MAT 1800 FINAL EXAM HOMEWORK
|
|
|
- Leslie Ball
- 5 years ago
- Views:
Transcription
1 MAT 800 FINAL EXAM HOMEWORK Read te directions to eac problem careully ALL WORK MUST BE SHOWN DO NOT USE A CALCULATOR Problems come rom old inal eams (SS4, W4, F, SS, W) Solving Equations: Let 5 Find all numbers, any, suc tat Let and g 6 Find all numbers, any, suc tat g Solve te equation 4 Solve te equation Finding Domain o Functions: 5 Find te domain o te unction 6 Find te domain o te unction 7 Find te domain o te unction 8 Find te domain o te unction 9 Find te domain o te unction Graping Piece-wise Functions: 0 Sketc a grap o te unction Sketc a grap o te unction Sketc a grap o te unction log 7e log log 4 5 State your answer in interval notation 5 State your answer in interval notation State your answer in interval notation 6 State your answer in interval notation log ln State your answer in interval notation 9 4 g g Sketc a grap o te unction g
2 4 Sketc a grap o te unction g 0 0 Inverse Functions: 5 Let log4 5 Find Let Find 7 Let Find 8 Let Find 9 Let Find Graping Polynomials: 0 Grap te polynomial p Grap te polynomial p Grap te polynomial 5 Grap te polynomial p p p 4 Grap te polynomial Composition o Functions & Evaluating Functions: 5 Let 7 4 and g 5 completely (a) g 6 Let Find 6 7 Let e and g 8ln is te inverse unction o is te inverse unction o is te inverse unction o is te inverse unction o is te inverse unction o, inding and labeling all intercepts, inding and labeling all intercepts, inding and labeling all intercepts, inding and labeling all intercepts, inding and labeling all intercepts Find eac o te ollowing and simply your answers and simply your answer completely Find and simply eac o te ollowing (a) g g 8 Let Find a a and simply your answer completely
3 4 4 Find and g 7 log 9 Let 0 0 Let a a g Find and simply and simply your answer completely Let and g g g Find and simply g 4 Let and g Find and simply g5 Let a a Find Ma/Min Story Problems: and simply your answer completely 4 A stone is launced o o a building wic is 95 eet ig Its eigt at time t is given by te unction t 950t 4t were time is measured in seconds and eigt is measured in eet At wat time does te stone reac its maimum eigt? Wat is te maimum eigt? 5 A ball is catapulted upwards Its eigt at time t is given by 40 t 6t t were time is measured in seconds and eigt is measured in meters Wat is te maimum eigt te ball will reac? Zeros o Polynomials: 6 6 Find all te zeros o te polynomial 0 te orm a bi 7 Given tat i p p 4 is a zero o te polynomial 8 zeros Please epress any non-real zeros in te orm 5 a bi 8 8 Find all te zeros o te polynomial 5 te orm a bi 4 9 Find all te zeros o te polynomial p te orm a bi p Please epress any non-real zeros in Find all te zeros o te polynomial p 4 4 zeros in te orm a bi, ind and list all oter Please epress any non-real zeros in Please epress any non-real zeros in Please epress any non-real Graping Rational Functions: 4 Grap te unction 5 4, labeling all intercepts and asymptotes 4
4 4 Grap te unction 4 Grap te unction 44 Grap te unction 45 Grap te unction Modeling wit Functions:, labeling all intercepts and asymptotes 6, labeling all intercepts and asymptotes 5, labeling all intercepts and asymptotes 9 4, labeling all intercepts and asymptotes A piece o wire inces long is bent into te sape o an equilateral triangle Find a unction o tat represents te area o te triangle and state te domain o te unction 47 A cardboard bo as a square base and a square top Te eigt o te bo is inces Epress te surace area A (te sum o te areas o all si sides o te bo) in terms o te lengt l o te bo 48 A crate as a eigt o 6 eet Te sum o te areas o all 6 sides o te crate is 40 square eet Epress te lengt l o te crate in terms o te widt w (ie write l as a unction o w) Evaluating Logaritms: ln5 log 49 Find te eact value o te epression log 5 65e
