Printed Name: Section #: Instructor:
|
|
- Dwight Gregory
- 5 years ago
- Views:
Transcription
1 Printed Name: Section #: Instructor: Please do not ask questions during tis exam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide te correct answer. Refer to tis page and te last page of te test for formulas, general directions, and calculator troublesooting tips. Any communication wit any person (oter tan te instructor or te designated proctor) during tis exam in any form, including written, signed, verbal or digital, is understood to be a violation of academic integrity. All devices, suc as computers, cell pones, cameras, watces and PDAs must be turned off and stowed away wile te student is in te testing room. Te only calculators to be used are TI-83, TI-83+, TI-84 or TI-84+. You may NOT borrow or sare a calculator wit anoter person taking tis test. Statement of Academic Integrity: I ave not and will not give or receive improper aid on tis test. In signing below, I acknowledge tat I ave read, understand, and agree to tese testing conditions. Student s Signature: (Tis test will not be accepted for grading unless it bears te signature of te student.) FR#1 FR # FR #3 FR #4 scantron Free Response Total Multiple Coice Total Total Possible Points Points Earned Useful Formulas: ( ) f x + f ( x) f ( x) = lim ; 0 f ( x) f ( a) f ( a) = lim x a x a rt r F( t) = P(1 + rt) F( t) = Pe F( t) = P 1+ n r r APY = ( e 1)100% or APY = % n n ( nt ) Page 1/1
2 MULTIPLE CHOICE: 64 points (3 points eac, unless oterwise noted) Use a # pencil and completely fill eac bubble on your scantron to answer eac multiple coice question. (For future reference, circle your answers on tis test paper.) Tere is no penalty for guessing on multiple coice. If you indicate more tan one answer, or you leave a blank, te question will be marked as incorrect. D C C B B D A B C A D A B C A D C B D C A A Use te following to answer te next tree questions: Te grap below sows te city of Clemson s population, in tousands of people, for various years. Draw appropriate lines on te grap to answer te questions below. 1. Between 1980 and 005, Clemson s population increased on average by tousand people per year. a b c. 0.0 d In 1975, Clemson s population was increasing by tousand people per year. a b c d Consider te slope of tangent lines to te above grap at te points x= 10, x= 0, x= 30, and x= 55. Order te points from least to greatest slope. a. 10, 0, 30, 55 b. 30, 55, 0, 10 c. 55, 30, 0, 10 d. 55, 0 30, 10 Page /1
3 Use te following table for te next two problems. x 1 f ( x) f (1) x 1 + x 1 f ( x) f (1) x Wat does te number in te saded cell represent? [ pts] a. Te instantaneous rate of cange at x= b. Te slope of te line passing troug points at x= 0.99 and x= 1. c. f ( x) f (1) lim. x 1 x 1 d. Te percentage rate of cange between x= 0.99 and x= Based on te above table, f (1) =. [ pts] a. 0 b..5 c. d. does not exist 6. For a smoot continuous function (wit no sarp points), to find te instantaneous rate of cange at a point T,. a. find te slope of te secant line at te point T b. find te average of te slopes of tangent lines nearby te point T c. find te limit of slopes of tangent lines at points nearby T, as tose points get closer and closer to T d. find te limit of slopes of secant lines at points nearby T, as tose points get closer and closer to T Page 3/1
4 Use te following grap for te next two problems. 7. Given tat f ( x ), graped to te rigt, is continuous at te inflection point at x = 3, wic one of te following is a reason wy te instantaneous rate of cange does not exist at x = 3? a. Tere is a vertical tangent line at x = 3. b. Tere is a orizontal tangent line at x = 3. c. Tere is a sarp corner at x = 3. d. lim f ( x) does not exist. x 3 8. Find te interval(s) on wic te slope grap of f ( x ) lies below te x-axis and is decreasing. a. (, 3),( 3,1) b. (, 3) c. ( 3,1) d. (1, ) 9. A cake taken out of a 35 o F oven will completely cool off to a room temperature of 68 o F after 37 minutes. T ( m ) degrees Fareneit gives te temperature of te cake, m minutes after it as been taken out of te oven, 0 m 37. Wen m= 15, determine weter T ( m) is positive or negative and give te units for T ( m). a. Positive; degrees Fareneit per minute b. Positive; degrees Fareneit c. Negative; degrees Fareneit per minute d. Negative; degrees Fareneit per our 10. According to Te Weater Cannel, istorically, te mean low temperature in Greenville for te mont of January is 30 o F wile te mean low temperature in Greenville for te mont of July is 68 o F. Complete te following sentence: Between January and July, te mean low temperature in Greenville increases by %. a b c d Page 4/1
5 11. Wic one of te following sows a correctly drawn tangent line at bot points A and at point B (were te function is decreasing most rapidly)? a. b. c. d. 1. A car dealer models te number of cars sold at eac of er two locations after te start of a sale. 3 n ( x) = x cars were sold at te first location and a( x) = 1.1( x ) cars were sold at te second location during te t x week after te start of a sale, 1 x 8. Find T ( x ), te total number of cars sold in bot locations during te Ten find te rate of cange formula T ( x) =. t x week after te start of te sale. 1 x 3 a. 8.68x b x + 1.1x c. 8.68x x d. + 3 x x Page 5/1
