. Let
More informationExam 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 informationOne of the most common applications of Calculus involves determining maximum or minimum values.
8 LESSON 5- MAX/MIN APPLICATIONS (OPTIMIZATION) One of the most common applications of Calculus involves determining maimum or minimum values. Procedure:. Choose variables and/or draw a labeled figure..
More informationAP Calculus AB Semester 2 Practice Final
lass: ate: I: P alculus Semester Practice Final Multiple hoice Identify the choice that best completes the statement or answers the question. Find the constants a and b such that the function f( x) = Ï
More informationJune 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(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 informationAP 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 informationMEMORIAL UNIVERSITY OF NEWFOUNDLAND
MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS FINAL EXAMINATION Solutions Mathematics 1000 FALL 2010 Marks [12] 1. Evaluate the following limits, showing your work. Assign
More informationChapter 2: Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point.
Chapter : Differentiation 1. Find the slope of the tangent line to the graph of the function below at the given point. f( ) 10, (, ) 10 1 E) none of the above. Find the slope of the tangent line to the
More informationMath 111 Calculus I Fall 2005 Practice Problems For Final December 5, 2005
Math 111 Calculus I Fall 2005 Practice Problems For Final December 5, 2005 As always, the standard disclaimers apply In particular, I make no claims that all the material which will be on the exam is represented
More informationMath 180, Lowman, Summer 2008, Old Exam Problems 1 Limit Problems
Math 180, Lowman, Summer 2008, Old Exam Problems 1 Limit Problems 1. Find the limit of f(x) = (sin x) x x 3 as x 0. 2. Use L Hopital s Rule to calculate lim x 2 x 3 2x 2 x+2 x 2 4. 3. Given the function
More informationAP Calculus Free-Response Questions 1969-present AB
AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions
More informationMath 2414 Activity 1 (Due by end of class July 23) Precalculus Problems: 3,0 and are tangent to the parabola axis. Find the other line.
Math 44 Activity (Due by end of class July 3) Precalculus Problems: 3, and are tangent to the parabola ais. Find the other line.. One of the two lines that pass through y is the - {Hint: For a line through
More informationMath 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 informationSolutions to review problems MAT 125, Fall 2004
Solutions to review problems MAT 125, Fall 200 1. For each of the following functions, find the absolute maimum and minimum values for f() in the given intervals. Also state the value where they occur.
More information4.1 & 4.2 Student Notes Using the First and Second Derivatives. for all x in D, where D is the domain of f. The number f()
4.1 & 4. Student Notes Using the First and Second Derivatives Deinition A unction has an absolute maimum (or global maimum) at c i ( c) ( ) or all in D, where D is the domain o. The number () c is called
More informationMA 125 CALCULUS I FALL 2006 December 08, 2006 FINAL EXAM. Name (Print last name first):... Instructor:... Section:... PART I
CALCULUS I, FINAL EXAM 1 MA 125 CALCULUS I FALL 2006 December 08, 2006 FINAL EXAM Name (Print last name first):............................................. Student ID Number:...........................
More information