MATH 150: Answers to even numbered HW assignment problems
|
|
- Theodora Mason
- 5 years ago
- Views:
Transcription
1 MATH 5: Answers to even numbered HW assignment problems Section. # 4: (a) When $ is spent on advertising, the number of sales per month is 35; (b) I; (c) the number of sales if no money is spent on advertising. # : f(5) = 4.. # 2 (a) and (b): Expected return * Risk # 4: (a) At t = 3 minutes the temperature was C. (b) Initial temperature of the object was a C. At time t = b the object s temperature is C. # 8: (a) III; (b) Vertical intercept represents the temperature of potato at t =. # 2: Heart rate time Section.2 # 2: Slope is 3/2, vertical intercept is 4. #8: y = 7+3x. # 2: (a) P =3, t; (b) P () = 39, 2. (c) Population will reach 45, in about 6.82 years (t =6.82), or during the year 26.
2 Section.3 # 2: concave up. # 6: (a) intervals between D and E, between H and I; (b) intervals between A and B, between E and F ; (c) intervals between C and D, between G and H; (d) intervals between B and C, between F and G; # 8: (a) 6.4 billion $; (b) 3.28 billion $ per year; (c) 6. billion $ between 2 and 2. Section.5 # 2: (a) initial amount = ; growth; growth rate = 7 % =.7; (b) initial amount = 5.3; growth; growth rate = 5.4 % =.54; (c) initial amount = 35; decay; decay rate = - 7 % = -.7; (b) initial amount = 2; decay; decay rate = -2 % =.2. #6: (a)q =3 2t, 3 Q (grams) 5 t (days) (b) Q =3 (.88) t, 3 Q (grams) 5 t (days) 2
3 # : (a) II; (b) I; (a) III; (b) V; IV shows exponential decay; VI shows linear decay. # 8: (a) neither; (b) exponential: s(t) =3.2 (.6) t ; (c) linear: g(u) =.5u # 24: (a) The investment was worth $ after years; (b) it will take about years to get the investment back to $,. Section.6 #8: t =ln 2.3. # 22: (a) Town D is growing the fastest. (b) Town C is largest at t =. (c)townb is decreasing in size. # 24. P =2 (/ e) t 2 (.665) t. Section.8 #2: (a)f(t +) = (t +) 2 + = t 2 +2t +2, (b) f(t 2 +) = (t 2 +) 2 + = t 4 +2t 2 +2, (c) f(2) = 5, (d) 2f(t) =2t 2 +2, (e) [f(t)] 2 +=t 4 +2t #8: (a)f(g(x)) = 2x 2 +2x + 8, (b) g(f(x)) = 2x 2 +3, (c) f(f(x)) = 8x 4. # 2: (a) y = u 6,whereu =5t 2 2; (b) P =2e u,whereu =.6t; (c) C =2ln(u), where u = q 3 +. # 3: (a) f(g()) = f(2) = 3; (b) f(g()) = f(3) = 4; (c) f(g(2)) = f(5) = ; (d) g(f(2)) = g(3) = 8; (e) g(f(3)) = g(4) = 2. Section.9 #2: yes,y =3x 2, k =3,p = 2. #6: yes,y =(5/2)x /2, k =5/2, p = /2. # 4: E = kv 3,wherek is a constant. Review for Chapter # 6: (b) 2; (c) 8; (d) 56; (e) decreasing; (f) concave down. # 24: y =.4x +2. # 32: g(x) = xcould be linear; h(x) =5.6 x could be exponential; f(x) is neither. Section 2. #4: slope 3: point F ; slope : point C; slope : point E; slope /2: point A; slope : point B; slope 2: point D. 3
4 # 6: (a) The average rate of change between x =andx =3isgreater than the average rate of change between x =3andx =5sinceslopeofAB > slope of BC y B * * C A * 3 5 x (b) The function is increasing faster at x = than at x =4. Thus, instantaneous rate of change at x = is greater than that at x =4. y This slope is larger 4 x # 4: x : d b c a e f (x) : # 24: (a) f(4) >f(3); (b) f(2) f() >f(3) f(2); (c) f(2) f() 2 > f(3) f() ; 3 (d) f () >f (4). 4
5 Section 2.2 # : IV. # 4: (a) f (2) 3; (b) f (x) is positive for <x<4and is negative for 4 <x<2 Section 2.3 #4: (a)f(2) = 35 means that it costs $35 to produce 2 gallons of ice cream; (b) f (2) =.4 means that when the number of gallons produced is 2, it costs $.4 to produce an additional gallon. # 2: (a) f(4) = 2 means that a patient weighing 4 pounds should receive a dose of 2 mg; f (4) = 3 tells us that if the weight of a patient increases by pound (from 4 pounds), the dose should be increased by 3 mg; (b) f(45) = 5 mg. # 22: f(22) f(2) + f (2) 2 = = 357. Section 2.4 #2: f (x) >, f (x) >. #4: f (x) <, f (x) =. # : f (t) > on the intervals <t<.4 and.7 <t<3.4; f (t) < on the intervals.4 <t<.7 and3.4 <t<4; f (t) > on the interval <t<2.6; f (t) < on the intervals <t<and2.6 <t<4. # 2: (a) f(x) < atx 4 and x 5 ; (b) f (x) < atx 3 and x 4 ; (c) f(x) is decreasing at x 3 and x 4 ; (d) f (x) is decreasing at x 2 and x 3 ; (e) slope of f(x) is positive at x, x 2 and x 5 ; (f) slope of f(x) isincreasingat x, x 4 and x 5. Review for Chapter 2 # : f (x) x # 8: f(26) f(25)+f (25) =3.4; f(3) f(25)+f (25) 5 =