6 1 x 13. For te function g( x) = +, g ( x) =. x a. 1 x b. x x 3 c. 1 x d. x + x Wic one of te following graps is te slope grap for te function sown in te grap below? a. b. c. d. Page 6/1
7 15. Wic one of te following graps is te slope grap for te function f ( x) sown in te grap below? a. b. c. d. 16. Suppose a function f ( x) is a smoot and continuous function (wit no sarp points). If te slope grap of f ( x ) as a zero (an x-intercept) at x=, te grap of f ( x) must ave a at x=. If te slope grap of f ( x) as a relative maximum at x= 5, te grap of f ( x) must ave at x= 5. a. zero; inflection point b. orizontal tangent; zero c. zero; orizontal tangent d. orizontal tangent; inflection point Page 7/1
8 Use te following to answer te next tree questions: T ( o ) minutes gives te amount of time it takes a mecanic to perform is Also, T (5) = Write a sentence of interpretation for T (5) = 3. t o oil cange of te day. a. Wen te mecanic performs is 5 t oil cange of te day, it takes im 3 minutes. b. After 5 minutes of canging oil, te number of oil canges te mecanic performs decreases by 3 oil canges per minute. c. Wen te mecanic performs is 5 t oil cange of te day, te time it takes im to perform an oil cange is decreasing by 3 minutes per oil cange. d. Between te 5 t and 6 t oil cange of te day, Wen te mecanic performs is 5 t oil cange, te time it takes te mecanic to perform an oil cange decreases on average by 3 minutes. 18. If it takes 16 minutes for te mecanic to perform is 5 t oil cange, find te percentage rate of cange for te 5 t oil cange. a b c d Wat are te units for te percentage rate of cange in te previous question? a. percent b. percent per minute c. minutes per oil cange d. percent per oil cange Use te following information to answer te following tree questions. Joe opens an investment account in a bank wit 3,150 dollars. Te bank manager offers im an investment (call it Plan A) tat pays an annual percentage rate (APR) of 3.8% compounded quarterly. 0. How long would Joe ave to wait for te initial investment of $3150 to double? a. 18 years 3 monts b. 18 years 4 monts c. 18 years 6 monts d. 19 years 1. If tere are no oter deposits or witdrawals, find te balance in te account if Joe decides to witdraw te money after 8 monts. a. $3,49.79 b. $3,440.6 c. $9,08.78 d. $3,495.7 Page 8/1
9 . If te bank manager offers im anoter investment tat pays an annual percentage rate of 3.75 compounded continuously, wat is te annual percentage yield (APY) of tis second investment (call it Plan B) and wic investment sould e coose? a. 3.81%; Plan A b. 3.81%; Plan B c. 3.75%; Plan A d. 3.75%; Plan B FREE RESPONSE: 36 points Sow work were possible. Read te directions at te back of te test on rounding, inclusion of units, and writing sentences and models. 1. Te following table sows te percentage of people, over 14 years old, awake in te US at various times after 9:00 PM. Hours after 9 pm Percent awake A. Use te table to find te average rate of cange in te percentage of people awake between 11:00 pm and 7:00 am. Sow work, rounding te answer to tree decimal places. Write a sentence of interpretation = Between 11:00 pm and 7:00 am, te percentage of people in te US, over 14 year old, wo are awake increases on average by.396 percentage points per our. Part A) 5 pts 1 pt wen 1 pt wat 1 pt increases on avg by 1 pt ow muc 1 pt units B. Te data in te table can be modeled as follows: A( x) =.731x x percent gives te percentage of people, over 14 years old, awake in te US, x ours after 9:00 PM, were 0 x 10. Ceck point: A (1) = Find te instantaneous rate of cange in te percentage of people awake at midnigt. Round te answer to tree decimal places. Write a sentence of interpretation. A (3) = At midnigt, te percentage of people in te US, over 14 year old, wo are awake is decreasing by percentage points per our. Part B) 5 pts 1 pt wen, 1 pt wat, 1 pt was decreasing by 1 pt ow muc 1 pt units units ( /10 pts ) Page 9/1
10 3. f ( t) = t 0.086t t + 7 tousand tons gives te yearly consumption of fertilizer in te US, t years since 1965, 0 t 46. Ceckpoint: f () = A. Calculate amount of cange in te yearly US consumption of fertilizer between 1975 and Sow work, round te answer to tree decimal places, and include units wit te answer. f (30) f (10) = = 4.98 tousand tons Part A) pts Part B) 3 pts B. Find f ( t) = t 0.17t Part C) pts: (Do NOT round any of te coefficients in te answer.) 1 pt units 1/ pt rate of cange 1/ pt output description C. Complete te completely defined rate-of-cange model for f ( t) by filling in te blanks: f ( t) = equation is in part B tousand tons per year (units) gives te RATE OF CHANGE in te yearly consumption of fertilizer in te US, t years since 1965, 0 t 46. D. How quickly is fertilizer consumption in te US canging in 1970? Round te answer to tree decimal places. Include units wit te answer. f (5) = tousand tons per year Part D) pts ( / 9 pts ) Test continues on next page Page 10/1
