The Review has 16 questions. Simplify all answers, include all units when appropriate.


 Ralf Foster
 8 months ago
 Views:
Transcription
1 Math 1 Midterm Eam Review with Answers Name Date The Review has 16 questions. Simplify all answers, include all units when appropriate. 1. [Sec. 1.] Solve the following problems. a. A company s profit increased linearly from $6 million at the end of year 1 to $1 million at the end of year. i. Use the two data points (year, profit) coordinates as (1,6) and (,1), to find the linear relationship y m b between years and y profit. ii. Find the company s profit at the end of 5 years. iii. Predict the year when the profit will be 0 million. b. A Telephone company charges a client $.95 for a service of 00 minutes of long distance, and charges another client $.95 for service of 00 minutes of long distance calls. i. Use the data points (minutes, charge) coordinates to find the linear relationship y=m+b between number of minutes and y dollars charged. ii. Find the company s charge for 100 minutes of long distance service. iii. Find the number of minutes of service for a client that was charged $ [Sec. 1.] Given the function a. f ( ) b. f ( ) 9 i. Write the domain in set notation. ii. Find the and y intercepts if any, and write as order pair. iii. Evaluate f () iv. Graph the function, label three points. Page 1 of 11
2 Math 1 Midterm Eam Review with Answers. [Sec. 1.] a) A group of students want to raise money to attend an international conference; the students want to build canoes during the summer in an old warehouse. The rental of the warehouse is $1500 for the summer, and the materials needed to build one canoe cost $15. The canoes can be sold for $75 apiece. i. Write the equation for the Profit. ii. How many canoes must the students sell to break even? iii. How many canoes must the students sell to make a profit of at least $1000? b) A manufacturer can produce bookcases at a cost of $80 apiece. Sales figures indicate that if the bookcases are sold for dollars apiece, approimately150 bookcases will be sold each month. i. Epress the manufacturer s monthly profit as a function of selling price. ii. Find the price where the manufacturer breaks even. iii. Find the price to maimize the profit. Page of 11
3 Math 1 Midterm Eam Review with Answers. [Sec. 1.1] If, a) i. Find f ( ) and g( ) iv. ii. Determine the domain of the function and, write in set notation. v. iii. Find the composition f ( g( )), simplify if possible. iv. Find the composition g ( f ( )), simplify if possible. b. If and i. Find ii. Determine the domain of the function and, write in set notation. iii. Find the composition f ( g( )), simplify if possible. iv. Find the composition g ( f ( )), simplify if possible. 5. [Sec1.6] a. Graph f ( ) 8 Label four points. Page of 11
4 Math 1 Midterm Eam Review with Answers ( ) ( ) EXIST / NOT EXIST (Circle One) b. Graph f ( ) Label four points. 7 ( ) ( ) ( ) ( ) EXIST / NOT EXIST (Circle One) Page of 11
5 Math 1 Midterm Eam Review with Answers 6. [Sec. 1.5] Find the it or if it does not eist. If it is infinite indicate whether it is + or  a. Lim b. Lim ( ) c. Lim 0 d. Lim 16 5 e. Lim 1 f. Lim [Sec.1] For the given function use the definition of the derivative to find f '( ), Show all the required steps. a. f ( ) b. f ( ) 7 8. [Sec..] Find the derivative, f '( ) a. f ( ) 5 6 b. f ( ) c. f ( ) d. f ( ) 5 9. [Sec.] Find the derivative of the function using the product rule of derivatives, f (), simplify. a. f ( ) ( )( 1) b. f ( ) ( )( ) Page 5 of 11
6 Math 1 Midterm Eam Review with Answers 10. [Sec.] Find the derivative, y, simplify if possible. a. 1 y b. 1 y [Sec.] Find the derivative, f (), simplify if possible. 1 a. f ( ) b. f ( ) 1. [Sec..] Evaluate the second derivative of the given function. a. f ''(1) for the function f ( ) 5 b. f ''(1) for the function f ( ) 1. [Sec.5] Solve the following applied problems, interpret results a. A steel mill finds that its cost function is C ( ) dollars, where is the daily production of steel (in tons). i. Find the Marginal Cost Function. ii. iii. Find the marginal cost when 6 tons of steel are produced. Interpret the results. b. The manufacturer determines that the profit P (in dollars) derived from selling units is given by P( ) i. Find the Marginal Profit Function. ii. Find the marginal profit for a production level of 5 units. iii. Interpret the results. Page 6 of 11