6 #2: (a) f(8) = 55: consuming 8 Calories per day results in a weight of 55 pounds; f (2) = : consuming 2 Calories per day causes neither weight gain nor loss; (b) units of dw/dc are pounds/(calories/day). # 26: B. Section: Focus on Theory (Chapter 2, pp. 35 4) # : x 2: NO, x.5: YES. # 6: YES. # 24: # 32: f (x) = lim h 5(x + h) 5x h = lim h 5=5. f (x) = lim h 2(x + h) 2 +(x + h) 2x 2 x h = lim h 4xh +2h 2 + h h Section 3. #4: y = 2x 3. # 4: y =24t 2 8t + 2. # 6: y = 2x 3 2x 2 6. # 24: y =2z 2z 2. = lim h (4x +2h +)=4x +. Section 3.2 #6: f =5 5 x ln(5) x ln(6). # 6: y = (ln ) x x. 2 # 8: D = /p. # 22: f = Ae t + B/t. # 26: f() = 4 megawatts; f(5) = 4 (.3) 5 = 53, 233 megawatts; f () = 4 ln(.3) = 273 megawatts/year; f (5) = 4 ln(.3) (.3) 5=3, 967 megawatts/year. Section 3.3 #6: w =5 (5r 6) 2. 6
7 # 6: f =3E 5x 2xe x2. # 22: f = 2t t 2 +. # 3: y =2(5+e x )e x. # 38: f(4) = 27e.4 (4) =5.4ng/ml; f (4) = 3.78e.4 (4) = 2.6 ng/ml per hour. Section 3.4 #8: y = e t (t 2 +2t +3). # 6: f = e z 2 z ze z. # 26: # 28: y (x) = e x ( + e x ) 2. y (z) = z ln z z z(ln z) 2. Section 3.5 #6: y =5cosx 5. #8: R =5cos(5t). # 4: y =2cos(2t) 4sin(4t). Review for Chapter 3 #8: s =5t 2 2t + 2. # 2: R =5(sint) 4 (cos t). # 36: h = 2p (3 + 2p 2 ) 2. Section 4. #8: f (x) =3x 2 6, and thus, f (x) =atx = ± 2. f (x) changes from positive to negative at x = 2, and so there is a local maximum at x = 2. f (x) changes from negative to positive at x =+ 2, and so there is a local minimum at x =+ 2. 7
8 # 2: f (x) =lnx +, so f (x) =whenlnx =, that is, for x = e.37. This is the only place where f changes sign. Since f () >, the function f increases for <x<e and increases for x>e.thus,we have local minimum at x = e. Section 4.2 # 6: critical points at x = (local min) and at x = (neither min nor max); inflection points at x =andatx =2/3. Section 4.3 # 22: Local and global maximum at x =2. # 3: de df =.25 2 (.7) F 3 =, thus, ( ) /3 2 (.7) F = =2.4 hours..25 This gives a local and global minimum. # 44: (a) At t =wehaveq() = ; (b) Maximum value occurs at t =ln2=.69 (where q (t) = ); maximum value is q(ln 2) = 5 mg; (c) as t we have q(t). Section 4.4 # 2: Profit function is positive for 5.5 <q<2.5 (whenr(q) >C(q)), and negative for <q<5.5, q>2.5(whenr(q) <C(q)). Profit maximized when R(q) >C(q) andr (q) =C (q) which occurs at about q =9.5. # 6: Profit is maximized at q = 75; profit = R(75) C(75) = $ Section 4.8 # 6: (a) At peak concentration C (t) = ; corresponding t =/.3 = 33.3 minutes;c(33.3) 245 ng/ml; (b) after 5 min C(5) 9 ng/ml; after one hour C(6) 98 ng/ml. Review for Chapter 4 # 8: (a) Increasing for all x. (b) No max or min. # : (a) Decreasing for x< ; <x<; increasing for x>; < x<. (b) f( ) and f() are local minima; f() is a local maximum. 8
9 Section 7. #6: t 8 /8+t 4 /4+C. # 4: # 8: ln z + C. # 46: # 5: 2x 4 +ln x + C. 2 3 z3/2 + C. e 2t 2 + C. Section 7.2 #4: e 5t+2 + C. # 2: 6 (x2 +3) 3 + C. # 2: 8 (cos θ +5)8 + C. # 34: # 36: 2e y + C. # 38: ln(2 + e x )+C. 2 ln(y2 +4)+C. Section 7.3 #6: # : # 22: 4 x dx =2. 5t 3 dt = x(x 2 +) 2 dx = Section 5.3 #2: Area=8. 9
10 y=x x # 4: Negative. #6: Zero. # 6: (a) 3; (b) 2; (c) ; (d) 5. Section 5.4 # 4: The change in velocity between times t =andt = 6 hours; it is measured in km/hr. # 2: 2627 acres. Section 5.5 # 6: The fixed cost is $5. Total variable cost is $ Total cost is $5 + $866.7 = $, Review for Chapter 5 # : 5 (x 2 +)dx = # 4: 3 ( ) x x ( ) z 2 (z +/z)dz = 2 +ln(z) # 32: Since f(x) = +x 3 is increasing for x 2, we have so that 2= f()dx dx f(x)dx f(x)dx # 36: Total cost is 4,25, riyals. f(2)dx, 3dx =6.
