College Calculus Final Review
|
|
|
- Carol Harrell
- 5 years ago
- Views:
Transcription
1 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.) does not exist
2 2. Let Determine the following limit. (Hint: Use the graph to calculate the limit.) does not exist 3. Let and. Find the limit
3 4. Find the following limit (if it exists). Write a simpler function that agrees with the given function at all but one point Find the limit (if it exists) Find the limit (if it exists). 6.
4 7. Use the graph as shown to determine the following limits, and discuss the continuity of the function at. (i) (ii) (iii) 2, 2, 2, 2, 2, 2, 8. Use the graph to determine the following limits, and discuss the continuity of the function at. (i) (ii) (iii)
5 9. Find the limit (if it exists). 10. Find the x-values (if any) at which is not continuous. 11. Find the x-values (if any) at which is not continuous. 12. Find the vertical asymptotes (if any) of the function. 13. Find the derivative of the function.
6 14. Find the derivative of the function. 15. Use the rules of differentiation to find the derivative of the function. 16. Find the slope of the graph of the function at the given valu when
7 17. Find the slope of the graph of the function at the given valu at 18. Find the derivative of the function. 19. Determine all values of, (if any), at which the graph of the function has a horizontal tangent. The graph has no horizontal tangents. 20. Find the derivative of the algebraic function.
8 21. Use the Product Rule to differentiate.
9 22. Use the Quotient Rule to differentiate the function. 23. Find the derivative of the function.
10 24. Find an equation of the tangent line to the graph of f at the given point. 25. The length of a rectangle is and its height is, where t is time in seconds and the dimensions are in inches. Find the rate of change of the area, A, with respect to tim square inches/second square inches/second square inches/second square inches/second square inches/second 26. Find the second derivative of the function.
11 27. Suppose that an automobile's velocity starting from rest is secon Find the acceleration at 9 seconds. Round your answer to one decimal plac 1.9 ft/sec ft/sec ft/sec ft/sec ft/sec 2 where v is measured in feet per 28. Find the derivative of the function. 29. Find the derivative of the function.
12 30. Find the derivative of the function. 31. Find the derivative of the function.
13 32. Find by implicit differentiation. 33. Find by implicit differentiation.
14 34. Find by implicit differentiation. 35. Find an equation of the tangent line to the graph of the function given below at the given point. (The coefficients below are given to two decimal places.) 36. The radius, r, of a circle is decreasing at a rate of centimeters per minut Find the rate of change of area, A, when the radius is. sq cm/min sq cm/min sq cm/min sq cm/min sq cm/min
15 37. A spherical balloon is inflated with gas at the rate of radius of the balloon increasing at the instant the radius is cubic centimeters per minut How fast is the centimeters? 38. A ladder feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of feet per secon How fast is the top of the ladder moving down the wall when its base is feet from the wall? Round your answer to two decimal places. ft/sec ft/sec ft/sec ft/sec ft/sec 39. Find all critical numbers of the function. critical numbers: critical numbers: critical numbers: critical numbers: no critical numbers
16 40. Identify the open intervals where the function is increasing or decreasing. decreasing: ; increasing: decreasing on increasing: increasing: increasing: ; decreasing: ; decreasing: ; decreasing: 41. Find the open interval(s) on which is increasing or decreasing. increasing on decreasing on increasing on decreasing on increasing on decreasing on increasing on decreasing on increasing on decreasing on
17 42. The graph of f is shown in the figur Sketch a graph of the derivative of f
18 43. Determine the open intervals on which the graph of upwar is concave downward or concave concave downward on concave upward on ; concave downward on concave upward on ; concave downward on concave upward on concave downward on ; concave upward on 44. Find all relative extrema of the function applicabl. Use the Second Derivative Test where relative max: ; no relative min no relative max; no relative min relative min: ; relative max: relative min: ; no relative max relative min: ; relative max: 45. Find the limit
19 46. Find the limit. 1 0 does not exist 47. Find the limit Find the limit. 1 6
20 49. The graph of a function f is is shown below. Sketch the graph of the derivative.
21 50. Find the length and width of a rectangle that has an area of 968 square feet and whose perimeter is a minimum. 51. Find the indefinite integral.
22 52. Find the indefinite integral. 53. Find the indefinite integral of the following function and check the result by differentiation.
23 54. Solve the differential equation.