5 ln e e ln 5 Find te eact value o te epression e ln e log ln6 5 Find te eact value o te epression 4 ln e log ln6 50 Find te eact value o te epression 5 e 5 Find te eact value o eac epression: (a) log log 4 Solving Logaritmic & Eponential Equations: 6 ln 7 e 6 log 5 log 54 Find all values o, any, suc tat 55 Find all values o, any, suc tat log log 8 log Solve te equation 7 log 57 Find all values o, any, suc tat log 58 Find all values o, any, suc tat e e 59 Find all values o, any, suc tat log4 8 log4 8 Graping Logaritmic & Eponential Functions: 60 Grap te unction ln e 6 Grap te unction 6 Grap te unction 6 Grap te unction log 64 Grap te unction Eponential Function Applications:, labeling all intercepts and asymptotes 7, labeling te y-intercept and any asymptotes 5, labeling te y-intercept and any asymptotes, labeling all intercepts and asymptotes log P t 00e 65 Te general unction, labeling all intercepts and asymptotes is used to model te number o bacteria in a culture P 00 0 is te initial population and t is time measured in ours Suppose te bacteria culture reaces 00 ater 5 ours How long will it take or te bacteria culture to triple in size? Simply your answer as muc as possible P t 640e 66 Te general unction is used to model a dying bird population P 640 is te initial population and t is time measured in days Suppose te bird population was reduced to one quarter o its initial size ater 9 days How long will it take beore tere are only 40 birds let in te population? Simply your answer as muc as possible 0 67 Te general unction P t P0 e is used to model an insect population P 0 is te initial population ( P 0) and t is time measured in ours Suppose te insect population tripled ater 7 0
6 ours How long will it take te insect population to grow to nine times its initial size? Simply your answer as muc as possible n t n0e 68 Te general unction is used to model te number o bacteria in a certain culture te time t is measured in ours Suppose te culture initially contains,000 bacteria Ater two ours te bacteria count is 8,000 Find te eact time it took or te bacteria count to triple n t n0e 69 Te general unction is used to model te number o bacteria in a certain culture n 0 is te initial population and t is time measured in ours Suppose te culture initially contains 80 bacteria and ater 5 ours te bacteria count decreases to 60 Wat would you epect te size o te culture to be ater 0 ours? Simply your answer Trigonometric Evaluation Problems: 70 Find te eact value o eac trigonometric unction at te given real number, it eists (a) cos csc 7 Find te eact value o eac trigonometric unction at te given real number, it eists 7 6 (a) sin cot 6 7 Find te eact value o eac trigonometric unction at te given real number, it eists (a) tan sin 7 Find te eact value o Find te eact value o cos 5 4 sec 75 Find te eact value o eac trigonometric unction at te given real number, it eists (a) csc sin 76 Find te eact value o 75 cot 7 77 Find te eact value o eac trigonometric unction at te given real number, it eists 0 9 (a) cos sec Graping Trigonometric Functions: 78 Find and state te amplitude and period lengt or te unction 4cos one complete period Be sure to label te igest and lowest points on te grap 79 Find and state te amplitude and period lengt or te unction sin grap one complete period Be sure to label te igest and lowest points on te grap 6 and ten grap and ten
7 80 Find and state te amplitude and period lengt or te unction cos one complete period Be sure to label te igest and lowest points on te grap cos 4 8 Find and state te amplitude and period lengt o te unction one complete period Be sure to label te igest and lowest points on te grap sin 8 Find and state te amplitude and period lengt o te unction one complete period Be sure to label te igest and lowest points on te grap Trigonometric Identities: 8 and ten grap and ten grap and ten grap 8 Given tat 84 Given tat 85 Given tat 86 Given tat 87 Given tat cos and 0, ind te eact value o sin tan and csc 0, ind te eact value o cos csc and cos 0, ind te value o cos 5 sec and tan 0, ind te value o sin 4 tan and csc 0, ind te value o cos Inverse Trigonometric Functions: 88 Find te eact value o eac epression, it eists 8 (a) csc cos 4 89 Find te eact value o eac epression, it eists 4 cos cos (a) sinsin csc tan 4 90 Find te eact value o eac epression, it eists 7 5 (a) cos cos 4 sin sin5 9 Find te eact value o sec sin 6 5
8 9 Find te eact value o eac epression, it eists (a) sinsin 8 9 Find te eact value o tansin 7 94 Find te eact value o eac epression, it eists 4 cos cos (a) cos cos Find te eact value o cot cos Solving Trigonometric Equations: tan tan 96 Find all primary solutions (ie 0 ) o te equation sec tan 97 Find all primary solutions (ie 0 cos 4 cos 98 Find all primary solutions (ie 99 Find all primary solutions (ie 0 00 Find all primary solutions (ie 0 Verying Trigonometric Identities: 0 Very tat te trigonometric equation is an identity sin ) o te equation 0 ) o te equation cos sin sin ) o te equation 9sin 9 4cos ) o te equation 4sin 7 8cos 4 4sincos 4sin cos 0 Very tat te trigonometric equation is an identity cos sin sin sin cos sin cos 0 Very tat te trigonometric equation is an identity cot sin sec csc 04 Very tat te trigonometric equation is an identity csc sin cos csc 05 Very tat te trigonometric equation is an identity tan sec cos sin