7 Math 1 Midterm Eam Review with Answers 1. [Sec..] A company s profit function is P ( ) a. Find the Relative Rate of Change of the Profit Function. b. Find the Marginal Profit Function. c. Evaluate the Relative Rate of Change of the Profit Function at = [Sec..] Solve the following applied problems, interpret results. d. The number of weeds (in hundreds) n in lawn weeks after a weed killer was applied is given by n ( ). Find the rate of change in the number of weeds in the lawn at the end of the second week. e. The velocity of an object in meters per second is v ( t) 1 1 9t, 0 t. Find the acceleration of the subject when t =.15 sec. 16. [Sec.1 &.] For the following functions: f. The function, f ( ) 6 9 1, g. The function, f ( ) 0 1 i. Make a sign diagram of f ' ( ) ii. Identify the relative etreme points and inflection points iii. Sketch the graph Page 7 of 11
8 Math 1 Midterm Eam Review with Answers Midterm Review Math 1 Answers: #1 a. i. y = + ii. y = $ million the end of the 7 th year b. i. y = or y ii. y = $ 1.95 iii. minutes # a. i. ii. intercept: None & yintercept: iii. f () = iv. Graph curve with label on any of three points (, ); (1, ); ) b. i. {  } ii. intercept: iii. f () = iv. Graph curve with label on any of three points: (0, 1); (, ); (,) # a. i. P ( ) ii. 10 canoes iii. 17 canoes b. i. P ( ) price of $80 and $150 per unit iii. price of $115 per unit # a. i. f() = 1; f(() = ; g() = 9 ii. Domain f() {R}; g() {R} iii. f(g()) = 9 iv. g(f()) = 9 b. i. f() = Undefined; f(0) = Undefined; g() = 5 1 ii. Domain f() ; ; g(){r} iii. f ( g( )) 6 iv. g ( f ( )) 1 1 Page 8 of 11
9 Math 1 Midterm Eam Review with Answers #5 a. Piecewise lines with points (0, 8), (1, 7), (, 6), (, 5); stop at the point (, 5) And line with points (, ), (, 5), (5, 7), (6, 9); (, 5) do not eist. f( ) 5 f( ) f( ) do not eist. b. Piecewise lines with points (0, 7), (1, 5), (, ), (, 1), (, 1); stop at the point (, 1) and line with points (, ), (5, ), (6, ); (, 1) do not eist. f( ) 1 f( ) f( ) do not eist. #6 a. 0 b. d. Does not eist e. 0 c. #7 a. f () = 8 b. f () =  #8 a. f () = b. f () = c. f () = 5  d. f () = 10 5 #9 a. f () = b. f () = #10 a. y = ( 1) 10 b. y = ( 5) 7 Page 9 of 11
10 Math 1 Midterm Eam Review with Answers (1 ) #11 a. f () = ( ) b. f () = ( ) #1 a. f (1) = 5 b. f (1) = 9 #1 a. i. MC() = ii. MC(6) = 87.5 iii. The cost is increasing by $87.5 for every ton of steel when the mill is producing 6 tons of steel. b. i. MP() = ii. MP(5) = 10. iii. The profit is increasing at $10. per unit when manufactures produces 5 units. #1 a. RRCP() = b. MP () 1 c. RRCP(50) = #15. a. n ()=, the rate of change is decreasing hundred units per week. b. a(.15) = .7, the object is decreasing in acceleration of.7 m/sec.. #16. a. i) ii) Etreme Points (1,) Relative Ma (,1) Relative Min. Inflection Point (, 1) b. i) ii) Etreme Points (5,87) Rel Minimum (0,1) Rel. Maimum (, ) Rel. Minimum. Inflection points (1.0817, 8.97), (.08, 8.8) Page 10 of 11
11 Math 1 Midterm Eam Review with Answers Page 11 of 11
5, 0. Math 112 Fall 2017 Midterm 1 Review Problems Page Which one of the following points lies on the graph of the function f ( x) (A) (C) (B)
Math Fall 7 Midterm Review Problems Page. Which one of the following points lies on the graph of the function f ( ) 5?, 5, (C) 5,,. Determine the domain of (C),,,, (E),, g. 5. Determine the domain of h
More informationMath Want to have fun with chapter 4? Find the derivative. 1) y = 5x2e3x. 2) y = 2xex  2ex. 3) y = (x22x + 3) ex. 9ex 4) y = 2ex + 1
Math 160  Want to have fun with chapter 4? Name Find the derivative. 1) y = 52e3 2) y = 2e  2e 3) y = (22 + 3) e 9e 4) y = 2e + 1 5) y = e  + 1 e e 6) y = 32 + 7 7) y = e31 5 Use calculus to find
More informationOptimization II. Now lets look at a few examples of the applications of extrema.