11 Section 6. #2: Average value = 3 f(x)dx =8. 3 # 4: Average value = 2. # 6: Average value # 2(a): Average inventory # 22: (c) < (a) < (b). Section 7.4 #6: F()= F()= x # 6: F () =, F (3) = 7, F () =, F (4) = 5. Review for Chapter 7 #6: ln x x 2x + C. 2 # 2: 3 sin(x)+7cos(x)+c. # 36: x2 +4+C. Section. # 2: (a) (III); (b) (V); (c) (I); (d) (II); (e) (IV). # 8: Rate of change of B =Ratein Rate out: db dt =.4B 2. Section.2 # 6: E.
12 # 8: A. # 22: (a) II; (b) I. Section.4 #2: w =3e 3r. #4: Q =5e t/5. #6: p = 64.87e.q. Section.5 #4: P = 4e t 4. #6: Q = 4 35e.3 t. 2
Section 3.1 Homework Solutions. 1. y = 5, so dy dx = y = 3x, so dy dx = y = x 12, so dy. dx = 12x11. dx = 12x 13
Math 122 1. y = 5, so dx = 0 2. y = 3x, so dx = 3 3. y = x 12, so dx = 12x11 4. y = x 12, so dx = 12x 13 5. y = x 4/3, so dx = 4 3 x1/3 6. y = 8t 3, so = 24t2 7. y = 3t 4 2t 2, so = 12t3 4t 8. y = 5x +
More informationGOOD LUCK! 2. a b c d e 12. a b c d e. 3. a b c d e 13. a b c d e. 4. a b c d e 14. a b c d e. 5. a b c d e 15. a b c d e. 6. a b c d e 16.
MA109 College Algebra Fall 2018 Practice Final Exam 2018-12-12 Name: Sec.: Do not remove this answer page you will turn in the entire exam. You have two hours to do this exam. No books or notes may be
More informationSpring 2015 Sample Final Exam
Math 1151 Spring 2015 Sample Final Exam Final Exam on 4/30/14 Name (Print): Time Limit on Final: 105 Minutes Go on carmen.osu.edu to see where your final exam will be. NOTE: This exam is much longer than
More informationb) The trend is for the average slope at x = 1 to decrease. The slope at x = 1 is 1.
Chapters 1 to 8 Course Review Chapters 1 to 8 Course Review Question 1 Page 509 a) i) ii) [2(16) 12 + 4][2 3+ 4] 4 1 [2(2.25) 4.5+ 4][2 3+ 4] 1.51 = 21 3 = 7 = 1 0.5 = 2 [2(1.21) 3.3+ 4][2 3+ 4] iii) =
More informationMath 1120 Calculus Final Exam
May 4, 2001 Name The first five problems count 7 points each (total 35 points) and rest count as marked. There are 195 points available. Good luck. 1. Consider the function f defined by: { 2x 2 3 if x
More informationy+2 x 1 is in the range. We solve x as x =
Dear Students, Here are sample solutions. The most fascinating thing about mathematics is that you can solve the same problem in many different ways. The correct answer will always be the same. Be creative
More informationMATH 122 FALL Final Exam Review Problems
MATH 122 FALL 2013 Final Exam Review Problems Chapter 1 1. As a person hikes down from the top of a mountain, the variable t represents the time, in minutes, since the person left the top of the mountain,
More informationFunctions. A function is a rule that gives exactly one output number to each input number.
Functions A function is a rule that gives exactly one output number to each input number. Why it is important to us? The set of all input numbers to which the rule applies is called the domain of the function.
More informationANSWERS, Homework Problems, Spring 2014 Now You Try It, Supplemental problems in written homework, Even Answers R.6 8) 27, 30) 25
ANSWERS, Homework Problems, Spring 2014, Supplemental problems in written homework, Even Answers Review Assignment: Precalculus Even Answers to Sections R1 R7 R.1 24) 4a 2 16ab + 16b 2 R.2 24) Prime 5x
More informationFinal Exam Review Packet
1 Exam 1 Material Sections A.1, A.2 and A.6 were review material. There will not be specific questions focused on this material but you should know how to: Simplify functions with exponents. Factor quadratics
More informationFinal Exam Review Packet
1 Exam 1 Material Sections A.1, A.2 and A.6 were review material. There will not be specific questions focused on this material but you should know how to: Simplify functions with exponents. Factor quadratics
More informationSection 12.2 The Second Derivative
Section 12.2 The Second Derivative Higher derivatives If f is a differentiable function, then f is also a function. So, f may have a derivative of its own, denoted by (f ) = f. This new function f is called
More informationLecture 5 - Logarithms, Slope of a Function, Derivatives
Lecture 5 - Logarithms, Slope of a Function, Derivatives 5. Logarithms Note the graph of e x This graph passes the horizontal line test, so f(x) = e x is one-to-one and therefore has an inverse function.
