Test 3 Review. fx ( ) ( x 2) 4/5 at the indicated extremum. y x 2 3x 2. Name: Class: Date: Short Answer

Math2413-TestReview2-Fall2016

Class: Date: Math413-TestReview-Fall016 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value of the derivative (if it exists) of the function

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:

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

AP Calculus AB Unit 3 Assessment

Class: Date: 2013-2014 AP Calculus AB Unit 3 Assessment Multiple Choice Identify the choice that best completes the statement or answers the question. A calculator may NOT be used on this part of the exam.

MATH 2413 TEST ON CHAPTER 4 ANSWER ALL QUESTIONS. TIME 1.5 HRS.

MATH 1 TEST ON CHAPTER ANSWER ALL QUESTIONS. TIME 1. HRS. M1c Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Use the summation formulas to rewrite the

Math 265 Test 3 Review

Name: Class: Date: ID: A Math 265 Test 3 Review. Find the critical number(s), if any, of the function f (x) = e x 2 x. 2. Find the absolute maximum and absolute minimum values, if any, of the function

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.

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

APPM 1350 Exam 2 Fall 2016

APPM 1350 Exam 2 Fall 2016 1. (28 pts, 7 pts each) The following four problems are not related. Be sure to simplify your answers. (a) Let f(x) tan 2 (πx). Find f (1/) (5 pts) f (x) 2π tan(πx) sec 2 (πx)

A.P. Calculus Holiday Packet

A.P. Calculus Holiday Packet Since this is a take-home, I cannot stop you from using calculators but you would be wise to use them sparingly. When you are asked questions about graphs of functions, do

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.

Formulas that must be memorized:

Formulas that must be memorized: Position, Velocity, Acceleration Speed is increasing when v(t) and a(t) have the same signs. Speed is decreasing when v(t) and a(t) have different signs. Section I: Limits

ch 3 applications of differentiation notebook.notebook January 17, 2018 Extrema on an Interval

Extrema on an Interval Extrema, or extreme values, are the minimum and maximum of a function. They are also called absolute minimum and absolute maximum (or global max and global min). Extrema that occur

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 5 of these questions. I reserve the right to change numbers and answers on

Midterm Review. Name: Class: Date: ID: A. Short Answer. 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k.

Name: Class: Date: ID: A Midterm Review Short Answer 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k. a) b) c) 2. Determine the domain and range of each 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

Test 3 Review. y f(a) = f (a)(x a) y = f (a)(x a) + f(a) L(x) = f (a)(x a) + f(a)

MATH 2250 Calculus I Eric Perkerson Test 3 Review Sections Covered: 3.11, 4.1 4.6. Topics Covered: Linearization, Extreme Values, The Mean Value Theorem, Consequences of the Mean Value Theorem, Concavity

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.

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

Final Examination 201-NYA-05 May 18, 2018

. ( points) Evaluate each of the following limits. 3x x + (a) lim x x 3 8 x + sin(5x) (b) lim x sin(x) (c) lim x π/3 + sec x ( (d) x x + 5x ) (e) lim x 5 x lim x 5 + x 6. (3 points) What value of c makes

Limits and Continuity. 2 lim. x x x 3. lim x. lim. sinq. 5. Find the horizontal asymptote (s) of. Summer Packet AP Calculus BC Page 4

Limits and Continuity t+ 1. lim t - t + 4. lim x x x x + - 9-18 x-. lim x 0 4-x- x 4. sinq lim - q q 5. Find the horizontal asymptote (s) of 7x-18 f ( x) = x+ 8 Summer Packet AP Calculus BC Page 4 6. x

Calculus 221 worksheet

Calculus 221 worksheet Graphing A function has a global maximum at some a in its domain if f(x) f(a) for all other x in the domain of f. Global maxima are sometimes also called absolute maxima. A function

Final Exam Review Packet

1 Exam 1 Material Sections A.1, A.2 and A.6 were review material. There will not be specific questions focused on this material but you should know how to: Simplify functions with exponents. Factor quadratics

Final Exam Review Packet

1 Exam 1 Material Sections A.1, A.2 and A.6 were review material. There will not be specific questions focused on this material but you should know how to: Simplify functions with exponents. Factor quadratics