Optimization II So far you have learned how to find the relative and absolute etrema of a function. This is an important concept because of how it can be applied to real life situations. In many situations
More informationPrinted Name: Section #: Instructor:
Printed Name: Section #: Instructor: Please do not ask questions during this eam. If you consider a question to be ambiguous, state your assumptions in the margin and do the best you can to provide the
More information3 2 (C) 1 (D) 2 (E) 2. Math 112 Fall 2017 Midterm 2 Review Problems Page 1. Let. . Use these functions to answer the next two questions.
Math Fall 07 Midterm Review Problems Page Let f and g. Evaluate and simplify f g. Use these functions to answer the net two questions.. (B) (E) None of these f g. Evaluate and simplify. (B) (E). Consider
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine from the graph whether the function has an absolute etreme values on the interval
More informationGraphing and Optimization
BARNMC_33886.QXD //7 :7 Page 74 Graphing and Optimization CHAPTER  First Derivative and Graphs  Second Derivative and Graphs 3 L Hôpital s Rule 4 CurveSketching Techniques  Absolute Maima and Minima
More informationChapter 1. Functions, Graphs, and Limits
Chapter 1 Functions, Graphs, and Limits MA1103 Business Mathematics I Semester I Year 016/017 SBM International Class Lecturer: Dr. Rinovia Simanjuntak 1.1 Functions Function A function is a rule that
More informationMath 026 Review Exercises for the Final Exam
Math 06 Review Eercises for the Final Eam The following are review eercises for the Math 06 final eam. These eercises are provided for you to practice or test yourself for readiness for the final eam.
More informationSECTION 3.1: Quadratic Functions
SECTION 3.: Quadratic Functions Objectives Graph and Analyze Quadratic Functions in Standard and Verte Form Identify the Verte, Ais of Symmetry, and Intercepts of a Quadratic Function Find the Maimum or
More informationK. Function Analysis. ). This is commonly called the first derivative test. f ( x) is concave down for values of k such that f " ( k) < 0.
K. Function Analysis What you are finding: You have a function f ( ). You want to find intervals where f ( ) is increasing and decreasing, concave up and concave down. You also want to find values of where
More 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)(312) = 6 3 (  4)(  6) Thus, the critical values are = 0, = 4, and = 6. Now we construct the sign chart
More informationM112 Short Course In Calculus V. J. Motto Spring 2013 Applications of Derivatives Worksheet
M11 Short Course In Calculus V. J. Motto Spring 01 Applications of Derivatives Worksheet 1. A tomato is thrown from the top of a tomato cart its distance from the ground in feet is modeled by the equation
More informationMathematics 2201 Midterm Exam Review
Mathematics 0 Midterm Eam Review Chapter : Radicals Chapter : Quadratic Functions Chapter 7: Quadratic Equations. Evaluate: 8 (A) (B) (C) (D). Epress as an entire radical. (A) (B) (C) (D). What is the
More informationFLC Ch 13 (except 1.4, 3.1, 3.2) Sec 1.2: Graphs of Equations in Two Variables; Intercepts, Symmetry
Math 370 Precalculus [Note to Student: Read/Review Sec 1.1: The Distance and Midpoint Formulas] Sec 1.2: Graphs of Equations in Two Variables; Intercepts, Symmetry Defns A graph is said to be symmetric
More information7.1 Functions of Two or More Variables
Hartfield MATH 2040 Unit 5 Page 1 7.1 Functions of Two or More Variables Definition: A function f of two variables is a rule such that each ordered pair (, y) in the domain of f corresponds to eactly one
More informationDescribe in words how the graph of each function below would differ from the graph of f (x).
MATH 111 Exam # Review (4.14.4, 6.1, 6.) Describe in words how the graph of each function below would differ from the graph of f (. 1. f ( x 7). f (. f ( 5 4. f ( 5. 7 f ( 6. f ( x ) 9 7. f ( 8. f ( 9.
More informatione) Find the average revenue when 100 units are made and sold.