More informationApril 9, 2009 Name The problems count as marked. The total number of points available is 160. Throughout this test, show your work.
April 9, 009 Name The problems count as marked The total number of points available is 160 Throughout this test, show your work 1 (15 points) Consider the cubic curve f(x) = x 3 + 3x 36x + 17 (a) Build
More information2. (12 points) Find an equation for the line tangent to the graph of f(x) =
November 23, 2010 Name The total number of points available is 153 Throughout this test, show your work Throughout this test, you are expected to use calculus to solve problems Graphing calculator solutions
More informationFree Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom
Free Response Questions 1969-010 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions
More information2015 Math Camp Calculus Exam Solution
015 Math Camp Calculus Exam Solution Problem 1: x = x x +5 4+5 = 9 = 3 1. lim We also accepted ±3, even though it is not according to the prevailing convention 1. x x 4 x+4 =. lim 4 4+4 = 4 0 = 4 0 = We
More information3. Find the slope of the tangent line to the curve given by 3x y e x+y = 1 + ln x at (1, 1).
1. Find the derivative of each of the following: (a) f(x) = 3 2x 1 (b) f(x) = log 4 (x 2 x) 2. Find the slope of the tangent line to f(x) = ln 2 ln x at x = e. 3. Find the slope of the tangent line to
More informationMath 106 Answers to Exam 1a Fall 2015
Math 06 Answers to Exam a Fall 05.. Find the derivative of the following functions. Do not simplify your answers. (a) f(x) = ex cos x x + (b) g(z) = [ sin(z ) + e z] 5 Using the quotient rule on f(x) and
More informationSection 4.2 Logarithmic Functions & Applications
34 Section 4.2 Logarithmic Functions & Applications Recall that exponential functions are one-to-one since every horizontal line passes through at most one point on the graph of y = b x. So, an exponential
More informationChapter 6: Exponential and Logarithmic Functions
Section 6.1: Algebra and Composition of Functions #1-9: Let f(x) = 2x + 3 and g(x) = 3 x. Find each function. 1) (f + g)(x) 2) (g f)(x) 3) (f/g)(x) 4) ( )( ) 5) ( g/f)(x) 6) ( )( ) 7) ( )( ) 8) (g+f)(x)
More informationSpring 2003, MTH Practice for Exam 3 4.2, 4.3, 4.4, 4.7, 4.8, 5.1, 5.2, 5.3, 5.4, 5.5, 6.1
Spring 23, MTH 3 - Practice for Exam 3 4.2, 4.3, 4.4, 4.7, 4.8, 5., 5.2, 5.3, 5.4, 5.5, 6.. An object travels with a velocity function given by the following table. Assume the velocity is increasing. t(hr)..5..5
More informationAP Calculus Free-Response Questions 1969-present AB
AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions
More informationMAT 122 Homework 7 Solutions
MAT 1 Homework 7 Solutions Section 3.3, Problem 4 For the function w = (t + 1) 100, we take the inside function to be z = t + 1 and the outside function to be z 100. The derivative of the inside function
More informationFinal Exam Study Guide
Final Exam Study Guide Final Exam Coverage: Sections 10.1-10.2, 10.4-10.5, 10.7, 11.2-11.4, 12.1-12.6, 13.1-13.2, 13.4-13.5, and 14.1 Sections/topics NOT on the exam: Sections 10.3 (Continuity, it definition
More informationMath Final Exam Review. 1. The following equation gives the rate at which the angle between two objects is changing during a game:
Math 131 Spring 2008 c Sherry Scarborough and Heather Ramsey Page 1 Math 131 - Final Exam Review 1. The following equation gives the rate at which the angle between two objects is changing during a game:
More informationShow all your work. If you use the calculator, say so and explain what you did. f(x) =(2x +5) 1 3
Old Exams, Math 142, Calculus, Dr. Bart Show all your work. If you use the calculator, say so and explain what you did. 1. Find the domain and range of the following functions: f(x) = p x 2 ; 4 f(x) =ln(x
More informationMatrix Theory and Differential Equations Homework 2 Solutions, due 9/7/6
Matrix Theory and Differential Equations Homework Solutions, due 9/7/6 Question 1 Consider the differential equation = x y +. Plot the slope field for the differential equation. In particular plot all
More informationMath 611b Assignment #6 Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Math 611b Assignment #6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a formula for the function graphed. 1) 1) A) f(x) = 5 + x, x < -
More information2. (10 points) Find an equation for the line tangent to the graph of y = e 2x 3 at the point (3/2, 1). Solution: y = 2(e 2x 3 so m = 2e 2 3
November 24, 2009 Name The total number of points available is 145 work Throughout this test, show your 1 (10 points) Find an equation for the line tangent to the graph of y = ln(x 2 +1) at the point (1,
More informationMath 121 Winter 2010 Review Sheet
Math 121 Winter 2010 Review Sheet March 14, 2010 This review sheet contains a number of problems covering the material that we went over after the third midterm exam. These problems (in conjunction with
More informationis all real numbers.