11 4 3. f ( x) = + 5 degrees Fareneit is te temperature on a late-summer evening in soutcentral Micigan, x ours after sunset, 0 x 6. Ceckpoint: f () = (0.6x+ 0.0) e A. Fill in te following table to numerically estimate te instantaneous rate of cange of f ( x ) at x= 3. Entries in te table must be rounded correctly to THREE decimal places for full credit. (Answers will be marked wrong if not rounded to exactly tree decimal places.) x 3 f ( x) f (3) x 3 + x 3 f ( x) f (3) x Part A) 4 pts entries in table, correct to tree decimal places Part B) 1 pt slope, correct to tree decimal places. Part C) pts B. According to te table, df =.87 (correct to tree decimal places). dx = x 3 C. Fill in te blank in te following sentence, wit numerical answers correct to tree decimal places. According to te table, te temperature 3 ours after sunset on a late-summer evening in sout-central Micigan was decreasing by.87 degrees Fareneit per our. ( / 7 pts ) Test continues on next page Page 11/1
12 4. Use te limit definition of te derivative to find te derivative of f ( x) = 3x 1.x + 5. For full credit, continue from te general limit definition (provided below), clearly sowing all necessary algebraic steps (cancellations, expansions, etc.) and including proper use of notation and equal sign f ( x + ) f ( x) f ( x) = lim 0 [3( x + ) 1.( x + ) + 5] [3x 1.x + 5] = = lim 0 x x x x x = lim 0 x x x x x = lim 0 6x = lim 0 (6x ) = lim 0 = lim(6x ) 0 = 6x 1. Tus, f ( x) = 6x 1. [3( + + ) 1.( + ) + 5] [ ] pts: Find slope of secant using given function: [f(x+) f(x)]/ 1 pt: Square (x+) correctly pts: Distribute 3, -1., and te -1 (minus sign) correctly 1 pt: Combine like terms and sow te result. 1 pt: Sow te limit of a completely simplified expression 1 pt: Evaluate limit of simplified expression to find derivative. Deductions: -1 pt if limit notation is missing; -½ pt if te limit notation is written incorrectly trougout proof -½ pt if equal signs not in correct places and used trougout ( / 9 pts) 1 point for correctly filling out and bubbling te scantron wit a # pencil, a correct XID, a correct test version AND te front of te test is completed wit your signature on te academic integrity statement. END OF TEST Page 1/1
13 General Directions: Sow work were possible. Answers witout supporting work (were work is appropriate) may receive little credit. Do not round intermediate calculations. Answers in context ALWAYS require units. Assume end of te year data unless stated oterwise. Round your answers to 3 decimal places UNLESS te answer needs to be rounded differently to make sense in te context of te problem OR te directions specify anoter type rounding OR te complete answer as fewer tan 3 decimal places. Wen asked to write a model, include all components of a model: an equation, a description of te input including units, a description of te output including units, and te input interval wen known. Wen asked to write a sentence of practical interpretation, answer te questions: wen?, wat?, and ow muc? using ordinary, conversational language. DO NOT use mat words, terms, or unnecessary prases. Always use a ruler wen estimating values off of a grap. HINTS FOR TROUBLESHOOTING YOUR CALCULATOR: If you lose your L1, L, etc., you may reinsert tem using STAT 5 (set-up editor) enter. Te SCATTER PLOT will not sow unless Plot 1 as been turned on and tere is data in L1 and L. ZOOM 0 may not work for graping if Plot 1 is turned on. DIM MISMATCH error usually means tat te lists in L1 and L are not of equal lengt. DATA TYPE error usually means tat you already ave someting in Y1 and you need to clear it before you can paste a new equation. INVALID DIM error usually means tat your plot(s) are on, but tat you ave no data in te lists. Refer to te second int above. If your batteries die, raise your and and old up your calculator. If your instructor as an extra calculator available, e/se will loan it to you for a few minutes. SYNTAX ERROR: Try GO TO. Tis will appen if you use a subtraction minus sign wen you sould use a negative sign. If you need to CLEAR MEMORY, use nd +, 7:Reset, 1:All Ram, :Reset Page 13/1
Printed Name: Section #: Instructor:
Printed Name: Section #: Instructor: Please do not ask questions during tis exam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide te correct
More informationMATH 1020 Answer Key TEST 2 VERSION B Fall Printed Name: Section #: Instructor:
Printed Name: Section #: Instructor: Please do not ask questions during tis exam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide te correct
More informationPrinted Name: Section #: Instructor:
Printed Name: Section #: Instructor: Please do not ask questions during tis eam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide te correct
More informationMATH 1020 TEST 2 VERSION A FALL 2014 ANSWER KEY. Printed Name: Section #: Instructor:
ANSWER KEY Printed Name: Section #: Instructor: Please do not ask questions during tis eam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide
More informationMATH 1020 TEST 2 VERSION A Fall Printed Name: Section #: Instructor:
Printed Name: Section #: Instructor: Please do not ask questions during this exam. If you consider a question to be ambiguous, state your assumptions in the margin and do the best you can to provide the
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 informationMath 1020 TEST 3 VERSION A Spring 2017
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 informationMath 1020 ANSWER KEY TEST 3 VERSION A Fall 2016
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 informationMath 1020 ANSWER KEY TEST 3 VERSION B Spring 2018
Math 100 ANSWER KEY TEST 3 VERSION B Spring 018 Printed Name: Section #: Instructor: Please do not ask questions during this exam. If you consider a question to be ambiguous, state your assumptions in
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 informationMATH 1020 TEST 1 VERSION A SPRING Printed Name: Section #: Instructor:
Printed Name: Section #: Instructor: Please do not ask questions during this exam. If you consider a question to be ambiguous, state your assumptions in the margin and do the best you can to provide the
More informationMath 1020 ANSWER KEY TEST 3 VERSION B Fall 2018
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 informationMath 1020 TEST 3 VERSION A Fall 2018
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 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 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 informationREVIEW LAB ANSWER KEY
REVIEW LAB ANSWER KEY. Witout using SN, find te derivative of eac of te following (you do not need to simplify your answers): a. f x 3x 3 5x x 6 f x 3 3x 5 x 0 b. g x 4 x x x notice te trick ere! x x g
More informationMAT 145. Type of Calculator Used TI-89 Titanium 100 points Score 100 possible points
MAT 15 Test #2 Name Solution Guide Type of Calculator Used TI-89 Titanium 100 points Score 100 possible points Use te grap of a function sown ere as you respond to questions 1 to 8. 1. lim f (x) 0 2. lim
More information2.11 That s So Derivative
2.11 Tat s So Derivative Introduction to Differential Calculus Just as one defines instantaneous velocity in terms of average velocity, we now define te instantaneous rate of cange of a function at a point
More information1. Which one of the following expressions is not equal to all the others? 1 C. 1 D. 25x. 2. Simplify this expression as much as possible.
004 Algebra Pretest answers and scoring Part A. Multiple coice questions. Directions: Circle te letter ( A, B, C, D, or E ) net to te correct answer. points eac, no partial credit. Wic one of te following
More informationMath Test No Calculator
Mat Test No Calculator MINUTES, QUESTIONS Turn to Section of your answer seet to answer te questions in tis section. For questions -, solve eac problem, coose te best answer from te coices provided, and
More informationIntroduction to Derivatives
Introduction to Derivatives 5-Minute Review: Instantaneous Rates and Tangent Slope Recall te analogy tat we developed earlier First we saw tat te secant slope of te line troug te two points (a, f (a))
More informationTime (hours) Morphine sulfate (mg)
Mat Xa Fall 2002 Review Notes Limits and Definition of Derivative Important Information: 1 According to te most recent information from te Registrar, te Xa final exam will be eld from 9:15 am to 12:15
More informationDerivatives. By: OpenStaxCollege
By: OpenStaxCollege Te average teen in te United States opens a refrigerator door an estimated 25 times per day. Supposedly, tis average is up from 10 years ago wen te average teenager opened a refrigerator
More information5. (a) Find the slope of the tangent line to the parabola y = x + 2x
MATH 141 090 Homework Solutions Fall 00 Section.6: Pages 148 150 3. Consider te slope of te given curve at eac of te five points sown (see text for figure). List tese five slopes in decreasing order and
More informationSection 2.1 The Definition of the Derivative. We are interested in finding the slope of the tangent line at a specific point.
Popper 6: Review of skills: Find tis difference quotient. f ( x ) f ( x) if f ( x) x Answer coices given in audio on te video. Section.1 Te Definition of te Derivative We are interested in finding te slope
More informationSECTION 1.10: DIFFERENCE QUOTIENTS LEARNING OBJECTIVES
(Section.0: Difference Quotients).0. SECTION.0: DIFFERENCE QUOTIENTS LEARNING OBJECTIVES Define average rate of cange (and average velocity) algebraically and grapically. Be able to identify, construct,
More informationSection 2: The Derivative Definition of the Derivative
Capter 2 Te Derivative Applied Calculus 80 Section 2: Te Derivative Definition of te Derivative Suppose we drop a tomato from te top of a 00 foot building and time its fall. Time (sec) Heigt (ft) 0.0 00
More information(a) At what number x = a does f have a removable discontinuity? What value f(a) should be assigned to f at x = a in order to make f continuous at a?