Math 142 Week in Review Set of Problems Week 7 1) Find the derivative, y ', if a) y=x 5 x 3/2 e 4 b) y= 1 5 x 4 c) y=7x 2 0.5 5 x 2 d) y=x 2 1.5 x 10 x e) y= x7 5x 5 2 x 4 2) The pricedemand function
More informationFind the volume of the solid generated by revolving the shaded region about the given axis. Use the disc/washer method 1) About the xaxis
Final eam practice for Math 6 Disclaimer: The actual eam is different Find the volume of the solid generated b revolving the shaded region about the given ais. Use the disc/washer method ) About the ais
More informationUniversidad Carlos III de Madrid
Universidad Carlos III de Madrid Eercise 1 2 3 4 5 6 Total Points Department of Economics Mathematics I Final Eam January 22nd 2018 LAST NAME: Eam time: 2 hours. FIRST NAME: ID: DEGREE: GROUP: 1 (1) Consider
More informationOnline Math 1314 Final Exam Review
Online Math 1314 Final Exam Review 1. The following table of values gives a company s annual profits in millions of dollars. Rescale the data so that the year 2003 corresponds to x = 0. Year 2003 2004
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Spring 0 Math 08 Eam Preparation Ch Dressler Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the quadratic equation b the square root propert.
More informationHW 5 Date: Name Use Scantron 882E to transfer the answers. Graph. 1) y = 5x
HW 5 Date: Name Use Scantron 88E to transfer the answers. Graph. ) = 5 ) A)             C) D)             Differentiate. ) f() = e8 A) e8 8e8 C) 8e D) 8 e 8 ) 3) = e9/ A) 9 e 9/
More informationReview for Final Review
Topics Review for Final Review 1. Functions and equations and graphing: linear, absolute value, quadratic, polynomials, rational (first 1/3 of semester) 2. Simple Interest, compounded interest, and continuously
More informationChapter 7: Quadratic Equations
Chapter 7: Quadratic Equations Section 7.1: Solving Quadratic Equations by Factoring Terminology: Quadratic Equation: A polynomial equation of the second degree; the standard form of a basic equation is
More informationMath 102 Final Exam Review
. Compute f ( + h) f () h Math 0 Final Eam Review for each of the following functions. Simplify your answers. f () 4 + 5 f ( ) f () + f ( ). Find the domain of each of the following functions. f( ) g (
More informationMathematics 2201 Midterm Exam Review
Mathematics 0 Midterm Eam Review Chapter : Radicals Chapter 6: Quadratic Functions Chapter 7: Quadratic Equations. Evaluate: 6 8 (A) (B) (C) (D). Epress as an entire radical. (A) (B) (C) (D). What is the
More informationBARUCH COLLEGE MATH 2205 FALL 2007
BARUCH COLLEGE MATH 05 FALL 007 MANUAL FOR THE UNIFORM FINAL EXAMINATION Joseph Collison, Warren Gordon, Walter Wang, April Allen Materowski, Sarah Harne The final eamination for Math 05 will consist of
More informationCollege Algebra. George Voutsadakis 1. LSSU Math 111. Lake Superior State University. 1 Mathematics and Computer Science
College Algebra George Voutsadakis 1 1 Mathematics and Computer Science Lake Superior State University LSSU Math 111 George Voutsadakis (LSSU) College Algebra December 2014 1 / 74 Outline 1 Additional
More informationPrecalculus Fall Final Exam REVIEW Evaluate the function at the specified value(s) of the independent variable and simplify.
Precalculus Fall Final Eam EVIEW 016017 1. Model the following situation with a linear equation in slopeintercept form. 4 The gas tank in a truck holds 15 gallons. The truck uses gallon per mile. 7.
More informationMath 1050 REVIEW for Exam 1. Use synthetic division to find the quotient and the remainder. 1) x3  x2 + 6 is divided by x + 2
Math 0 REVIEW for Eam 1 Use snthetic division to find the quotient and the remainder. 1) 32 + 6 is divided b + 2 Use snthetic division to determine whether  c is a factor of the given polnomial. 2) 332
More informationMount Olive High School Summer Assignment for
Name: Mount Olive High School Summer Assignment for Precalculus CP Students who may wish to complete this packet: Anyone entering: Precalculus CP in September 2017 Directions: Skills Review It is necessary
More informationQUESTIONS 146 REVIEW THE OBJECTIVES OF CHAPTER 2.