Math 140 Spring 2017 Suggested Final Review Problems 1. Is each of the following statements true or false? Explain. (a) If f(x) = x 2, then f(x + h) = x 2 + h 2. (b) If g(x) = 3 x, then g(x) can never
More informationChapter 2 Describing Change: Rates
Chapter Describing Change: Rates Section.1 Change, Percentage Change, and Average Rates of Change 1. 3. $.30 $0.46 per day 5 days = The stock price rose an average of 46 cents per day during the 5-day
More informationDoug Clark The Learning Center 100 Student Success Center learningcenter.missouri.edu Overview
Math 1400 Final Exam Review Saturday, December 9 in Ellis Auditorium 1:00 PM 3:00 PM, Saturday, December 9 Part 1: Derivatives and Applications of Derivatives 3:30 PM 5:30 PM, Saturday, December 9 Part
More informationMath 251, Spring 2005: Exam #2 Preview Problems
Math 5, Spring 005: Exam # Preview Problems. Using the definition of derivative find the derivative of the following functions: a) fx) = e x e h. Use the following lim =, e x+h = e x e h.) h b) fx) = x
More informationLecture 26: Section 5.3 Higher Derivatives and Concavity
L26-1 Lecture 26: Section 5.3 Higher Derivatives and Concavity ex. Let f(x) = ln(e 2x + 1) 1) Find f (x). 2) Find d dx [f (x)]. L26-2 We define f (x) = Higher Order Derivatives For y = f(x), we can write
More informationMath Exam 02 Review
Math 10350 Exam 02 Review 1. A differentiable function g(t) is such that g(2) = 2, g (2) = 1, g (2) = 1/2. (a) If p(t) = g(t)e t2 find p (2) and p (2). (Ans: p (2) = 7e 4 ; p (2) = 28.5e 4 ) (b) If f(t)
More informationMathematics for Economics ECON MA/MSSc in Economics-2017/2018. Dr. W. M. Semasinghe Senior Lecturer Department of Economics
Mathematics for Economics ECON 53035 MA/MSSc in Economics-2017/2018 Dr. W. M. Semasinghe Senior Lecturer Department of Economics MATHEMATICS AND STATISTICS LERNING OUTCOMES: By the end of this course unit
More informationAB CALCULUS SEMESTER A REVIEW Show all work on separate paper. (b) lim. lim. (f) x a. for each of the following functions: (b) y = 3x 4 x + 2
AB CALCULUS Page 1 of 6 NAME DATE 1. Evaluate each it: AB CALCULUS Show all work on separate paper. x 3 x 9 x 5x + 6 x 0 5x 3sin x x 7 x 3 x 3 5x (d) 5x 3 x +1 x x 4 (e) x x 9 3x 4 6x (f) h 0 sin( π 6
More informationBusiness and Life Calculus
Business and Life Calculus George Voutsadakis Mathematics and Computer Science Lake Superior State University LSSU Math 2 George Voutsadakis (LSSU) Calculus For Business and Life Sciences Fall 203 / 55
More informationReview Assignment II
MATH 11012 Intuitive Calculus KSU Name:. Review Assignment II 1. Let C(x) be the cost, in dollars, of manufacturing x widgets. Fill in the table with a mathematical expression and appropriate units corresponding
More informationa x a y = a x+y a x a = y ax y (a x ) r = a rx and log a (xy) = log a (x) + log a (y) log a ( x y ) = log a(x) log a (y) log a (x r ) = r log a (x).
You should prepare the following topics for our final exam. () Pre-calculus. (2) Inverses. (3) Algebra of Limits. (4) Derivative Formulas and Rules. (5) Graphing Techniques. (6) Optimization (Maxima and
More informationSolutions to Selected Exercises
59 Solutions to Selected Exercises Chapter Section.. a. f 0 b. Tons of garbage per week is produced by a city with a population of 5,000.. a. In 995 there are 0 ducks in the lake b. In 000 there are 0
More informationMath Final Solutions - Spring Jaimos F Skriletz 1
Math 160 - Final Solutions - Spring 2011 - Jaimos F Skriletz 1 Answer each of the following questions to the best of your ability. To receive full credit, answers must be supported by a sufficient amount
More informationReview for the Final Exam
Math 171 Review for the Final Exam 1 Find the limits (4 points each) (a) lim 4x 2 3; x x (b) lim ( x 2 x x 1 )x ; (c) lim( 1 1 ); x 1 ln x x 1 sin (x 2) (d) lim x 2 x 2 4 Solutions (a) The limit lim 4x
More informationLogarithmic Functions
Logarithmic Functions Definition 1. For x > 0, a > 0, and a 1, y = log a x if and only if x = a y. The function f(x) = log a x is called the logarithmic function with base a. Example 1. Evaluate the following
More informationMath 180, Exam 2, Practice Fall 2009 Problem 1 Solution. f(x) = arcsin(2x + 1) = sin 1 (3x + 1), lnx
Math 80, Exam, Practice Fall 009 Problem Solution. Differentiate the functions: (do not simplify) f(x) = x ln(x + ), f(x) = xe x f(x) = arcsin(x + ) = sin (3x + ), f(x) = e3x lnx Solution: For the first
More informationMath Exam 3 Review
Math 142 Spring 2009 c Heather Ramsey Page 1 Math 142 - Exam 3 Review NOTE: Exam 3 covers sections 5.4-5.6, 6.1, 6.2, 6.4, 6.5, 7.1, and 7.2. This review is intended to highlight the material covered on
More informationMath 120 Final Exam Practice Problems, Form: A
Math 120 Final Exam Practice Problems, Form: A Name: While every attempt was made to be complete in the types of problems given below, we make no guarantees about the completeness of the problems. Specifically,
More informationExam 3 MATH Calculus I