9 Solving non-linear Inequalities: 06 Solve te inequality 07 Let State your answer in interval notation 4 Find all numbers, any, suc tat 7 Please state your answer in interval notation 08 Let Find all numbers, any, suc tat answer in interval notation Please state your 09 Let and g Find all numbers, any, suc tat g Average Rate o Cange Problems: t t 6t were time is 0 A ball is catapulted upwards Its eigt at time t is given by measured in seconds and eigt is measured in meters Wat is te average rate o cange o te eigt wit respect to time rom t to t? Find te average rate o cange o te unction log rom to 8 A painting as just been purcased At t years rom te date o purcase, te value o te 0 50t painting V in dollars is given by te unction 500 V t t Wat is te average rate o cange in te value o te painting during te time interval rom te 4 t year ater purcase to te 9 t year ater purcase? Please state your answer using proper units Trigonometric Applications: A sip is tied to two ancors on te soreline Te ancor line on te let orms a 46 angle wit te soreline and is 50 eet long Te ancor line on te rigt orms a 6 angle wit te soreline and is 8 eet long Find te eact distance (in eet) between te two ancors (A general picture is given below) Sip Ancor Soreline Ancor 4 Two wires stretc rom a pole to two points on te ground wic are 5 eet apart Te irst wire is to te let o te pole and orms a 0 angle wit te ground Te second wire is to te rigt o te pole and orms a 60 angle wit te ground How tall is te pole? Simply your answer 5 Greg watces as a ot air balloon rises and comes to a stop at a eigt o 7 eet Te angle o elevation o te ot air balloon rom were e is currently standing is 7 How ar does Greg need to walk e wants to stand directly underneat te balloon?
Honors Calculus Midterm Review Packet
Name Date Period Honors Calculus Midterm Review Packet TOPICS THAT WILL APPEAR ON THE EXAM Capter Capter Capter (Sections. to.6) STRUCTURE OF THE EXAM Part No Calculators Miture o multiple-coice, matcing,
CALCULUS MPT SAMPLE QUESTIONS
CALCULUS MPT SAMPLE QUESTIONS Important Note: Calculators are not permitted wen writing te Mat Placement Test. In order to fully enefit from tese practice prolems, you sould solve tem witout te aid of
Math 102 TEST CHAPTERS 3 & 4 Solutions & Comments Fall 2006
Mat 102 TEST CHAPTERS 3 & 4 Solutions & Comments Fall 2006 f(x+) f(x) 10 1. For f(x) = x 2 + 2x 5, find ))))))))) and simplify completely. NOTE: **f(x+) is NOT f(x)+! f(x+) f(x) (x+) 2 + 2(x+) 5 ( x 2
Section 2.4: Definition of Function
Section.4: Definition of Function Objectives Upon completion of tis lesson, you will be able to: Given a function, find and simplify a difference quotient: f ( + ) f ( ), 0 for: o Polynomial functions
MATH Fall 08. y f(x) Review Problems for the Midterm Examination Covers [1.1, 4.3] in Stewart
![MATH Fall 08. y f(x) Review Problems for the Midterm Examination Covers [1.1, 4.3] in Stewart](/thumbs/87/95118706.jpg "MATH Fall 08. y f(x) Review Problems for the Midterm Examination Covers [1.1, 4.3] in Stewart")
MATH 121 - Fall 08 Review Problems for te Midterm Eamination Covers [1.1, 4.3] in Stewart 1. (a) Use te definition of te derivative to find f (3) wen f() = π 1 2. (b) Find an equation of te tangent line
INTRODUCTION TO CALCULUS LIMITS
Calculus can be divided into two ke areas: INTRODUCTION TO CALCULUS Differential Calculus dealing wit its, rates of cange, tangents and normals to curves, curve sketcing, and applications to maima and
3.1 Extreme Values of a Function
.1 Etreme Values of a Function Section.1 Notes Page 1 One application of te derivative is finding minimum and maimum values off a grap. In precalculus we were only able to do tis wit quadratics by find
MATH 111 CHAPTER 2 (sec )
MATH CHAPTER (sec -0) Terms to know: function, te domain and range of te function, vertical line test, even and odd functions, rational power function, vertical and orizontal sifts of a function, reflection
Integral Calculus, dealing with areas and volumes, and approximate areas under and between curves.