4.1 Analysis of functions I: Increase, decrease and concavity

4.1 Analysis of functions I: Increase, decrease and concavity Definition Let f be defined on an interval and let x 1 and x 2 denote points in that interval. a) f is said to be increasing on the interval

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

Particle Motion Problems

Particle Motion Problems Particle motion problems deal with particles that are moving along the x or y axis. Thus, we are speaking of horizontal or vertical movement. The position, velocity, or acceleration

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

Math 261 Exam 3 - Practice Problems. 1. The graph of f is given below. Answer the following questions. (a) Find the intervals where f is increasing:

Math 261 Exam - Practice Problems 1. The graph of f is given below. Answer the following questions. (a) Find the intervals where f is increasing: ( 6, 4), ( 1,1),(,5),(6, ) (b) Find the intervals where

AB CALCULUS SEMESTER A REVIEW Show all work on separate paper. (b) lim. lim. (f) x a. for each of the following functions: (b) y = 3x 4 x + 2

AB CALCULUS Page 1 of 6 NAME DATE 1. Evaluate each it: AB CALCULUS Show all work on separate paper. x 3 x 9 x 5x + 6 x 0 5x 3sin x x 7 x 3 x 3 5x (d) 5x 3 x +1 x x 4 (e) x x 9 3x 4 6x (f) h 0 sin( π 6

Math 211 Business Calculus TEST 3. Question 1. Section 2.2. Second Derivative Test.

Math 211 Business Calculus TEST 3 Question 1. Section 2.2. Second Derivative Test. p. 1/?? Math 211 Business Calculus TEST 3 Question 1. Section 2.2. Second Derivative Test. Question 2. Section 2.3. Graph

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

Math 112 (Calculus I) Midterm Exam 3 KEY

Math 11 (Calculus I) Midterm Exam KEY Multiple Choice. Fill in the answer to each problem on your computer scored answer sheet. Make sure your name, section and instructor are on that sheet. 1. Which of

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

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

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

Section 5-1 First Derivatives and Graphs

Name Date Class Section 5-1 First Derivatives and Graphs Goal: To use the first derivative to analyze graphs Theorem 1: Increasing and Decreasing Functions For the interval (a,b), if f '( x ) > 0, then

f ', the first derivative of a differentiable function, f. Use the

f, f ', and The graph given to the right is the graph of graph to answer the questions below. f '' Relationships and The Extreme Value Theorem 1. On the interval [0, 8], are there any values where f(x)

Section 3.1 Extreme Values

Math 132 Extreme Values Section 3.1 Section 3.1 Extreme Values Example 1: Given the following is the graph of f(x) Where is the maximum (x-value)? What is the maximum (y-value)? Where is the minimum (x-value)?

Test one Review Cal 2

Name: Class: Date: ID: A Test one Review Cal 2 Short Answer. Write the following expression as a logarithm of a single quantity. lnx 2ln x 2 ˆ 6 2. Write the following expression as a logarithm of a single

Unit #5 Applications of the Derivative Part II Homework Packet

Unit #5 Applications of the Derivative Part II Homework Packet 1. For which of the following functions is the Extreme Value Theorem NOT APPLICABLE on the interval [a, b]? Give a reason for your answer.

What makes f '(x) undefined? (set the denominator = 0)

Chapter 3A Review 1. Find all critical numbers for the function ** Critical numbers find the first derivative and then find what makes f '(x) = 0 or undefined Q: What is the domain of this function (especially

Math 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

Chapters 1 and 2 Test

Class: Date: Chapters 1 and 2 Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. 2r 9 6 Solve the inequality. Graph the solution set. a. r 1 1 2 c. r

Math Exam 03 Review

Math 10350 Exam 03 Review 1. The statement: f(x) is increasing on a < x < b. is the same as: 1a. f (x) is on a < x < b. 2. The statement: f (x) is negative on a < x < b. is the same as: 2a. f(x) is on

MTH Calculus with Analytic Geom I TEST 1

MTH 229-105 Calculus with Analytic Geom I TEST 1 Name Please write your solutions in a clear and precise manner. SHOW your work entirely. (1) Find the equation of a straight line perpendicular to the line

Chapter 3: The Derivative in Graphing and Applications

Chapter 3: The Derivative in Graphing and Applications Summary: The main purpose of this chapter is to use the derivative as a tool to assist in the graphing of functions and for solving optimization problems.