Trinity College December 03, 2015 MATH 131-01 Calculus I By signing below, you attest that you have neither given nor received help of any kind on this exam. Signature: Printed Name: Instructions: Show
More informationCHAPTER FIVE. Solutions for Section 5.1. Skill Refresher. Exercises
CHAPTER FIVE 5.1 SOLUTIONS 265 Solutions for Section 5.1 Skill Refresher S1. Since 1,000,000 = 10 6, we have x = 6. S2. Since 0.01 = 10 2, we have t = 2. S3. Since e 3 = ( e 3) 1/2 = e 3/2, we have z =
More informationUnit #1 - Transformation of Functions, Exponentials and Logarithms
Unit #1 - Transformation of Functions, Exponentials and Logarithms Some problems and solutions selected or adapted from Hughes-Hallett Calculus. Note: This unit, being review of pre-calculus has substantially
More informationMath 131 Final Exam Spring 2016
Math 3 Final Exam Spring 06 Name: ID: multiple choice questions worth 5 points each. Exam is only out of 00 (so there is the possibility of getting more than 00%) Exam covers sections. through 5.4 No graphing
More informationMAC 2233, Survey of Calculus, Exam 3 Review This exam covers lectures 21 29,
MAC 2233, Survey of Calculus, Exam 3 Review This exam covers lectures 21 29, This review includes typical exam problems. It is not designed to be comprehensive, but to be representative of topics covered
More informationCore 3 (A2) Practice Examination Questions
Core 3 (A) Practice Examination Questions Trigonometry Mr A Slack Trigonometric Identities and Equations I know what secant; cosecant and cotangent graphs look like and can identify appropriate restricted
More informationMath 2413 General Review for Calculus Last Updated 02/23/2016
Math 243 General Review for Calculus Last Updated 02/23/206 Find the average velocity of the function over the given interval.. y = 6x 3-5x 2-8, [-8, ] Find the slope of the curve for the given value of
More informationNO CALCULATORS. NO BOOKS. NO NOTES. TURN OFF YOUR CELL PHONES AND PUT THEM AWAY.
FINAL EXAM-MATH 3 FALL TERM, R. Blute & A. Novruzi Name(Print LEGIBLY) I.D. Number Instructions- This final examination consists of multiple choice questions worth 3 points each. Your answers to the multiple
More informationMath 180, Lowman, Summer 2008, Old Exam Problems 1 Limit Problems
Math 180, Lowman, Summer 2008, Old Exam Problems 1 Limit Problems 1. Find the limit of f(x) = (sin x) x x 3 as x 0. 2. Use L Hopital s Rule to calculate lim x 2 x 3 2x 2 x+2 x 2 4. 3. Given the function
More informationChapter 4 Analyzing Change: Applications of Derivatives
Chapter 4 Analyzing Change: Applications of Derivatives Section 4.1 Approximating Change 1. 3% (4 percentage points per hour) 1 ( ) = 1 1 hour 30 % 3 3. 300 mph + (00 mph per hour) ( hour ) 316 3. f (3.5)
More informationSection 5-1 First Derivatives and Graphs
Name Date Class Section 5-1 First Derivatives and Graphs Goal: To use the first derivative to analyze graphs Theorem 1: Increasing and Decreasing Functions For the interval (a,b), if f '( x ) > 0, then
More informationReview for the Final Exam
Calculus Lia Vas. Integrals. Evaluate the following integrals. (a) ( x 4 x 2 ) dx (b) (2 3 x + x2 4 ) dx (c) (3x + 5) 6 dx (d) x 2 dx x 3 + (e) x 9x 2 dx (f) x dx x 2 (g) xe x2 + dx (h) 2 3x+ dx (i) x
More informationMA 109 College Algebra EXAM 3 - REVIEW
MA 109 College Algebra EXAM - REVIEW Name: Sec.: 1. In the picture below, the graph of y = f(x) is the solid graph, and the graph of y = g(x) is the dashed graph. Find a formula for g(x). y (a) g(x) =f(2x)
More informationLSU AP Calculus Practice Test Day
LSU AP Calculus Practice Test Day AP Calculus AB 2018 Practice Exam Section I Part A AP CALCULUS AB: PRACTICE EXAM SECTION I: PART A NO CALCULATORS ALLOWED. YOU HAVE 60 MINUTES. 1. If y = ( 1 + x 5) 3
More informationBig Picture I. MATH 1003 Review: Part 3. The Derivatives of Functions. Big Picture I. Introduction to Derivatives
Big Picture I MATH 1003 Review: Part 3. The Derivatives of Functions Maosheng Xiong Department of Mathematics, HKUST What would the following questions remind you? 1. Concepts: limit, one-sided limit,
More informationThe Princeton Review AP Calculus BC Practice Test 1
8 The Princeton Review AP Calculus BC Practice Test CALCULUS BC SECTION I, Part A Time 55 Minutes Number of questions 8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions: Solve each
More informationMATH 236 ELAC FALL 2017 TEST 3 NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
MATH 6 ELAC FALL 7 TEST NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the integral using integration by parts. ) 9x ln x dx ) ) x 5 -
More information( + ) 3. AP Calculus BC Chapter 6 AP Exam Problems. Antiderivatives. + + x + C. 2. If the second derivative of f is given by f ( x) = 2x cosx
Chapter 6 AP Eam Problems Antiderivatives. ( ) + d = ( + ) + 5 + + 5 ( + ) 6 ( + ). If the second derivative of f is given by f ( ) = cos, which of the following could be f( )? + cos + cos + + cos + sin
More informationFinal Exam Review. MATH Intuitive Calculus Fall 2013 Circle lab day: Mon / Fri. Name:. Show all your work.