Calculus can be divided into two ke areas: Differential Calculus dealing wit its, rates of cange, tangents and normals to curves, curve sketcing, and applications to maima and minima problems Integral
1. 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
UNIT #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.
Chapter 2 Limits and Continuity. Section 2.1 Rates of Change and Limits (pp ) Section Quick Review 2.1
Section. 6. (a) N(t) t (b) days: 6 guppies week: 7 guppies (c) Nt () t t t ln ln t ln ln ln t 8. 968 Tere will be guppies ater ln 8.968 days, or ater nearly 9 days. (d) Because it suggests te number o
2.8 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
Sec 3.1. lim and lim e 0. Exponential Functions. f x 9, write the equation of the graph that results from: A. Limit Rules
Sec 3. Eponential Functions A. Limit Rules. r lim a a r. I a, then lim a and lim a 0 3. I 0 a, then lim a 0 and lim a 4. lim e 0 5. e lim and lim e 0 Eamples:. Starting with the graph o a.) Shiting 9 units
MA119-A Applied Calculus for Business Fall Homework 4 Solutions Due 9/29/ :30AM
MA9-A Applied Calculus for Business 006 Fall Homework Solutions Due 9/9/006 0:0AM. #0 Find te it 5 0 + +.. #8 Find te it. #6 Find te it 5 0 + + = (0) 5 0 (0) + (0) + =.!! r + +. r s r + + = () + 0 () +
Math Final Review. 1. Match the following functions with the given graphs without using your calculator: f3 (x) = x4 x 5.
Mat 5 Final Review. Matc te following functions wit te given graps witout using our calculator: f () = /3 f4 () = f () = /3 54 5 + 5 f5 () = f3 () = 4 5 53 5 + 5 f6 () = 5 5 + 5 (Ans: A, E, D, F, B, C)
MAT 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
Some Review Problems for First Midterm Mathematics 1300, Calculus 1
Some Review Problems for First Midterm Matematics 00, Calculus. Consider te trigonometric function f(t) wose grap is sown below. Write down a possible formula for f(t). Tis function appears to be an odd,
Exam 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),
Continuity and Differentiability
Continuity and Dierentiability Tis capter requires a good understanding o its. Te concepts o continuity and dierentiability are more or less obvious etensions o te concept o its. Section - INTRODUCTION
Math 151 Project 1 (60 points) Due Thursday 20 th September
Mat 151 Project 1 (60 points) Due Tursday 0 t September Students Name: Tis Project is to elp you to review some of te concepts from Precalc I and II tat you will use in tis class. Tese questions need to
Chapter 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 ( )(
CHAPTER (A) When x = 2, y = 6, so f( 2) = 6. (B) When y = 4, x can equal 6, 2, or 4.
SECTION 3-1 101 CHAPTER 3 Section 3-1 1. No. A correspondence between two sets is a function only if eactly one element of te second set corresponds to eac element of te first set. 3. Te domain of a function
1 2 x Solution. The function f x is only defined when x 0, so we will assume that x 0 for the remainder of the solution. f x. f x h f x.
Problem. Let f x x. Using te definition of te derivative prove tat f x x Solution. Te function f x is only defined wen x 0, so we will assume tat x 0 for te remainder of te solution. By te definition of
Pre-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
Midterm #1B. x 8 < < x 8 < 11 3 < x < x > x < 5 or 3 2x > 5 2x < 8 2x > 2
Mat 30 College Algebra Februar 2, 2016 Midterm #1B Name: Answer Ke David Arnold Instructions. ( points) For eac o te ollowing questions, select te best answer and darken te corresponding circle on our
Excerpt from "Calculus" 2013 AoPS Inc.