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

MTH4100 Calculus I. Week 8 (Thomas Calculus Sections 4.1 to 4.4) Rainer Klages. School of Mathematical Sciences Queen Mary, University of London

MTH4100 Calculus I Week 8 (Thomas Calculus Sections 4.1 to 4.4) Rainer Klages School of Mathematical Sciences Queen Mary, University of London Autumn 2008 R. Klages (QMUL) MTH4100 Calculus 1 Week 8 1 /

MATH 1314 Test 2 Review

Name: Class: Date: MATH 1314 Test 2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find ( f + g)(x). f ( x) = 2x 2 2x + 7 g ( x) = 4x 2 2x + 9

1. Which one of the following points is a singular point of. f(x) = (x 1) 2/3? f(x) = 3x 3 4x 2 5x + 6? (C)

Math 1120 Calculus Test 3 November 4, 1 Name In the first 10 problems, each part counts 5 points (total 50 points) and the final three problems count 20 points each Multiple choice section Circle the correct

Math 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

Name: Instructor: 1. a b c d e. 15. a b c d e. 2. a b c d e a b c d e. 16. a b c d e a b c d e. 4. a b c d e... 5.

Name: Instructor: Math 155, Practice Final Exam, December The Honor Code is in effect for this examination. All work is to be your own. No calculators. The exam lasts for 2 hours. Be sure that your name

Work 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

c) xy 3 = cos(7x +5y), y 0 = y3 + 7 sin(7x +5y) 3xy sin(7x +5y) d) xe y = sin(xy), y 0 = ey + y cos(xy) x(e y cos(xy)) e) y = x ln(3x + 5), y 0

Some Math 35 review problems With answers 2/6/2005 The following problems are based heavily on problems written by Professor Stephen Greenfield for his Math 35 class in spring 2005. His willingness to

M408 C Fall 2011 Dr. Jeffrey Danciger Exam 2 November 3, Section time (circle one): 11:00am 1:00pm 2:00pm

M408 C Fall 2011 Dr. Jeffrey Danciger Exam 2 November 3, 2011 NAME EID Section time (circle one): 11:00am 1:00pm 2:00pm No books, notes, or calculators. Show all your work. Do NOT open this exam booklet

Math 206 Practice Test 3

Class: Date: Math 06 Practice Test. The function f (x) = x x + 6 satisfies the hypotheses of the Mean Value Theorem on the interval [ 9, 5]. Find all values of c that satisfy the conclusion of the theorem.

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?

Calculus I 5. Applications of differentiation

2301107 Calculus I 5. Applications of differentiation Chapter 5:Applications of differentiation C05-2 Outline 5.1. Extreme values 5.2. Curvature and Inflection point 5.3. Curve sketching 5.4. Related rate

MATH 2413 TEST ON CHAPTER 4 ANSWER ALL QUESTIONS. TIME 1.5 HRS

MATH 1 TEST ON CHAPTER ANSWER ALL QUESTIONS. TIME 1. HRS M1c Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the general solution of the differential

MA 113 Calculus I Fall 2012 Exam 3 13 November Multiple Choice Answers. Question

MA 113 Calculus I Fall 2012 Exam 3 13 November 2012 Name: Section: Last 4 digits of student ID #: This exam has ten multiple choice questions (five points each) and five free response questions (ten points

. CALCULUS AB. Name: Class: Date:

Class: _ Date: _. 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, using

Resources: http://www.calcchat.com/book/calculus-9e/ http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/27.html http://www.calculus.org/ http://cow.math.temple.edu/ http://www.mathsisfun.com/calculus/

APPLICATIONS OF DIFFERENTIATION

4 APPLICATIONS OF DIFFERENTIATION APPLICATIONS OF DIFFERENTIATION The method we used to sketch curves in Section 4.5 was a culmination of much of our study of differential calculus. The graph was the final