Solutions to Test 1 Fall 016 1pt 1. Te grap of a function f(x) is sown at rigt below. Part I. State te value of eac limit. If a limit is infinite, state weter it is or. If a limit does not exist (but is
More informationMaterial for Difference Quotient
Material for Difference Quotient Prepared by Stepanie Quintal, graduate student and Marvin Stick, professor Dept. of Matematical Sciences, UMass Lowell Summer 05 Preface Te following difference quotient
More informationSAT Practice Test #1 IMPORTANT REMINDERS. A No. 2 pencil is required for the test. Do not use a mechanical pencil or pen.
SAT Practice Test # IMPORTANT REMINDERS A No. pencil is required for te test. Do not use a mecanical pencil or pen. Saring any questions wit anyone is a violation of Test Security and Fairness policies
More information. Compute the following limits.
Today: Tangent Lines and te Derivative at a Point Warmup:. Let f(x) =x. Compute te following limits. f( + ) f() (a) lim f( +) f( ) (b) lim. Let g(x) = x. Compute te following limits. g(3 + ) g(3) (a) lim
More informationChapter 2 Describing Change: Rates
Capter Describing Cange: Rates Section.1 Cange, Percentage Cange, and Average Rates of Cange 1.. 3. $.30 $0.46 per day 5 days = Te stock price rose an average of 46 cents per day during te 5-day period.
More information3.4 Worksheet: Proof of the Chain Rule NAME
Mat 1170 3.4 Workseet: Proof of te Cain Rule NAME Te Cain Rule So far we are able to differentiate all types of functions. For example: polynomials, rational, root, and trigonometric functions. We are
More informationPreface. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
Preface Here are my online notes for my course tat I teac ere at Lamar University. Despite te fact tat tese are my class notes, tey sould be accessible to anyone wanting to learn or needing a refreser
More informationThe derivative function
Roberto s Notes on Differential Calculus Capter : Definition of derivative Section Te derivative function Wat you need to know already: f is at a point on its grap and ow to compute it. Wat te derivative
More informationSection 3: The Derivative Definition of the Derivative
Capter 2 Te Derivative Business Calculus 85 Section 3: Te Derivative Definition of te Derivative Returning to te tangent slope problem from te first section, let's look at te problem of finding te slope
More information. If lim. x 2 x 1. f(x+h) f(x)
Review of Differential Calculus Wen te value of one variable y is uniquely determined by te value of anoter variable x, ten te relationsip between x and y is described by a function f tat assigns a value
More informationLab 6 Derivatives and Mutant Bacteria
Lab 6 Derivatives and Mutant Bacteria Date: September 27, 20 Assignment Due Date: October 4, 20 Goal: In tis lab you will furter explore te concept of a derivative using R. You will use your knowledge
More informationExam 1 Review Solutions
Exam Review Solutions Please also review te old quizzes, and be sure tat you understand te omework problems. General notes: () Always give an algebraic reason for your answer (graps are not sufficient),
More informationCombining functions: algebraic methods
Combining functions: algebraic metods Functions can be added, subtracted, multiplied, divided, and raised to a power, just like numbers or algebra expressions. If f(x) = x 2 and g(x) = x + 2, clearly f(x)
More informationHow to Find the Derivative of a Function: Calculus 1
Introduction How to Find te Derivative of a Function: Calculus 1 Calculus is not an easy matematics course Te fact tat you ave enrolled in suc a difficult subject indicates tat you are interested in te
More informationThe Derivative The rate of change
Calculus Lia Vas Te Derivative Te rate of cange Knowing and understanding te concept of derivative will enable you to answer te following questions. Let us consider a quantity wose size is described by
More informationFunction Composition and Chain Rules
Function Composition and s James K. Peterson Department of Biological Sciences and Department of Matematical Sciences Clemson University Marc 8, 2017 Outline 1 Function Composition and Continuity 2 Function
More informationSolve exponential equations in one variable using a variety of strategies. LEARN ABOUT the Math. What is the half-life of radon?
8.5 Solving Exponential Equations GOAL Solve exponential equations in one variable using a variety of strategies. LEARN ABOUT te Mat All radioactive substances decrease in mass over time. Jamie works in
More informationMAT244 - Ordinary Di erential Equations - Summer 2016 Assignment 2 Due: July 20, 2016
MAT244 - Ordinary Di erential Equations - Summer 206 Assignment 2 Due: July 20, 206 Full Name: Student #: Last First Indicate wic Tutorial Section you attend by filling in te appropriate circle: Tut 0
More informationMath 115 Test 1 Sample Problems for Dr. Hukle s Class
Mat 5 Test Sample Problems for Dr. Hukle s Class. Demand for a Jayawk pen at te Union is known to be D(p) = 26 pens per mont wen te selling p price is p dollars and eac p 3. A supplier for te bookstore
More informationb 1 A = bh h r V = pr
. Te use of a calculator is not permitted.. All variables and expressions used represent real numbers unless oterwise indicated.. Figures provided in tis test are drawn to scale unless oterwise indicated..