MATH 11012 Intuitive Calculus Fall 2013 Circle lab day: Mon / Fri Dr. Kracht Name:. 1. Consider the function f depicted below. Final Exam Review Show all your work. y 1 1 x (a) Find each of the following
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) ±
Final Review for Pre Calculus 009 Semester Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation algebraically. ) v + 5 = 7 - v
More informationBig Picture I. MATH 1003 Review: Part 3. The Derivatives of Functions. Big Picture I. Introduction to Derivatives
Big Picture I MATH 1003 Review: Part 3. The Derivatives of Functions Maosheng Xiong Department of Mathematics, HKUST What would the following questions remind you? 1. Concepts: limit, one-sided limit,
More information24. Partial Differentiation
24. Partial Differentiation The derivative of a single variable function, d f(x), always assumes that the independent variable dx is increasing in the usual manner. Visually, the derivative s value at
More informationISLAMIYA ENGLISH SCHOOL ABU DHABI U. A. E.
ISLAMIYA ENGLISH SCHOOL ABU DHABI U. A. E. MATHEMATICS ASSIGNMENT-1 GRADE-A/L-II(Sci) CHAPTER.NO.1,2,3(C3) Algebraic fractions,exponential and logarithmic functions DATE:18/3/2017 NAME.------------------------------------------------------------------------------------------------
More informationUNIT 3: DERIVATIVES STUDY GUIDE
Calculus I UNIT 3: Derivatives REVIEW Name: Date: UNIT 3: DERIVATIVES STUDY GUIDE Section 1: Section 2: Limit Definition (Derivative as the Slope of the Tangent Line) Calculating Rates of Change (Average
More informationMath Fall 08 Final Exam Review
Math 173.7 Fall 08 Final Exam Review 1. Graph the function f(x) = x 2 3x by applying a transformation to the graph of a standard function. 2.a. Express the function F(x) = 3 ln(x + 2) in the form F = f
More informationExam A. Exam 3. (e) Two critical points; one is a local maximum, the other a local minimum.
1.(6 pts) The function f(x) = x 3 2x 2 has: Exam A Exam 3 (a) Two critical points; one is a local minimum, the other is neither a local maximum nor a local minimum. (b) Two critical points; one is a local
More informationStudy Guide - Part 2
Math 116 Spring 2015 Study Guide - Part 2 1. Which of the following describes the derivative function f (x) of a quadratic function f(x)? (A) Cubic (B) Quadratic (C) Linear (D) Constant 2. Find the derivative
More informationMath Exam 03 Review
Math 10350 Exam 03 Review 1. The statement: f(x) is increasing on a < x < b. is the same as: 1a. f (x) is on a < x < b. 2. The statement: f (x) is negative on a < x < b. is the same as: 2a. f(x) is on
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 informationFINAL REVIEW FALL 2017
FINAL REVIEW FALL 7 Solutions to the following problems are found in the notes on my website. Lesson & : Integration by Substitution Ex. Evaluate 3x (x 3 + 6) 6 dx. Ex. Evaluate dt. + 4t Ex 3. Evaluate
More informationThis Week. Basic Problem. Instantaneous Rate of Change. Compute the tangent line to the curve y = f (x) at x = a.