CHAPTER 4: APPLICATIONS OF DERIVATIVES

(Exercises for Section 4.1: Extrema) E.4.1 CHAPTER 4: APPLICATIONS OF DERIVATIVES SECTION 4.1: EXTREMA 1) For each part below, find the absolute maximum and minimum values of f on the given interval. Also

Final Exam Review Exercise Set A, Math 1551, Fall 2017

Final Exam Review Exercise Set A, Math 1551, Fall 2017 This review set gives a list of topics that we explored throughout this course, as well as a few practice problems at the end of the document. A complete

Math 142 Week-in-Review #11 (Final Exam Review: All previous sections as well as sections 6.6 and 6.7)

Math 142 Week-in-Review #11 (Final Exam Review: All previous sections as well as sections 6.6 and 6.7) Note: This review is intended to highlight the topics covered on the Final Exam (with emphasis on

(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)

MAXIMA AND MINIMA CHAPTER 7.1 INTRODUCTION 7.2 CONCEPT OF LOCAL MAXIMA AND LOCAL MINIMA

CHAPTER 7 MAXIMA AND MINIMA 7.1 INTRODUCTION The notion of optimizing functions is one of the most important application of calculus used in almost every sphere of life including geometry, business, trade,

Final Exam Study Guide

Final Exam Study Guide Final Exam Coverage: Sections 10.1-10.2, 10.4-10.5, 10.7, 11.2-11.4, 12.1-12.6, 13.1-13.2, 13.4-13.5, and 14.1 Sections/topics NOT on the exam: Sections 10.3 (Continuity, it definition

Final Exam 12/11/ (16 pts) Find derivatives for each of the following: (a) f(x) = 3 1+ x e + e π [Do not simplify your answer.

Math 105 Final Exam 1/11/1 Name Read directions carefully and show all your work. Partial credit will be assigned based upon the correctness, completeness, and clarity of your answers. Correct answers

Math Fall 08 Final Exam Review

Math 173.7 Fall 08 Final Exam Review 1. Graph the function f(x) = x 2 3x by applying a transformation to the graph of a standard function. 2.a. Express the function F(x) = 3 ln(x + 2) in the form F = f

Spring 2015 Sample Final Exam

Math 1151 Spring 2015 Sample Final Exam Final Exam on 4/30/14 Name (Print): Time Limit on Final: 105 Minutes Go on carmen.osu.edu to see where your final exam will be. NOTE: This exam is much longer than

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

MCV4U - Practice Mastery Test #9 & #10

Name: Class: Date: ID: A MCV4U - Practice Mastery Test #9 & #10 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. x + 2 is a factor of i) x 3 3x 2 + 6x 8

Applications of Differentiation

Applications of Differentiation Definitions. A function f has an absolute maximum (or global maximum) at c if for all x in the domain D of f, f(c) f(x). The number f(c) is called the maximum value of f

Review for the Final Exam

Math 171 Review for the Final Exam 1 Find the limits (4 points each) (a) lim 4x 2 3; x x (b) lim ( x 2 x x 1 )x ; (c) lim( 1 1 ); x 1 ln x x 1 sin (x 2) (d) lim x 2 x 2 4 Solutions (a) The limit lim 4x

AP CALCULUS (AB) Outline Chapter 4 Overview. 2) Recovering a function from its derivatives and a single point;

AP CALCULUS (AB) Outline Chapter 4 Overview NAME Date Objectives of Chapter 4 1) Using the derivative to determine extreme values of a function and the general shape of a function s graph (including where

Part A: Short Answer Questions

Math 111 Practice Exam Your Grade: Fall 2015 Total Marks: 160 Instructor: Telyn Kusalik Time: 180 minutes Name: Part A: Short Answer Questions Answer each question in the blank provided. 1. If a city grows

Test # 3 Review. È 3. Compare the graph of n 1 ÎÍ. Name: Class: Date: Short Answer. 1. Find the standard form of the quadratic function shown below:

Name: Class: Date: ID: A Test # 3 Review Short Answer 1. Find the standard form of the quadratic function shown below: 2. Compare the graph of m ( x) 9( x 7) 2 5 with m ( x) x 2. È 3. Compare the graph

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 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

MA 137 Calculus 1 with Life Science Applications Monotonicity and Concavity (Section 5.2) Extrema, Inflection Points, and Graphing (Section 5.