Excerpt from "Calculus" 03 AoPS Inc. Te term related rates refers to two quantities tat are dependent on eac oter and tat are canging over time. We can use te dependent relationsip between te quantities
SFU 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
REVIEW SHEET 1 SOLUTIONS ( ) ( ) ( ) x 2 ( ) t + 2. t x +1. ( x 2 + x +1 + x 2 # x ) 2 +1 x ( 1 +1 x +1 x #1 x ) = 2 2 = 1
REVIEW SHEET SOLUTIONS Limit Concepts and Problems + + + e sin t + t t + + + + + e sin t + t t e cos t + + t + + + + + + + + + + + + + t + + t + t t t + + + + + + + + + + + + + + + + t + + a b c - d DNE
MVT 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
Differentiation. introduction to limits
9 9A Introduction to limits 9B Limits o discontinuous, rational and brid unctions 9C Dierentiation using i rst principles 9D Finding derivatives b rule 9E Antidierentiation 9F Deriving te original unction
Name Date. Show all work! Exact answers only unless the problem asks for an approximation.
Advanced Calculus & AP Calculus AB Summer Assignment Name Date Show all work! Eact answers only unless the problem asks for an approimation. These are important topics from previous courses that you must
= h. Geometrically this quantity represents the slope of the secant line connecting the points
Section 3.7: Rates of Cange in te Natural and Social Sciences Recall: Average rate of cange: y y y ) ) ), ere Geometrically tis quantity represents te slope of te secant line connecting te points, f (
MATH 3208 MIDTERM REVIEW. (B) {x 4 x 5 ; x ʀ} (D) {x x ʀ} Use the given functions to answer questions # 3 5. determine the value of h(7).
MATH 08 MIDTERM REVIEW. If () = (f + g)() wat is te domain of () { 5 4 ; ʀ} { 4 4 ; ʀ} { 4 5 ; ʀ} { ʀ}. Given p() = and g() = wic function represents k() k() = p() g() + + Use te given functions to answer
1. Consider the trigonometric function f(t) whose graph is shown below. Write down a possible formula for f(t).
. Consider te trigonometric function f(t) wose grap is sown below. Write down a possible formula for f(t). Tis function appears to be an odd, periodic function tat as been sifted upwards, so we will use
Continuity 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;
Math Final Review. 1. Match the following functions with the given graphs without using your calculator: f 5 (x) = 5x3 25 x.
Mat 5 Final Review. Matc te following functions wit te given graps witout using our calculator: f () = /3 f () = /3 f 3 () = 4 5 (A) f 4 () = 54 5 + 5 (B) f 5 () = 53 5 + 5 (C) (D) f 6 () = 5 5 + 5 (E)
Name: Sept 21, 2017 Page 1 of 1
MATH 111 07 (Kunkle), Eam 1 100 pts, 75 minutes No notes, books, electronic devices, or outside materials of an kind. Read eac problem carefull and simplif our answers. Name: Sept 21, 2017 Page 1 of 1
6.2 TRIGONOMETRY OF RIGHT TRIANGLES
8 CHAPTER 6 Trigonometric Functions: Rigt Triangle Approac 6. TRIGONOMETRY OF RIGHT TRIANGLES Trigonometric Ratios Special Triangles; Calculators Applications of Trigonometry of Rigt Triangles In tis section
2.11 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
Answer Key-Math 11- Optional Review Homework For Exam 2
Answer Key-Math - Optional Review Homework For Eam 2. Compute the derivative or each o the ollowing unctions: Please do not simpliy your derivatives here. I simliied some, only in the case that you want
MATH1901 Differential Calculus (Advanced)
MATH1901 Dierential Calculus (Advanced) Capter 3: Functions Deinitions : A B A and B are sets assigns to eac element in A eactl one element in B A is te domain o te unction B is te codomain o te unction
Recall from our discussion of continuity in lecture a function is continuous at a point x = a if and only if
Computational Aspects of its. Keeping te simple simple. Recall by elementary functions we mean :Polynomials (including linear and quadratic equations) Eponentials Logaritms Trig Functions Rational Functions
Math 1160 Final Review (Sponsored by The Learning Center) cos xcsc tan. 2 x. . Make the trigonometric substitution into