24 College Calculus Final Review Answer Section MULTIPLE CHOICE 1. D 2. C 3. B 4. B 5. A 6. D 7. A 8. C 9. D 10. D 11. A 12. B 13. E 14. D 15. C 16. D 17. A 18. B 19. A 20. D 21. D 22. A 23. B 24. C 25. C 26. C 27. B 28. B 29. B 30. E 31. C 32. D 33. A 34. B 35. C 36. C 37. C 38. C 39. B 40. D 41. E
25 42. C 43. D 44. D 45. E 46. D 47. C 48. B 49. B 50. B 51. E 52. B 53. B 54. E
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
Calculus 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.
Math 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(
Ï ( ) Ì ÓÔ. Math 2413 FRsu11. Short Answer. 1. Complete the table and use the result to estimate the limit. lim x 3. x 2 16x+ 39
Math 43 FRsu Short Answer. Complete the table and use the result to estimate the it. x 3 x 3 x 6x+ 39. Let f x x.9.99.999 3.00 3.0 3. f(x) Ï ( ) Ô = x + 5, x Ì ÓÔ., x = Determine the following it. (Hint:
MATH1910Chapter2TestReview
Class: Date: MATH1910Chapter2TestReview Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the slope m of the line tangent to the graph of the function
AP 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
m2413c2 the limiting process. 4. Use the alternative form of the derivative to find the derivative of the function at. a. b. c. d. e.
m2413c2 Multiple Choice Identify the choice that best completes the statement or answers the question 1 Find the derivative of the following function using the limiting process 2 Find the derivative of
Implicit Differentiation
Implicit Differentiation Much of our algebraic study of mathematics has dealt with functions. In pre-calculus, we talked about two different types of equations that relate x and y explicit and implicit.
AP Calculus AB Chapter 4 Packet Implicit Differentiation. 4.5: Implicit Functions
4.5: Implicit Functions We can employ implicit differentiation when an equation that defines a function is so complicated that we cannot use an explicit rule to find the derivative. EXAMPLE 1: Find dy
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+
AP 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
AP 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
m2413f 4. Suppose that and . Find the following limit b. 10 c. 3 d Determine the limit (if it exists). 2. Find the lmit. a. 1 b. 0 c. d.
m2413f Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find an equation of the line that passes through the point and has the slope. 4. Suppose that and
4.1 Implicit Differentiation
4.1 Implicit Differentiation Learning Objectives A student will be able to: Find the derivative of variety of functions by using the technique of implicit differentiation. Consider the equation We want
Unit 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?
AP Calculus Related Rates Worksheet
AP Calculus Related Rates Worksheet 1. A small balloon is released at a point 150 feet from an observer, who is on level ground. If the balloon goes straight up at a rate of 8 feet per second, how fast
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
MAT 210 TEST 2 REVIEW (Ch 12 and 13)
Class: Date: MAT 0 TEST REVIEW (Ch and ) Multiple Choice Identify the choice that best completes the statement or answers the question.. The population P is currently 0,000 and growing at a rate of 7,000
Name Date Class. Logarithmic/Exponential Differentiation and Related Rates Review AP Calculus. Find dy. dx. 1. y 4 x. y 6. 3e x.
Name Date Class Find dy d. Logarithmic/Eponential Differentiation and Related Rates Review AP Calculus 1. y 4. 1 y ln. y ln 1 4. y log9 1 5. e y 6. y log 7. y e 8. e y e 4 1 1 9. y e e 10. 1 y ln 1 e 11.
Days 3 & 4 Notes: Related Rates
AP Calculus Unit 4 Applications of the Derivative Part 1 Days 3 & 4 Notes: Related Rates Implicitly differentiate the following formulas with respect to time. State what each rate in the differential equation
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
Workbook for Calculus I
Workbook for Calculus I By Hüseyin Yüce New York 2007 1 Functions 1.1 Four Ways to Represent a Function 1. Find the domain and range of the function f(x) = 1 + x + 1 and sketch its graph. y 3 2 1-3 -2-1
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
Period: Unit 2 Differentiation Date: mole rat QUIZ 4 Implicit differentiation (calculator OK but unnecessary)
Unit Differentiation mole rat QUIZ 4 Implicit differentiation (calculator OK but unnecessary) Standard.5: I can find the slope of an equation implicitly (when explicit differentiation is impossible*).