This Week Basic Problem Compute the tangent line to the curve y = f (x) at x = a. Read Sections 2.7,2.8 and 3.1 in Stewart Homework #2 due 11:30 Thursday evening worksheet #3 in section on Tuesday slope
More informationDifferentiation. 1. What is a Derivative? CHAPTER 5
CHAPTER 5 Differentiation Differentiation is a technique that enables us to find out how a function changes when its argument changes It is an essential tool in economics If you have done A-level maths,
More informationPurdue University Study Guide for MA Credit Exam
Purdue University Study Guide for MA 16010 Credit Exam Students who pass the credit exam will gain credit in MA16010. The credit exam is a two-hour long exam with multiple choice questions. No books or
More informationCollege of the Holy Cross MATH 133, Calculus With Fundamentals 1 Solutions for Final Examination Friday, December 15
College of the Holy Cross MATH 33, Calculus With Fundamentals Solutions for Final Examination Friday, December 5 I. The graph y = f(x) is given in light blue. Match each equation with one of the numbered
More informationPart A: Short Answer Questions
Math 111 Practice Exam Your Grade: Fall 2015 Total Marks: 160 Instructor: Telyn Kusalik Time: 180 minutes Name: Part A: Short Answer Questions Answer each question in the blank provided. 1. If a city grows
More information2.1 The Tangent and Velocity Problems
2.1 The Tangent and Velocity Problems Tangents What is a tangent? Tangent lines and Secant lines Estimating slopes from discrete data: Example: 1. A tank holds 1000 gallons of water, which drains from
More informationApplied Calculus I Practice Final Exam Solution Notes
AMS 5 (Fall, 2009). Solve for x: 0 3 2x = 3 (.2) x Taking the natural log of both sides, we get Applied Calculus I Practice Final Exam Solution Notes Joe Mitchell ln 0 + 2xln 3 = ln 3 + xln.2 x(2ln 3 ln.2)
More informationMATH 115 SECOND MIDTERM EXAM
MATH 115 SECOND MIDTERM EXAM November 22, 2005 NAME: SOLUTION KEY INSTRUCTOR: SECTION NO: 1. Do not open this exam until you are told to begin. 2. This exam has 10 pages including this cover. There are
More information3.1 Derivative Formulas for Powers and Polynomials
3.1 Derivative Formulas for Powers and Polynomials First, recall that a derivative is a function. We worked very hard in 2.2 to interpret the derivative of a function visually. We made the link, in Ex.
More information14 Increasing and decreasing functions
14 Increasing and decreasing functions 14.1 Sketching derivatives READING Read Section 3.2 of Rogawski Reading Recall, f (a) is the gradient of the tangent line of f(x) at x = a. We can use this fact to
More informationSolutions to Intermediate and College Algebra by Rhodes
Solutions to Intermediate and College Algebra by Rhodes Section 1.1 1. 20 2. -21 3. 105 4. -5 5. 18 6. -3 7. 65/2 = 32.5 8. -36 9. 539 208 2.591 10. 13/3 11. 81 12. 60 = 2 15 7.746 13. -2 14. -1/3 15.
More informationMath 131 Week-in-Review #11 (Final Exam Review: All previous sections as well as sections 5.5, 6.1, 6.5, and 6.7)
Math 131 Week-in-Review #11 (Final Exam Review: All previous sections as well as sections 5.5, 6.1, 6.5, and 6.7) Note: This collection of questions is intended to be a brief overview of the exam material
More informationPractice Questions From Calculus II. 0. State the following calculus rules (these are many of the key rules from Test 1 topics).
Math 132. Practice Questions From Calculus II I. Topics Covered in Test I 0. State the following calculus rules (these are many of the key rules from Test 1 topics). (Trapezoidal Rule) b a f(x) dx (Fundamental
More informationAnswer Key for AP Calculus AB Practice Exam, Section I
Answer Key for AP Calculus AB Practice Exam, Section I Multiple-Choice Questions Question # Key B B 3 A 4 E C 6 D 7 E 8 C 9 E A A C 3 D 4 A A 6 B 7 A 8 B 9 C D E B 3 A 4 A E 6 A 7 A 8 A 76 E 77 A 78 D
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) x 8. C) y = x + 3 2
Precalculus Fall Final Exam Review Name Date Period MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. Assume that the variables
More informationIntermediate Algebra Study Guide
Chapter 1 Intermediate Algebra Study Guide 1. Simplify the following. (a) ( 6) + ( 4) ( 9) (b) ( 7) ( 6)( )( ) (c) 8 5 9 (d) 6x(xy x ) x (y 6x ) (e) 7x {6 [8 (x ) (6 x)]} (f) Evaluate x y for x =, y =.
More informationApplied Calculus I. Review Solutions. Qaisar Latif. October 25, 2016
Applied Calculus I Review Solutions Qaisar Latif October 25, 2016 2 Homework 1 Problem 1. The number of people living with HIV infections increased worldwide approximately exponentially from 2.5 million
More informationfor every x in the gomain of g
Section.7 Definition of Inverse Function Let f and g be two functions such that f(g(x)) = x for every x in the gomain of g and g(f(x)) = x for every x in the gomain of f Under these conditions, the function
More informationSection 11.3 Rates of Change:
Section 11.3 Rates of Change: 1. Consider the following table, which describes a driver making a 168-mile trip from Cleveland to Columbus, Ohio in 3 hours. t Time (in hours) 0 0.5 1 1.5 2 2.5 3 f(t) Distance
More informationMATH 205 Practice Final Exam Name:
Name: This test is closed-book and closed-notes. No calculator is allowed for this test. For full credit show all of your work (legibly!), unless otherwise specified. For the purposes of this exam, all
More informationClassroom Voting Questions: Precalculus
Classroom Voting Questions: Precalculus Exponential Functions 1. The graph of a function is either concave up or concave down. (a) True, and I am very confident (b) True, but I am not very confident (c)
More information