Math 60 Final Review (Sponsored by The Learning Center). Simplify cot csc csc. Prove the following identities: cos csc csc sin. Let 7sin simplify.. Prove: tan y csc y cos y sec y cos y cos sin y cos csc
Section 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
MTH 119 Pre Calculus I Essex County College Division of Mathematics Sample Review Questions 1 Created April 17, 2007
MTH 9 Pre Calculus I Essex County College Division of Matematics Sample Review Questions Created April 7, 007 At Essex County College you sould be prepared to sow all work clearly and in order, ending
= 0 and states ''hence there is a stationary point'' All aspects of the proof dx must be correct (c)
Paper 1: Pure Matematics 1 Mark Sceme 1(a) (i) (ii) d d y 3 1x 4x x M1 A1 d y dx 1.1b 1.1b 36x 48x A1ft 1.1b Substitutes x = into teir dx (3) 3 1 4 Sows d y 0 and states ''ence tere is a stationary point''
Derivatives 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
Chapter 2. Limits and Continuity 16( ) 16( 9) = = 001. Section 2.1 Rates of Change and Limits (pp ) Quick Review 2.1
Capter Limits and Continuity Section. Rates of Cange and Limits (pp. 969) Quick Review..... f ( ) ( ) ( ) 0 ( ) f ( ) f ( ) sin π sin π 0 f ( ). < < < 6. < c c < < c 7. < < < < < 8. 9. 0. c < d d < c
AP Calculus BC Summer Review
AP Calculus BC 07-08 Summer Review Due September, 07 Name: All students entering AP Calculus BC are epected to be proficient in Pre-Calculus skills. To enhance your chances for success in this class, it
Precalculus 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.
AP CALCULUS AB,...) of Topical Understandings ~
Name: Precalculus Teacher: AP CALCULUS AB ~ (Σer) ( Force Distance) and ( L, L,...) of Topical Understandings ~ As instructors of AP Calculus, we have etremely high epectations of students taking our courses.
Solutions Exam 4 (Applications of Differentiation) 1. a. Applying the Quotient Rule we compute the derivative function of f as follows:
MAT 4 Solutions Eam 4 (Applications of Differentiation) a Applying the Quotient Rule we compute the derivative function of f as follows: f () = 43 e 4 e (e ) = 43 4 e = 3 (4 ) e Hence f '( ) 0 for = 0
* Circle these problems: 23-27, 37, 40-44, 48, No Calculator!
AdvPreCal 1 st Semester Final Eam Review Name 1. Solve using interval notation: 7 8 * Circle these problems: -7, 7, 0-, 8, 6-66 No Calculator!. Solve and graph: 0. Solve using a number line and leave answer
Math 262 Exam 1 - Practice Problems. 1. Find the area between the given curves:
Mat 6 Exam - Practice Problems. Find te area between te given curves: (a) = x + and = x First notice tat tese curves intersect wen x + = x, or wen x x+ =. Tat is, wen (x )(x ) =, or wen x = and x =. Next,
Polynomial Functions. Linear Functions. Precalculus: Linear and Quadratic Functions
Concepts: definition of polynomial functions, linear functions tree representations), transformation of y = x to get y = mx + b, quadratic functions axis of symmetry, vertex, x-intercepts), transformations
Solutions 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
Differential Equaitons Equations
Welcome to Multivariable Calculus / Dierential Equaitons Equations The Attached Packet is or all students who are planning to take Multibariable Multivariable Calculus/ Dierential Equations in the all.
Name: 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
pancakes. A typical pancake also appears in the sketch above. The pancake at height x (which is the fraction x of the total height of the cone) has
Volumes One can epress volumes of regions in tree dimensions as integrals using te same strateg as we used to epress areas of regions in two dimensions as integrals approimate te region b a union of small,
MATH 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
Conductance from Transmission Probability
Conductance rom Transmission Probability Kelly Ceung Department o Pysics & Astronomy University o Britis Columbia Vancouver, BC. Canada, V6T1Z1 (Dated: November 5, 005). ntroduction For large conductors,
Chapter 1 Functions and Graphs. Section 1.5 = = = 4. Check Point Exercises The slope of the line y = 3x+ 1 is 3.