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
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:
Purdue University Study Guide for MA Credit Exam
Purdue University Study Guide for MA 16010 Credit Exam Students who pass the credit exam will gain credit in MA16010. The credit exam is a two-hour long exam with multiple choice questions. No books or
Name: 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
4.1 & 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
Applications of Derivatives
ApplicationsDerivativesII.nb 1 Applications of Derivatives Now that we have covered the basic concepts and mechanics of derivatives it's time to look at some applications. We will start with a summary
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
Sections Practice AP Calculus AB Name
Sections 4.1-4.5 Practice AP Calculus AB Name Be sure to show work, giving written explanations when requested. Answers should be written exactly or rounded to the nearest thousandth. When the calculator
Exam 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Find dy/dx by implicit differentiation. x3 + y3 = 5 A)
MATH 135 Calculus 1 Solutions/Answers for Exam 3 Practice Problems November 18, 2016
MATH 35 Calculus Solutions/Answers for Exam 3 Practice Problems November 8, 206 I. Find the indicated derivative(s) and simplify. (A) ( y = ln(x) x 7 4 ) x Solution: By the product rule and the derivative
Analyzing Functions. Implicit Functions and Implicit Differentiation
Analyzing Functions Implicit Functions and Implicit Differentiation In mathematics, an implicit function is a generalization of the concept of a function in which the dependent variable, say, has not been
Applications 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.
( ) 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:
CHAPTER 3: DERIVATIVES
(Exercises for Section 3.1: Derivatives, Tangent Lines, and Rates of Change) E.3.1 CHAPTER 3: DERIVATIVES SECTION 3.1: DERIVATIVES, TANGENT LINES, and RATES OF CHANGE In these Exercises, use a version
Section 1.1: A Preview of Calculus When you finish your homework, you should be able to
Section 1.1: A Preview of Calculus When you finish your homework, you should be able to π Understand what calculus is and how it compares with precalculus π Understand that the tangent line problem is
Math 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
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
(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)
QUIZ ON CHAPTER 4 APPLICATIONS OF DERIVATIVES; MATH 150 FALL 2016 KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS
Math 150 Name: QUIZ ON CHAPTER 4 APPLICATIONS OF DERIVATIVES; MATH 150 FALL 2016 KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% Show all work, simplify as appropriate, and use good form and procedure
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
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
SHOW WORK! Chapter4Questions. NAME ID: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
NAME ID: Date: Chapter4Questions Multiple Choice Identify the choice that best completes the statement or answers the question. SHOW WORK! 1. Find the indefinite integral 1u 4u du. a. 4u u C b. 1u 4u C
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
Name: Date: Period: Calculus Honors: 4-2 The Product Rule
Name: Date: Period: Calculus Honors: 4- The Product Rule Warm Up: 1. Factor and simplify. 9 10 0 5 5 10 5 5. Find ' f if f How did you go about finding the derivative? Let s Eplore how to differentiate
1. Find all critical numbers of the function. 2. Find any critical numbers of the function.
1. Find all critical numbers of the function. a. critical numbers: *b. critical numbers: c. critical numbers: d. critical numbers: e. no critical numbers 2. Find any critical numbers of the function. a.
Chapter 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
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
AP Calculus Worksheet: Chapter 2 Review Part I
AP Calculus Worksheet: Chapter 2 Review Part I 1. Given y = f(x), what is the average rate of change of f on the interval [a, b]? What is the graphical interpretation of your answer? 2. The derivative
Chapter 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
( ) 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
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,
MATH 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
Stewart - Calculus 8e Chapter 2 Form A. 1. Differentiate. 2. Find the limit. 3. Differentiate.
Stewart - Calculus 8e Chapter 2 Form A Multivariable Calculus 8th Edition Stewart TEST BANK Full clear download at: https://testbankreal.com/download/multivariable-calculus-8th-editionstewart-test-bank/
Math 131. Related Rates Larson Section 2.6
Math 131. Related Rates Larson Section 2.6 There are many natural situations when there are related variables that are changing with respect to time. For example, a spherical balloon is being inflated
AP Calculus. Applications of Derivatives. Table of Contents
AP Calculus 2015 11 03 www.njctl.org Table of Contents click on the topic to go to that section Related Rates Linear Motion Linear Approximation & Differentials L'Hopital's Rule Horizontal Tangents 1 Related
Calculus Test Chapter 5 You can use a calculator on all of the test. Each multiple choice & each part of the free response is worth 5 points.