MAT 101 Course Review Questions Valid for Fall 2014, Spring 2015 and Summer 2015 MIDTERM EXAM FINAL EXAM Questions 186 are covered on the Midterm. There are 25 questions on the midterm, all multiple choice,
More information4. (6 points) Express the domain of the following function in interval notation:
Eam 1A L. Ballou Name Math 131 Calculus I September 1, 016 NO Calculator Allowed BOX YOUR ANSWER! Show all work for full credit! 1. (4 points) Write an equation of a line with yintercept 4 and intercept
More informationFind the integral. 12) 15)
Find the location of the indicated absolute etremum within the specified domain. ) Minimum of f() = / /; [0, ] 8) Maimum h() ) Minimum of f() =  +  ; [, ] ) Minimum of f() = ( + )/; [, ] ) Maimum
More information26 Questions EOC Review #1 EOC REVIEW
Name Period 6 Questions EOC Review # EOC REVIEW Solve each: Give the BEST Answer. You may use a graphing calculator.. Which quadrant contains the verte of the following: f ( ) 8 st nd rd d. 4th. What type
More informationName: Period: SM Starter on Reading Quadratic Graph. This graph and equation represent the path of an object being thrown.
SM Name: Period: 7.5 Starter on Reading Quadratic Graph This graph and equation represent the path of an object being thrown. 1. What is the ais measuring?. What is the yais measuring? 3. What are the
More informationAlgebra 1 Midterm Review
Name Block Algebra 1 Midterm Review MULTIPLE CHOICE Write the letter for the correct answer at the left of each question. 1. Solve: A. 8 C. 2. Solve: A. 43 C. 42 3. Solve the compound inequality and graph
More informationChapters 8 & 9 Review for Final
Math 203  Intermediate Algebra Professor Valdez Chapters 8 & 9 Review for Final SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the formula for
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 information2.1 Intercepts; Symmetry; Graphing Key Equations
Ch. Graphs.1 Intercepts; Smmetr; Graphing Ke Equations 1 Find Intercepts from an Equation MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. List the
More informationM122 College Algebra Review for Final Exam
M1 College Algebra Review for Final Eam Revised Fall 017 for College Algebra  Beecher All answers should include our work (this could be a written eplanation of the result, a graph with the relevant feature
More informationNTI Work Day #1 Math. 4. What is the slope of the line that passes through the origin and (3, 2)? a. 3 2 b. 2 3 c. 0 d. 2 3 e.
NTI Work Day #1 Math 1. 2 0 + 2 3 2 2 =? a. 4 b. 6 1 4 c. 7 d. 8 3 4 e. 9 3 4 2. The figure below is a graph of which of the following equations? a. y = 3x + 5 b. y = 2x + 2 c. y = 3 2 x 2 d. y = 2 3
More informationName: Class: Date: ID: A
Name: Class: Date: 8th Grade Advanced Topic III, Linear Equations and Systems of Linear Equations, MA.8.A.1.1, MA.8.1.1.2, MA.8.A.1.3, *MA.8.A.1.4, MA.8.A.1.5, MA.8.A.1.6 Multiple Choice Identify the choice
More informationMath 101: Final Exam Review Sheet
Math 101: Final Exam Review Sheet (Answers are at the end.) Exam Coverage: Everything we learned in the course. Exam Date: Friday, December 11, 2015 Exam Time: 10:30 am 12:30 pm (Arrive at least 10 minutes
More informationGrade 11 Mathematics Page 1 of 6 Final Exam Review (updated 2013)
Grade Mathematics Page of Final Eam Review (updated 0) REVIEW CHAPTER Algebraic Tools for Operating With Functions. Simplify ( 9 ) (7 ).. Epand and simplify. ( ) ( ) ( ) ( 0 )( ). Simplify each of the
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 informationSOLUTIONS 1 (27) 2 (18) 3 (18) 4 (15) 5 (22) TOTAL (100) PROBLEM NUMBER SCORE MIDTERM 2. Form A. Recitation Instructor : Recitation Time :
Math 5 March 8, 206 Form A Page of 8 Name : OSU Name.# : Lecturer:: Recitation Instructor : SOLUTIONS Recitation Time : SHOW ALL WORK in problems, 2, and 3. Incorrect answers with work shown may receive
More informationSect 2.4 Linear Functions
36 Sect 2.4 Linear Functions Objective 1: Graphing Linear Functions Definition A linear function is a function in the form y = f(x) = mx + b where m and b are real numbers. If m 0, then the domain and
More informationChapter 1: Linear Equations and Functions