Capter Functions and Graps Section. Ceck Point Exercises. Te slope of te line y x+ is. y y m( x x y ( x ( y ( x+ point-slope y x+ 6 y x+ slope-intercept. a. Write te equation in slope-intercept form: x+
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
1. State whether the function is an exponential growth or exponential decay, and describe its end behaviour using limits.
Questions 1. State weter te function is an exponential growt or exponential decay, and describe its end beaviour using its. (a) f(x) = 3 2x (b) f(x) = 0.5 x (c) f(x) = e (d) f(x) = ( ) x 1 4 2. Matc te
Honors Accelerated Pre-Calculus Midterm Exam Review Name: January 2010 Chapter 1: Functions and Their Graphs
Honors Accelerated Pre-Calculus Midterm Eam Review Name: January 010 Chapter 1: Functions and Their Graphs 1. Evaluate the function at each specified value of the independent variable and simplify. 1 f
4.1 & 4.2 Student Notes Using the First and Second Derivatives. for all x in D, where D is the domain of f. The number f()
4.1 & 4. Student Notes Using the First and Second Derivatives Deinition A unction has an absolute maimum (or global maimum) at c i ( c) ( ) or all in D, where D is the domain o. The number () c is called
Review for Exam IV MATH 1113 sections 51 & 52 Fall 2018
Review for Exam IV MATH 111 sections 51 & 52 Fall 2018 Sections Covered: 6., 6., 6.5, 6.6, 7., 7.1, 7.2, 7., 7.5 Calculator Policy: Calculator use may be allowed on part of te exam. Wen instructions call
3.4 Algebraic Limits. Ex 1) lim. Ex 2)
Calculus Maimus.4 Algebraic Limits At tis point, you sould be very comfortable finding its bot grapically and numerically wit te elp of your graping calculator. Now it s time to practice finding its witout
MTH-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
R3.6 Solving Linear Inequalities. 3) Solve: 2(x 4) - 3 > 3x ) Solve: 3(x 2) > 7-4x. R8.7 Rational Exponents
Level D Review Packet - MMT This packet briefly reviews the topics covered on the Level D Math Skills Assessment. If you need additional study resources and/or assistance with any of the topics below,
AP Calculus AB Summer Assignment
AP Calculus AB Summer Assignment As Advanced placement students, our irst assignment or the 07-08 school ear is to come to class the ver irst da in top mathematical orm. Calculus is a world o change. While
MATH 2 - PROBLEM SETS
MATH - PROBLEM SETS Problem Set 1: 1. Simplify and write without negative eponents or radicals: a. c d p 5 y cd b. 5p 1 y. Joe is standing at the top of a 100-foot tall building. Mike eits the building
Continuity and Differentiability of the Trigonometric Functions
[Te basis for te following work will be te definition of te trigonometric functions as ratios of te sides of a triangle inscribed in a circle; in particular, te sine of an angle will be defined to be te
Math 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
Finding 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
1. Evaluate the function at each specified value of the independent variable and simplify. f 2a.)
Honors Pre-Calculus Midterm Eam Review Name: January 04 Chapter : Functions and Their Graphs. Evaluate the function at each specified value of the independent variable and simplify. f ( ) f () b. f ( )
5.1 We will begin this section with the definition of a rational expression. We
Basic Properties and Reducing to Lowest Terms 5.1 We will begin tis section wit te definition of a rational epression. We will ten state te two basic properties associated wit rational epressions and go
1. sin 2. Honors Pre-Calculus Final Exam Review 2 nd semester June TRIGONOMETRY Solve for 0 2. without using a calculator: 2. csc 2 3.
Honors Pre-Calculus Name: Final Eam Review nd semester June 05 TRIGONOMETRY Solve for 0 without using a calculator:. sin. csc. tan. cos ) ) ) ) Solve for in degrees giving all solutions. 5. sin 6. cos
Math 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
Directions: Please read questions carefully. It is recommended that you do the Short Answer Section prior to doing the Multiple Choice.
