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9 Pages

### 1-F02

Course: MATH 131, Fall 2008
School: UMass (Amherst)
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Word Count: 467

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OF DEPARTMENT MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Fall 2002 EXAM 1 Your Name: Your Instructors Name: This exam paper consists of 7 questions. It has 9 pages, where the last is a blank page. On this exam, you may use a calculator, but no books or notes. It is not sucient to just write the answers. You must explain how you arrive at your answers. If you draw a graph, you must include...

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OF DEPARTMENT MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Fall 2002 EXAM 1 Your Name: Your Instructors Name: This exam paper consists of 7 questions. It has 9 pages, where the last is a blank page. On this exam, you may use a calculator, but no books or notes. It is not sucient to just write the answers. You must explain how you arrive at your answers. If you draw a graph, you must include the value of the range variables and show the tick marks on the axes, if any. If your drawing includes the graphs of more than one function, you must label them so that we can tell which is which. 1. (15) 2. (15) 3. (15) 4. (10) 5. (15) 6. (15) 7. (15) TOTAL (100) Math 131FALL 2002 EXAM 1 page 2 1. a) (10) Evaluate the limit 2x2 5x + 2 x2 x3 4x by an algebraic procedure. Show all your algebraic steps. lim b) (5) Support your result in part a) with a calculator. Describe your procedure and show as much data as possible. Math 131FALL 2002 2. Given the function EXAM 1 page 3 f (x) = where a, b are constants. x2 + 1 for x 1 ax + b for x > 1, a) (5) Find lim f (x) and lim f (x). + x1 x1 b) (5) What conditions do a and b have to satisfy, so that f (x) is continuous at x = 1. c) (5) Find a and b, such that f (x) is everywhere dierentiable. Math 131FALL 2002 EXAM 1 page 4 3. a) (10) Find all horizontal and vertical for asymptotes the function f (x) = Explain your reasons. 3x2 + 1 (2x + 3)(x 1) b) (5) Graph the function in part a) indicating all horizontal and vertical asymptotes. Math 131FALL 2002 EXAM 1 page 5 4. (10) Determine the derivative f (x) of the given function using the denition of the derivative as a limit f (x) = x+1 x1 Math 131FALL 2002 EXAM 1 page 6 5. A ball is dropped from a tower of height H feet. Its height after t seconds, in feet above the ground, is given by the formula h(t) = H 16t2 . a) (5) Find the velocity of the ball after t seconds. b) (5) It is observed, that the ball hits the ground with a speed of 128 feet per second. How long was the ball in the air? Hint: The speed is the absolute value of the velocity. c) (5) Use the information in part b) to determine the height of th...

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UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS EXAM 1: MATH 131 Spring 2003 12 March 2003Your Name: Your Instructor's Name: This exam paper consists of 10 questions, all of equal weight. It has 9 pages. On this exam, you may use a c
UMass (Amherst) - MATH - 131
Fall '01 - Exam 1(1) (15 pts) (a) The following is a table of values for the function f (x) = 2x/(x2 + 1). Compute the slopes of the secant lines through each of these points and the point (0, 0). Use your table to estimate the slope of the tangent line
UMass (Amherst) - MATH - 131
2Spring 01 - Exam 1(1) (10 pts) Evaluate the limitx1lim1x 1 xshowing all your steps clearly. (2) (10 pts) Calculate the derivative f (x) of the function f (x) = 1/x2 directly from the denition. (3) (10 pts) You are given the function (1 2x)(1 x) g(x
Texas A&M - M - 151
M151B Practice Problems for Final ExamCalculators will not be allowed on the exam. Unjustified answers will not receive credit. On the exam you will be given the following identities: n(n + 1) ; k= 2 k=1nn(n + 1)(2n + 1) k = ; 6 k=12nnk3 =k=1n(n
Texas A&M - M - 151
Additional problems, due Tuesday Nov. 181. Use the method of Riemann sums to compute2 1x2 dx.2. Use the method of Riemann sums to compute1 0x3 dx.3. Use the method of Riemann sums to compute1 0ex dx.Hint 1. Use the following summation formula: f
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M151B, Fall 2008, Practice Problems for Exam 2Calculators will not be allowed on the exam. 1. Let f (x) = cos x - sin x, and compute 2. Show thatdf -1 (1). dx-3 x , 4 41 d cos-1 x = - , dx 1 - x2 y = xtan x ,-1 &lt; x &lt; +1. , 23. Let 0x&lt; and computed
Texas A&M - M - 151
M151B Practice Problems for Exam 1Calculators will not be allowed on the exam. Unjustified answers will not receive credit. 1. Compute each of the following limits: 1a. x2 - 4 . x2 x - 2 limx31b. lim - x2x . - 2x - 3 sin 7x . x1c.x0lim1d.x1lim
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University of Toronto - MATH - 477
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Journal of Mathematical Sciences, Vol. 133, No. 4, 2006ON THE TRANSLOCATION OF MASSES L. V. KantorovichThe original paper was published in Dokl. Akad. Nauk SSSR, 37, No. 78, 227229 (1942).We assume that R is a compact metric space, though some of the d
University of Toronto - MATH - 477
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National Taiwan University - CSE - 200
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University of Toronto - STA - 247
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University of Toronto - STA - 247
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University of Toronto - STA - 247
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: old-mid-sol.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMR12 CMTI12 CMEX10 CMMI12 CMSY10 CMMI8 CMR8 %EndComments %DVIPSWebPage: (www.radica
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