Chapter : Linear Equations and Functions Eercise.. 7 8+ 7+ 7 8 8+ + 7 8. + 8 8( + ) + 8 8+ 8 8 8 8 7 0 0. 8( ) ( ) 8 8 8 8 + 0 8 8 0 7. ( ) 8. 8. ( 7) ( + ) + + +. 7 7 7 7 7 7 ( ). 8 8 0 0 7. + + + 8 +
More informationLecture 6: Sections 2.2 and 2.3 Polynomial Functions, Quadratic Models
L61 Lecture 6: Sections 2.2 and 2.3 Polynomial Functions, Quadratic Models Polynomial Functions Def. A polynomial function of degree n is a function of the form f(x) = a n x n + a n 1 x n 1 +... + a 1
More informationMAT09X FINAL EXAM REVIEW C) 86 D) ) A) 14r + 37 B) 6r + 30 C) 6r + 45 D) 6r ) 3 C) 1 D) 3 2
MAT09X FINAL EXAM REVIEW NAME MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question. Perform the indicated operations ) ( ) ) 6 86 Evaluate the epression,
More information5. 2. The solution set is 7 6 i, 7 x. Since b = 20, add
Chapter : Quadratic Equations and Functions Chapter Review Eercises... 5 8 6 8 The solution set is 8, 8. 5 5 5 5 5 5 The solution set is 5,5. Rationalize the denominator. 6 The solution set is. 8 8 9 6
More informationMHF 4U Unit 2 Rational Functions Outline
MHF 4U Unit Rational Functions Outline Day 1 Lesson Title Specific Epectations Rational Functions and Their Essential Characteristics C.1,.,.3 (Lesson Included) Rational Functions and Their Essential Characteristics
More informationMat 210 Business Calculus Final Exam Review Spring Final on April 28 in COOR HALL 199 at 7:30 AM
f ( Mat Business Calculus Final Eam Review Spring Final on April 8 in COOR HALL 99 at 7: AM. A: Find the limit (if it eists) as indicated. Justify your answer. 8 a) lim (Ans: 6) b) lim (Ans: ) c) lim
More informationSALES AND MARKETING Department MATHEMATICS. 2nd Semester. Bivariate statistics. Tutorials and exercises
SALES AND MARKETING Department MATHEMATICS 2nd Semester Bivariate statistics Tutorials and exercises Online document: http://jffduttc.weebly.com section DUT Maths S2. IUT de SaintEtienne Département
More informationTo find the absolute extrema on a continuous function f defined over a closed interval,
Question 4: How do you find the absolute etrema of a function? The absolute etrema of a function is the highest or lowest point over which a function is defined. In general, a function may or may not have
More informationTHE 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.
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 informationParticle 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
More information26 Analyzing Functions with Successive Differences
Graph each set of ordered pairs. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function. 1. ( 2, 8), ( 1, 5), (0, 2), (1, 1) linear 3. ( 3, 8),
More information12.1 The Extrema of a Function
. The Etrema of a Function Question : What is the difference between a relative etremum and an absolute etremum? Question : What is a critical point of a function? Question : How do you find the relative
More informationLesson 25 Solving Linear Trigonometric Equations
Lesson 25 Solving Linear Trigonometric Equations IB Math HL  Santowski EXPLAIN the difference between the following 2 equations: (a) Solve sin(x) = 0.75 (b) Solve sin 1 (0.75) = x Now, use you calculator
More informationAP Calculus AB Summer Review Packet
AP Calculus AB Summer Review Packet 016017 Mr. Le jtle1@gmail.com Leuzinger High School Rm. G0 The following packet is designed to help you review topics that are important to your SUCCESS in AP Calculus.
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. 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 information5. Determine the discriminant for each and describe the nature of the roots.
4. Quadratic Equations Notes Day 1 1. Solve by factoring: a. 3 16 1 b. 3 c. 8 0 d. 9 18 0. Quadratic Formula: The roots of a quadratic equation of the form A + B + C = 0 with a 0 are given by the following
More informationMarginal Propensity to Consume/Save
Marginal Propensity to Consume/Save The marginal propensity to consume is the increase (or decrease) in consumption that an economy experiences when income increases (or decreases). The marginal propensity
More information1. Find all relations which are functions. 2. Find all one to one functions.