More information. h I B. Average velocity can be interpreted as the slope of a tangent line. I C. The difference quotient program finds the exact value of f ( a)
Capter Review Packet (questions - ) KEY. In eac case determine if te information or statement is correct (C) or incorrect (I). If it is incorrect, include te correction. f ( a ) f ( a) I A. represents
More information2.8 The Derivative as a Function
.8 Te Derivative as a Function Typically, we can find te derivative of a function f at many points of its domain: Definition. Suppose tat f is a function wic is differentiable at every point of an open
More information1. AB Calculus Introduction
1. AB Calculus Introduction Before we get into wat calculus is, ere are several eamples of wat you could do BC (before calculus) and wat you will be able to do at te end of tis course. Eample 1: On April
More informationMVT and Rolle s Theorem
AP Calculus CHAPTER 4 WORKSHEET APPLICATIONS OF DIFFERENTIATION MVT and Rolle s Teorem Name Seat # Date UNLESS INDICATED, DO NOT USE YOUR CALCULATOR FOR ANY OF THESE QUESTIONS In problems 1 and, state
More information4. The slope of the line 2x 7y = 8 is (a) 2/7 (b) 7/2 (c) 2 (d) 2/7 (e) None of these.
Mat 11. Test Form N Fall 016 Name. Instructions. Te first eleven problems are wort points eac. Te last six problems are wort 5 points eac. For te last six problems, you must use relevant metods of algebra
More informationModels and Applications
Models and Applications 1 Modeling Tis Not tis 2 In Tis Section Create mat model from verbal description Simple interest problems Percentage problems Geometry formulas Literal equations Angle measurements
More informationName: Answer Key No calculators. Show your work! 1. (21 points) All answers should either be,, a (finite) real number, or DNE ( does not exist ).
Mat - Final Exam August 3 rd, Name: Answer Key No calculators. Sow your work!. points) All answers sould eiter be,, a finite) real number, or DNE does not exist ). a) Use te grap of te function to evaluate
More informationCalculus I Practice Exam 1A
Calculus I Practice Exam A Calculus I Practice Exam A Tis practice exam empasizes conceptual connections and understanding to a greater degree tan te exams tat are usually administered in introductory
More information1 Limits and Continuity
1 Limits and Continuity 1.0 Tangent Lines, Velocities, Growt In tion 0.2, we estimated te slope of a line tangent to te grap of a function at a point. At te end of tion 0.3, we constructed a new function
More informationPractice Problem Solutions: Exam 1
Practice Problem Solutions: Exam 1 1. (a) Algebraic Solution: Te largest term in te numerator is 3x 2, wile te largest term in te denominator is 5x 2 3x 2 + 5. Tus lim x 5x 2 2x 3x 2 x 5x 2 = 3 5 Numerical
More informationPre-Calculus Review Preemptive Strike
Pre-Calculus Review Preemptive Strike Attaced are some notes and one assignment wit tree parts. Tese are due on te day tat we start te pre-calculus review. I strongly suggest reading troug te notes torougly
More informationy = 3 2 x 3. The slope of this line is 3 and its y-intercept is (0, 3). For every two units to the right, the line rises three units vertically.
Mat 2 - Calculus for Management and Social Science. Understanding te basics of lines in te -plane is crucial to te stud of calculus. Notes Recall tat te and -intercepts of a line are were te line meets
More informationSFU UBC UNBC Uvic Calculus Challenge Examination June 5, 2008, 12:00 15:00
SFU UBC UNBC Uvic Calculus Callenge Eamination June 5, 008, :00 5:00 Host: SIMON FRASER UNIVERSITY First Name: Last Name: Scool: Student signature INSTRUCTIONS Sow all your work Full marks are given only
More informationNUMERICAL DIFFERENTIATION. James T. Smith San Francisco State University. In calculus classes, you compute derivatives algebraically: for example,
NUMERICAL DIFFERENTIATION James T Smit San Francisco State University In calculus classes, you compute derivatives algebraically: for example, f( x) = x + x f ( x) = x x Tis tecnique requires your knowing
More informationMain Points: 1. Limit of Difference Quotients. Prep 2.7: Derivatives and Rates of Change. Names of collaborators:
Name: Section: Names of collaborators: Main Points:. Definition of derivative as limit of difference quotients. Interpretation of derivative as slope of grap. Interpretation of derivative as instantaneous
More information1. Questions (a) through (e) refer to the graph of the function f given below. (A) 0 (B) 1 (C) 2 (D) 4 (E) does not exist
Mat 1120 Calculus Test 2. October 18, 2001 Your name Te multiple coice problems count 4 points eac. In te multiple coice section, circle te correct coice (or coices). You must sow your work on te oter
More informationMAT Calculus for Engineers I EXAM #1
MAT 65 - Calculus for Engineers I EXAM # Instructor: Liu, Hao Honor Statement By signing below you conrm tat you ave neiter given nor received any unautorized assistance on tis eam. Tis includes any use
More informationCalculus I Homework: The Derivative as a Function Page 1
Calculus I Homework: Te Derivative as a Function Page 1 Example (2.9.16) Make a careful sketc of te grap of f(x) = sin x and below it sketc te grap of f (x). Try to guess te formula of f (x) from its grap.