Calculus Test 2013- Chapter 5 Name You can use a calculator on all of the test. Each multiple choice & each part of the free response is worth 5 points. 1. A bug begins to crawl up a vertical wire at time
AP Calculus Chapter 4 Testbank (Mr. Surowski)
AP Calculus Chapter 4 Testbank (Mr. Surowski) Part I. Multiple-Choice Questions 1. Let f(x) = x 3 + 3x 2 45x + 4. Then the local extrema of f are (A) a local minimum of 179 at x = 5 and a local maximum
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
Free Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom
Free Response Questions 1969-010 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions
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
Implicit Differentiation and Related Rates
Math 3A Discussion Notes Week 5 October 7 and October 9, 05 Because of the mierm, we re a little behind lecture, but this week s topics will help prepare you for the quiz. Implicit Differentiation and
Unit V Applications of Derivatives
Unit V Applications of Derivatives Curve Sketching Inequalities (Not covered in 3205) Polynomial Rational Functions Related Rate Problems Optimization (Max/Min) Problems 1 Inequalities Linear Polynomial
Unit V Applications of Derivatives
Unit V Applications of Derivatives Curve Sketching Inequalities (Covered in 2200) Polynomial Rational Functions Related Rate Problems Optimization (Max/Min) Problems 1 Inequalities Linear Polynomial Rational
AP Calculus. Slide 1 / 101. Slide 2 / 101. Slide 3 / 101. Applications of Derivatives. Table of Contents
Slide 1 / 101 Slide 2 / 101 AP Calculus Applications of Derivatives 2015-11-03 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 101 Related Rates Linear Motion Linear
4.3 How Derivatives Aect the Shape of a Graph
11/3/2010 What does f say about f? Increasing/Decreasing Test Fact Increasing/Decreasing Test Fact If f '(x) > 0 on an interval, then f interval. is increasing on that Increasing/Decreasing Test Fact If
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
Using the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles
Math 154 Chapter 9.6: Applications of Radical Equations Objectives: Finding legs of right triangles Finding hypotenuse of right triangles Solve application problems involving right triangles Pythagorean
UNIT 2 SIMPLE APPLICATION OF DIFFERENTIAL CALCULUS
Calculus UNIT 2 SIMPLE APPLICATION OF DIFFERENTIAL CALCULUS Structure 2.0 Introduction 2.1 Objectives 2.2 Rate of Change of Quantities 2.3 Increasing and Decreasing Function 2.4 Maima and Minima of Functions
Topics Covered in Calculus BC
Topics Covered in Calculus BC Calculus BC Correlation 5 A Functions, Graphs, and Limits 1. Analysis of graphs 2. Limits or functions (including one sides limits) a. An intuitive understanding of the limiting
*Finding the tangent line at a point P boils down to finding the slope of the tangent line at point P.
The Derivative & Tangent Line Problem *Finding the tangent line at a point P boils down to finding the slope of the tangent line at point P. 1 The Derivative & Tangent Line Problem We can approximate using
The volume of a sphere and the radius of the same sphere are related by the formula:
Related Rates Today is a day in which we explore the behavior of derivatives rather than trying to get new formulas for derivatives. Example Let s ask the following question: Suppose that you are filling
NO 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
Review Sheet 2 Solutions
Review Sheet Solutions 1. If y x 3 x and dx dt 5, find dy dt when x. We have that dy dt 3 x dx dt dx dt 3 x 5 5, and this is equal to 3 5 10 70 when x.. A spherical balloon is being inflated so that its
Semester 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
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
Math 125: Exam 3 Review
Math 125: Exam 3 Review Since we re using calculators, to keep the playing field level between all students, I will ask that you refrain from using certain features of your calculator, including graphing.
Applications of Derivatives
Applications of Derivatives Big Ideas Connecting the graphs of f, f, f Differentiability Continuity Continuity Differentiability Critical values Mean Value Theorem for Derivatives: Hypothesis: If f is
Additional Exercises 10.1 Form I Solving Quadratic Equations by the Square Root Property
Additional Exercises 10.1 Form I Solving Quadratic Equations by the Square Root Property Solve the quadratic equation by the square root property. If possible, simplify radicals or rationalize denominators.