1 PRACTICE PROBLEMS FOR FINAL (1) Function or not (vertical line test or y = x expression) 1. Find all relations which are functions. (A) x + y = (C) y = x (B) y = x 1 x+ (D) y = x 5 x () One to one function
More informationA.P. Calculus Summer Assignment
A.P. Calculus Summer Assignment This assignment is due the first day of class at the beginning of the class. It will be graded and counts as your first test grade. This packet contains eight sections and
More informationUnit 4: Rules of Differentiation
Unit : Rules of Differentiation DAY TOPIC ASSIGNMENT Power Rule p. Power Rule Again p. Even More Power Rule p. 5 QUIZ 5 Rates of Change p. 67 6 Rates of Change p. 89 7 QUIZ 8 Product Rule p. 09 Quotient
More informationCHAPTER 1 Functions and Their Graphs
PART I CHAPTER Functions and Their Graphs Section. Lines in the Plane....................... Section. Functions........................... Section. Graphs of Functions..................... Section. Shifting,
More informationLinear Models Practice EOC Practice Standard ACED.2
Linear Models Practice EOC Practice Standard ACED.2 6. An ice cream shop charges $1 for a cone and $2 per scoop of ice cream. Which equation models the cost of an ice cream cone, y, with x scoops of ice
More informationMA 223 PRACTICE QUESTIONS FOR THE FINAL 3/97 A. B. C. D. E.
MA 223 PRACTICE QUESTIONS FOR THE FINAL 3/97 1. Which of the lines shown has slope 1/3? 2. Suppose 280 tons of corn were harvested in 5 days and 940 tons in 20 days. If the relationship between tons T
More informationTO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet.
MATH TEST 4 REVIEW TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet. PART NONCALCULATOR DIRECTIONS: The problems
More informationChapter 3. Exponential and Logarithmic Functions. Selected Applications
Chapter 3 Eponential and Logarithmic Functions 3. Eponential Functions and Their Graphs 3.2 Logarithmic Functions and Their Graphs 3.3 Properties of Logarithms 3.4 Solving Eponential and Logarithmic Equations
More informationALGEBRA I ENDOFCOURSE EXAM: PRACTICE TEST
Page 1 ALGEBRA I ENDOFCOURSE EXAM: PRACTICE TEST 1. Order the following numbers from least to greatest:, 6, 8.7 10 0, 19 b. 19,, 8.7 100, 6 6, 8.7 10 0,, 19 c. d. 8.7 10 0,, 19, 6, 6, 19, 8.7 100. If
More informationMATH 150/GRACEY EXAM 2 PRACTICE/CHAPTER 2. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MATH 0/GRACEY EXAM PRACTICE/CHAPTER Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated derivative. ) Find if = 8 sin. A) = 8
More informationAlgebra 1 EndofCourse Assessment Practice Test with Solutions
Algebra 1 EndofCourse Assessment Practice Test with Solutions For Multiple Choice Items, circle the correct response. For Fillin Response Items, write your answer in the box provided, placing one digit
More informationExam 2 Review Math1324. Solve the system of two equations in two variables. 1) 8x + 7y = 36 3x  4y = 13 A) (1, 5) B) (0, 5) C) No solution D) (1, 4)
Eam Review Math3 Solve the sstem of two equations in two variables. ) + 7 = 3 3  = 3 (, 5) B) (0, 5) C) No solution D) (, ) ) 3 + 5 = + 30 = , B) No solution 3 C)  5 3 + 3, for an real number D) 3,
More informationThe speed the speed of light is 30,000,000,000 m/s. Write this number in scientific notation.
Chapter 1 Section 1.1 Scientific Notation Powers of Ten 1 1 1.1.1.1.1 Standard Scientific Notation N n where 1 N and n is an integers Eamples of numbers in scientific notation. 8.17 11 Using Scientific
More informationName Class Date. Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Travels in Air. Distance (miles) Time (seconds)
Practice  Rate of Change and Slope Find the slope of each line.... O O O Find the slope of the line that passes through each pair of points.. (, ), (7, 5) 5. (8, ), (, ). (, 5), (, 7) 7. (, 7), (, )
More information3.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS
Section. Logarithmic Functions and Their Graphs 7. LOGARITHMIC FUNCTIONS AND THEIR GRAPHS Ariel Skelle/Corbis What ou should learn Recognize and evaluate logarithmic functions with base a. Graph logarithmic
More informationMath 113 Final Exam Practice Problem Solutions. f(x) = ln x x. lim. lim. x x = lim. = lim 2
Math 3 Final Eam Practice Problem Solutions. What are the domain and range of the function f() = ln? Answer: is only defined for, and ln is only defined for >. Hence, the domain of the function is >. Notice
More informationChiang/Wainwright: Fundamental Methods of Mathematical Economics
Chiang/Wainwright: Fundamental Methods of Mathematical Economics CHAPTER 9 EXERCISE 9.. Find the stationary values of the following (check whether they are relative maima or minima or inflection points),
More information1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined?