More informationSection 2.7 Derivatives and Rates of Change Part II Section 2.8 The Derivative as a Function. at the point a, to be. = at time t = a is
Mat 180 www.timetodare.com Section.7 Derivatives and Rates of Cange Part II Section.8 Te Derivative as a Function Derivatives ( ) In te previous section we defined te slope of te tangent to a curve wit
More informationBlueprint Algebra I Test
Blueprint Algebra I Test Spring 2003 2003 by te Commonwealt of Virginia Department of Education, James Monroe Building, 101 N. 14t Street, Ricmond, Virginia, 23219. All rigts reserved. Except as permitted
More informationMTH-112 Quiz 1 Name: # :
MTH- Quiz Name: # : Please write our name in te provided space. Simplif our answers. Sow our work.. Determine weter te given relation is a function. Give te domain and range of te relation.. Does te equation
More informationDerivatives of Exponentials
mat 0 more on derivatives: day 0 Derivatives of Eponentials Recall tat DEFINITION... An eponential function as te form f () =a, were te base is a real number a > 0. Te domain of an eponential function
More informationf a h f a h h lim lim
Te Derivative Te derivative of a function f at a (denoted f a) is f a if tis it exists. An alternative way of defining f a is f a x a fa fa fx fa x a Note tat te tangent line to te grap of f at te point
More information1watt=1W=1kg m 2 /s 3
Appendix A Matematics Appendix A.1 Units To measure a pysical quantity, you need a standard. Eac pysical quantity as certain units. A unit is just a standard we use to compare, e.g. a ruler. In tis laboratory
More information2.1 THE DEFINITION OF DERIVATIVE
2.1 Te Derivative Contemporary Calculus 2.1 THE DEFINITION OF DERIVATIVE 1 Te grapical idea of a slope of a tangent line is very useful, but for some uses we need a more algebraic definition of te derivative
More informationMath 312 Lecture Notes Modeling
Mat 3 Lecture Notes Modeling Warren Weckesser Department of Matematics Colgate University 5 7 January 006 Classifying Matematical Models An Example We consider te following scenario. During a storm, a
More informationContinuity and Differentiability Worksheet
Continuity and Differentiability Workseet (Be sure tat you can also do te grapical eercises from te tet- Tese were not included below! Typical problems are like problems -3, p. 6; -3, p. 7; 33-34, p. 7;
More informationSolution. Solution. f (x) = (cos x)2 cos(2x) 2 sin(2x) 2 cos x ( sin x) (cos x) 4. f (π/4) = ( 2/2) ( 2/2) ( 2/2) ( 2/2) 4.
December 09, 20 Calculus PracticeTest s Name: (4 points) Find te absolute extrema of f(x) = x 3 0 on te interval [0, 4] Te derivative of f(x) is f (x) = 3x 2, wic is zero only at x = 0 Tus we only need
More information1 The concept of limits (p.217 p.229, p.242 p.249, p.255 p.256) 1.1 Limits Consider the function determined by the formula 3. x since at this point
MA00 Capter 6 Calculus and Basic Linear Algebra I Limits, Continuity and Differentiability Te concept of its (p.7 p.9, p.4 p.49, p.55 p.56). Limits Consider te function determined by te formula f Note
More informationKey Concepts. Important Techniques. 1. Average rate of change slope of a secant line. You will need two points ( a, the formula: to find value
AB Calculus Unit Review Key Concepts Average and Instantaneous Speed Definition of Limit Properties of Limits One-sided and Two-sided Limits Sandwic Teorem Limits as x ± End Beaviour Models Continuity
More informationUNIT #6 EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS
Answer Key Name: Date: UNIT # EXPONENTS, EXPONENTS, AND MORE EXPONENTS REVIEW QUESTIONS Part I Questions. Te epression 0 can be simpliied to () () 0 0. Wic o te ollowing is equivalent to () () 8 8? 8.
More informationMathematics 105 Calculus I. Exam 1. February 13, Solution Guide
Matematics 05 Calculus I Exam February, 009 Your Name: Solution Guide Tere are 6 total problems in tis exam. On eac problem, you must sow all your work, or oterwise torougly explain your conclusions. Tere
More informationDifferential Calculus (The basics) Prepared by Mr. C. Hull
Differential Calculus Te basics) A : Limits In tis work on limits, we will deal only wit functions i.e. tose relationsips in wic an input variable ) defines a unique output variable y). Wen we work wit
More informationHigher Derivatives. Differentiable Functions
Calculus 1 Lia Vas Higer Derivatives. Differentiable Functions Te second derivative. Te derivative itself can be considered as a function. Te instantaneous rate of cange of tis function is te second derivative.