AP Calculus 2 Summer Review Packet
AP Calculus Summer Review Packet This review packet is to be completed by all students enrolled in AP Calculus. This packet must be submitted on the Monday of the first full week of class. It will be used
UNIVERSITY OF REGINA Department of Mathematics and Statistics. Calculus I Mathematics 110. Final Exam, Winter 2013 (April 25 th )
UNIVERSITY OF REGINA Department of Mathematics and Statistics Calculus I Mathematics 110 Final Exam, Winter 2013 (April 25 th ) Time: 3 hours Pages: 11 Full Name: Student Number: Instructor: (check one)
AP 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
A. 1 B. 2 C. 4.5 D. 7 E. 8
Calculus & Advanced Topics Spring 2011 1. The derivative of x 2 cos(x) is 2x sin(x) x 2 sin(x) 2x cos(x) x 2 sin(x) 2x sin(x) 2x cos(x) 2. 1 2 4.5 7 8 3. 0 1 6/5 3/2 undefined 4. Find the derivative of
WORKBOOK. MATH 31. CALCULUS AND ANALYTIC GEOMETRY I.
WORKBOOK. MATH 31. CALCULUS AND ANALYTIC GEOMETRY I. DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE Contributors: U. N. Iyer and P. Laul. (Many problems have been directly taken from Single Variable Calculus,
THE USE OF A CALCULATOR, CELL PHONE, OR ANY OTHER ELECTRONIC DEVICE IS NOT PERMITTED IN THIS EXAMINATION.
MATH 110 FINAL EXAM SPRING 2008 FORM A NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBER This examination will be machine processed by the University Testing Service. Use only a number 2 pencil on your scantron.
ARE YOU READY 4 CALCULUS
ARE YOU READY 4 CALCULUS TEACHER NAME: STUDENT NAME: PERIOD: 50 Problems - Calculator allowed for some problems SCORE SHEET STUDENT NAME: Problem Answer Problem Answer 1 26 2 27 3 28 4 29 5 30 6 31 7 32
Guidelines for implicit differentiation
Guidelines for implicit differentiation Given an equation with x s and y s scattered, to differentiate we use implicit differentiation. Some informal guidelines to differentiate an equation containing
MAC 2311 Review
Name: Class: Date: MAC 2311 Review 2.6-2.9 Numeric Response 1. Calculate y. xy 4 +x 2 y =2x +3y 2. Calculate y. cos xy =x 6 y 3. The position function of a particle is given by s =t 3 10.5t 2 2t,t 0 When
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
Log1 Contest Round 2 Theta Geometry
008 009 Log Contest Round Theta Geometry Name: Leave answers in terms of π. Non-integer rational numbers should be given as a reduced fraction. Units are not needed. 4 points each What is the perimeter
Calculus I (Math 241) (In Progress)
Calculus I (Math 241) (In Progress) The following is a collection of Calculus I (Math 241) problems. Students may expect that their final exam is comprised, more or less, of one problem from each section,
Correlation with College Board Advanced Placement Course Descriptions
Correlation with College Board Advanced Placement Course Descriptions The following tables show which sections of Calculus: Concepts and Applications cover each of the topics listed in the 2004 2005 Course
Section MWF 12 1pm SR 117
Math 1431 Section 12485 MWF 12 1pm SR 117 Dr. Melahat Almus almus@math.uh.edu http://www.math.uh.edu/~almus COURSE WEBSITE: http://www.math.uh.edu/~almus/1431_sp16.html Visit my website regularly for announcements
MAT 1320 Study Sheet for the final exam. Format. Topics
MAT 1320 Study Sheet for the final exam August 2015 Format The exam consists of 10 Multiple Choice questions worth 1 point each, and 5 Long Answer questions worth 30 points in total. Please make sure that
(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
, find the value(s) of a and b which make f differentiable at bx 2 + x if x 2 x = 2 or explain why no such values exist.
Math 171 Exam II Summary Sheet and Sample Stuff (NOTE: The questions posed here are not necessarily a guarantee of the type of questions which will be on Exam II. This is a sampling of questions I have
Choose the correct answer: Derivative: 1 If y = csc( ), then =
Choose the correct answer: Derivative: 1 If y = csc( ), then = a b ( ) c ( ) ( ) d ( ) ( ) If y =( + ), then = a ( ) b c d ( ) -- 3 If y =4, then = a - 8 b zero c 4 d 16-4 If ( ) =, then = a - b c 4 d