MA 137 Calculus 1 with Life Science Applications Monotonicity and Concavity (Section 52) Extrema, Inflection Points, and Graphing (Section 53) Alberto Corso albertocorso@ukyedu Department of Mathematics

MAT 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.........................

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

PERT Practice Test #2

Class: Date: PERT Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. Ê 1. What is the quotient of 6y 6 9y 4 + 12y 2 ˆ Ê 3y 2 ˆ? a. 2y 4 + 3y

Calculus I Announcements

Slide 1 Calculus I Announcements Read sections 4.2,4.3,4.4,4.1 and 5.3 Do the homework from sections 4.2,4.3,4.4,4.1 and 5.3 Exam 3 is Thursday, November 12th See inside for a possible exam question. Slide

MATH 1241 FINAL EXAM FALL 2012 Part I, No Calculators Allowed

MATH 11 FINAL EXAM FALL 01 Part I, No Calculators Allowed 1. Evaluate the limit: lim x x x + x 1. (a) 0 (b) 0.5 0.5 1 Does not exist. Which of the following is the derivative of g(x) = x cos(3x + 1)? (a)

1. Write the definition of continuity; i.e. what does it mean to say f(x) is continuous at x = a?

Review Worksheet Math 251, Winter 15, Gedeon 1. Write the definition of continuity; i.e. what does it mean to say f(x) is continuous at x = a? 2. Is the following function continuous at x = 2? Use limits

Learning Target: I can sketch the graphs of rational functions without a calculator. a. Determine the equation(s) of the asymptotes.

Learning Target: I can sketch the graphs of rational functions without a calculator Consider the graph of y= f(x), where f(x) = 3x 3 (x+2) 2 a. Determine the equation(s) of the asymptotes. b. Find the

Assessment Exemplars: Polynomials, Radical and Rational Functions & Equations

Class: Date: Assessment Exemplars: Polynomials, Radical and Rational Functions & Equations 1 Express the following polynomial function in factored form: P( x) = 10x 3 + x 2 52x + 20 2 SE: Express the following

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

Math 180, Exam 2, Practice Fall 2009 Problem 1 Solution. f(x) = arcsin(2x + 1) = sin 1 (3x + 1), lnx

Math 80, Exam, Practice Fall 009 Problem Solution. Differentiate the functions: (do not simplify) f(x) = x ln(x + ), f(x) = xe x f(x) = arcsin(x + ) = sin (3x + ), f(x) = e3x lnx Solution: For the first

(2) Let f(x) = a 2 x if x<2, 4 2x 2 ifx 2. (b) Find the lim f(x). (c) Find all values of a that make f continuous at 2. Justify your answer.

(1) Let f(x) = x x 2 9. (a) Find the domain of f. (b) Write an equation for each vertical asymptote of the graph of f. (c) Write an equation for each horizontal asymptote of the graph of f. (d) Is f odd,

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Math 1325 Ch.12 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 extremum for the function. 1)

Suppose that f is continuous on [a, b] and differentiable on (a, b). Then

Lectures 1/18 Derivatives and Graphs When we have a picture of the graph of a function f(x), we can make a picture of the derivative f (x) using the slopes of the tangents to the graph of f. In this section

1.18 Multiple Choice Questions on Limits

24 The AP CALCULUS PROBLEM BOOK 3x 4 2x + 33. lim x 7x 8x 5 =.8 Multiple Choice Questions on Limits A) B) C) 0 D) 3 7 E) 3 8 34. lim x 0 x = A) B) C) 0 D) E) does not exist 9x 2 35. lim x /3 3x = A) B)

2. Find the intervals where function is increasing and decreasing. Then find all relative extrema.

MATH 1071Q Exam #2 Review Fall 2011 1. Find the elasticity at the given points and determine whether demand is inelastic, elastic, or unit elastic. Explain the significance of your answer. (a) x = 10 2p

AP Calculus AB. Chapter IV Lesson B. Curve Sketching

AP Calculus AB Chapter IV Lesson B Curve Sketching local maxima Absolute maximum F I A B E G C J Absolute H K minimum D local minima Summary of trip along curve critical points occur where the derivative