More informationSECTION 3.2: DERIVATIVE FUNCTIONS and DIFFERENTIABILITY
(Section 3.2: Derivative Functions and Differentiability) 3.2.1 SECTION 3.2: DERIVATIVE FUNCTIONS and DIFFERENTIABILITY LEARNING OBJECTIVES Know, understand, and apply te Limit Definition of te Derivative
More informationStudent s Printed Name:
Student s Printed Name: Instructor: CUID: Section # : You are not permitted to use a calculator on any portion of this test. You are not allowed to use any textbook, notes, cell phone, laptop, PDA, smart
More informationConsider a function f we ll specify which assumptions we need to make about it in a minute. Let us reformulate the integral. 1 f(x) dx.
Capter 2 Integrals as sums and derivatives as differences We now switc to te simplest metods for integrating or differentiating a function from its function samples. A careful study of Taylor expansions
More informationLines, Conics, Tangents, Limits and the Derivative
Lines, Conics, Tangents, Limits and te Derivative Te Straigt Line An two points on te (,) plane wen joined form a line segment. If te line segment is etended beond te two points ten it is called a straigt
More informationPrecalculus Test 2 Practice Questions Page 1. Note: You can expect other types of questions on the test than the ones presented here!
Precalculus Test 2 Practice Questions Page Note: You can expect oter types of questions on te test tan te ones presented ere! Questions Example. Find te vertex of te quadratic f(x) = 4x 2 x. Example 2.
More informationLIMITS AND DERIVATIVES CONDITIONS FOR THE EXISTENCE OF A LIMIT
LIMITS AND DERIVATIVES Te limit of a function is defined as te value of y tat te curve approaces, as x approaces a particular value. Te limit of f (x) as x approaces a is written as f (x) approaces, as
More informationLesson 6: The Derivative
Lesson 6: Te Derivative Def. A difference quotient for a function as te form f(x + ) f(x) (x + ) x f(x + x) f(x) (x + x) x f(a + ) f(a) (a + ) a Notice tat a difference quotient always as te form of cange
More informationUNIVERSITY OF MANITOBA DEPARTMENT OF MATHEMATICS MATH 1510 Applied Calculus I FIRST TERM EXAMINATION - Version A October 12, :30 am
DEPARTMENT OF MATHEMATICS MATH 1510 Applied Calculus I October 12, 2016 8:30 am LAST NAME: FIRST NAME: STUDENT NUMBER: SIGNATURE: (I understand tat ceating is a serious offense DO NOT WRITE IN THIS TABLE
More informationChapters 19 & 20 Heat and the First Law of Thermodynamics
Capters 19 & 20 Heat and te First Law of Termodynamics Te Zerot Law of Termodynamics Te First Law of Termodynamics Termal Processes Te Second Law of Termodynamics Heat Engines and te Carnot Cycle Refrigerators,
More informationFinding and Using Derivative The shortcuts
Calculus 1 Lia Vas Finding and Using Derivative Te sortcuts We ave seen tat te formula f f(x+) f(x) (x) = lim 0 is manageable for relatively simple functions like a linear or quadratic. For more complex
More informationAverage Rate of Change
Te Derivative Tis can be tougt of as an attempt to draw a parallel (pysically and metaporically) between a line and a curve, applying te concept of slope to someting tat isn't actually straigt. Te slope
More informationSolutions Manual for Precalculus An Investigation of Functions
Solutions Manual for Precalculus An Investigation of Functions David Lippman, Melonie Rasmussen 1 st Edition Solutions created at Te Evergreen State College and Soreline Community College 1.1 Solutions
More information1 1. Rationalize the denominator and fully simplify the radical expression 3 3. Solution: = 1 = 3 3 = 2
MTH - Spring 04 Exam Review (Solutions) Exam : February 5t 6:00-7:0 Tis exam review contains questions similar to tose you sould expect to see on Exam. Te questions included in tis review, owever, are
More informationExponentials and Logarithms Review Part 2: Exponentials
Eponentials and Logaritms Review Part : Eponentials Notice te difference etween te functions: g( ) and f ( ) In te function g( ), te variale is te ase and te eponent is a constant. Tis is called a power
More informationMath 1241 Calculus Test 1
February 4, 2004 Name Te first nine problems count 6 points eac and te final seven count as marked. Tere are 120 points available on tis test. Multiple coice section. Circle te correct coice(s). You do
More informationGENTLY REMOVE THIS PAGE.
GENTLY REMOVE THIS PAGE. Note that it WILL be collected with your test. MATH 2070 Test 3 Formula Sheet When you are asked to show work or the notation that leads to your answer, be sure to write the notation
More informationChapter 2 Limits and Continuity
4 Section. Capter Limits and Continuity Section. Rates of Cange and Limits (pp. 6) Quick Review.. f () ( ) () 4 0. f () 4( ) 4. f () sin sin 0 4. f (). 4 4 4 6. c c c 7. 8. c d d c d d c d c 9. 8 ( )(
More informationExponential and logarithmic functions (pp ) () Supplement October 14, / 1. a and b positive real numbers and x and y real numbers.
MA123, Supplement Exponential and logaritmic functions pp. 315-319) Capter s Goal: Review te properties of exponential and logaritmic functions. Learn ow to differentiate exponential and logaritmic functions.
More information