Graphing Linear Equations Chapter Questions 1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined? 3. Why do we need to be careful about
More informationUNIVERSITY OF KWAZULU NATAL
UNIVERSITY OF KWAZULU NATAL EXAMINATIONS: June 006 Solutions Subject, course and code: Mathematics 34 MATH34P Multiple Choice Answers. B. B 3. E 4. E 5. C 6. A 7. A 8. C 9. A 0. D. C. A 3. D 4. E 5. B
More informationNO CALCULATORS: 1. Find A) 1 B) 0 C) D) 2. Find the points of discontinuity of the function y of discontinuity.
AP CALCULUS BC NO CALCULATORS: MIDTERM REVIEW 1. Find lim 7x 6x x 7 x 9. 1 B) 0 C) D). Find the points of discontinuity of the function y of discontinuity. x 9x 0. For each discontinuity identify the type
More informationACP Algebra 1 Page 1 of 18 Final Exam Review Packet Equation Review
ACP Algebra 1 Page 1 of 18 Final Eam Review Packet 015016 Equation Review 1. Solve the equations. a. 3( 6) = 6( + 4) b. (3 + 5) = ( + 5) c. ( 3) + 4( 3) = 4( + 5) d. (m ) + 6 = 4m +. Solve the equation
More informationAlgebra 1 Practice Test. Algebra 1. Practice Test. Copyright Karin Hutchinson, All rights reserved.
Algebra 1 Practice Test Copyright Karin Hutchinson, 2011. All rights reserved. Please respect the time, effort, and careful planning spent to prepare these materials. The distribution of this ebook via
More informationSolve Linear Systems by Substitution
5.2 Solve Linear Systems by Substitution Systems of linear equations can be used to help determine the best selling price for products and services. Investigate A Class Problem Tools graphing calculator
More information3. Write 2 different possible equations of a line that contains (9, 8) and (7, 8) in point slope form:
1. Given the points: (3, 7) and (2, 8) a. Write an equation in pointslope form of the line that passes through the given points. b. Rewrite the equation in slopeintercept form. c. Now, rewrite the
More informationMath 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
More informationPattern & Algebra Practice Problems
Pattern & Algebra Practice Problems Solve Linear Inequalities 1. Solve for x. A. x > 3 B. x > 0 C. x < 0 D. x < 3 4x < 6 + 2x Symbolize Problem Situations 2. Scott is draining his swimming pool. The
More informationAlgebra 1 STAAR Review Name: Date:
Algebra 1 STAAR Review Name: Date: 1. Which graph does not represent y as a function of x? I. II. III. A) I only B) II only C) III only D) I and III E) I and II 2. Which expression is equivalent to? 3.
More informationQuadratic Application Problems
Name Quadratic Application Problems 1. A roof shingle is dropped from a rooftop that is 100 feet above the ground. The height y (in feet) of the dropped roof shingle is given by the function y = 16t 2
More informationWorking with Quadratic Functions: Standard and Factored Forms
14 Chapter 3 Working with Quadratic Functions: Standard and Factored Forms GOALS You will be able to Epand and simplify quadratic epressions, solve quadratic equations, and relate the roots of a quadratic
More information76 Growth and Decay. Let t = 7 in the salary equation above. So, Ms. Acosta will earn about $37, in 7 years.
1. SALARY Ms. Acosta received a job as a teacher with a starting salary of $34,000. According to her contract, she will receive a 1.5% increase in her salary every year. How much will Ms. Acosta earn in
More informationUnit 4 Study Guide Part I: Equations of Lines
Unit 4 Study Guide Part I: Equations of Lines Write out the general equations for: Point Slope Form: SlopeIntercept Form: Standard Form: 1. Given the points: (3, 7) and (2, 8) a. Write an equation in
More informationAnswer Key 1973 BC 1969 BC 24. A 14. A 24. C 25. A 26. C 27. C 28. D 29. C 30. D 31. C 13. C 12. D 12. E 3. A 32. B 27. E 34. C 14. D 25. B 26.
Answer Key 969 BC 97 BC. C. E. B. D 5. E 6. B 7. D 8. C 9. D. A. B. E. C. D 5. B 6. B 7. B 8. E 9. C. A. B. E. D. C 5. A 6. C 7. C 8. D 9. C. D. C. B. A. D 5. A 6. B 7. D 8. A 9. D. E. D. B. E. E 5. E.
More information