AP Calculus AB SUMMER ASSIGNMENT Multiple Choice Section Directions: Please read questions carefully It is recommended that you do the Short Answer Section prior to doing the Multiple Choice Show all work
Exercises for numerical differentiation. Øyvind Ryan
Exercises for numerical differentiation Øyvind Ryan February 25, 2013 1. Mark eac of te following statements as true or false. a. Wen we use te approximation f (a) (f (a +) f (a))/ on a computer, we can
HOMEWORK HELP 2 FOR MATH 151
HOMEWORK HELP 2 FOR MATH 151 Here we go; te second round of omework elp. If tere are oters you would like to see, let me know! 2.4, 43 and 44 At wat points are te functions f(x) and g(x) = xf(x)continuous,
Math 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
1. sin 2. csc 2 3. tan 1 2. Cos 8) Sin 10. sec. Honors Pre-Calculus Final Exam Review 2 nd semester. TRIGONOMETRY Solve for 0 2
Honors Pre-Calculus Final Eam Review nd semester Name: TRIGONOMETRY Solve for 0 without using a calculator: 1 1. sin. csc 3. tan 1 4. cos 1) ) 3) 4) Solve for in degrees giving all solutions. 5. sin 1
Higher 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.
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.
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 NON-CALCULATOR DIRECTIONS: The problems
INTRODUCTION AND MATHEMATICAL CONCEPTS
Capter 1 INTRODUCTION ND MTHEMTICL CONCEPTS PREVIEW Tis capter introduces you to te basic matematical tools for doing pysics. You will study units and converting between units, te trigonometric relationsips
Exam Review 2 nd Semester 6-1 Operations on Functions
NAME DATE PERIOD Exam Review 2 nd Semester 6-1 Operations on Functions Find (f + g)(x), (f g)(x), (f g)(x), and (x) for each f(x) and g(x). 1. f(x) = 8x 3; g(x) = 4x + 5 2. f(x) = + x 6; g(x) = x 2 If
qwertyuiopasdfghjklzxcvbnmqwerty uiopasdfghjklzxcvbnmqwertyuiopasd fghjklzxcvbnmqwertyuiopasdfghjklzx cvbnmqwertyuiopasdfghjklzxcvbnmq
qwertyuiopasdfgjklzxcbnmqwerty uiopasdfgjklzxcbnmqwertyuiopasd fgjklzxcbnmqwertyuiopasdfgjklzx cbnmqwertyuiopasdfgjklzxcbnmq Projectile Motion Quick concepts regarding Projectile Motion wertyuiopasdfgjklzxcbnmqwertyui
( ) 2 + 2x 3! ( x x ) 2
Review for The Final Math 195 1. Rewrite as a single simplified fraction: 1. Rewrite as a single simplified fraction:. + 1 + + 1! 3. Rewrite as a single simplified fraction:! 4! 4 + 3 3 + + 5! 3 3! 4!
Technical Calculus I Homework. Instructions
Technical Calculus I Homework Instructions 1. Each assignment is to be done on one or more pieces of regular-sized notebook paper. 2. Your name and the assignment number should appear at the top of the
2.3 More Differentiation Patterns
144 te derivative 2.3 More Differentiation Patterns Polynomials are very useful, but tey are not te only functions we need. Tis section uses te ideas of te two previous sections to develop tecniques for
Limits and an Introduction to Calculus
Limits and an Introduction to Calculus. Introduction to Limits. Tecniques for Evaluating Limits. Te Tangent Line Problem. Limits at Infinit and Limits of Sequences.5 Te Area Problem In Matematics If a
( ) 9 b) y = x x c) y = (sin x) 7 x d) y = ( x ) cos x
NYC College of Technology, CUNY Mathematics Department Spring 05 MAT 75 Final Eam Review Problems Revised by Professor Africk Spring 05, Prof. Kostadinov, Fall 0, Fall 0, Fall 0, Fall 0, Fall 00 # Evaluate
Exponentials 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
Calculus 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.
2. Use your graphing calculator to graph each of the functions below over the interval 2, 2
MSLC Math 0 Final Eam Review Disclaimer: This should NOT be used as your only guide for what to study. if 0. Use the piece-wise defined function f( ) to answer the following: if a. Compute f(0), f(), f(-),
Section 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
INTRODUCTION AND MATHEMATICAL CONCEPTS
INTODUCTION ND MTHEMTICL CONCEPTS PEVIEW Tis capter introduces you to te basic matematical tools for doing pysics. You will study units and converting between units, te trigonometric relationsips of sine,