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APPM 1350 Midterm #1 Summer 2011 On the front of your bluebook, please write: a grading key, your name, student ID, and instructor’s name (Guinn). This exam is worth 100 points and has 5 questions. Show all work! Answers with no justification will receive no points. Please begin each problem on a new page. No notes, calculators, or electronic devices are permitted. 1, (15 points) True or False. If the statement is true, write out the word TRUE. If the statement is false, write the word FALSE. For this problem only, no explanation is needed. (a) If a function is continuous at a point z = a, then it is differentiable at z = a. (b) The function f(x) = Jy +2 is even. (c) Let f(z) = 4, g(a) =z -1, and A(x) = Ye +1. Then f (9 (h(z))) has domain [-1,00). (d) The normal line to s(t) = 3t? — 1 at (1,1) has a slope of -6. (e) The graph of a function can never cross its horizontal asymptote(s). 2, (15 points) Consider f(t) = v'# sin(1/t). For each of the following, clearly state (i) if the limit exists, (ii) a brief explanation as to why it does or does not exist, and (iii) the value of the limit if it exists. (@) jim FQ) (0) jim £@ () lim FO) 3. (20 points) Evaluate four of the following five limits and show all supporting work. If a limit does not exist, clearly state that fact and explain your reasoning. Please clearly mark which four limitis you wauld like to be graded. . 1—cos*(4z) oo? — Ta + 12 vuti—3 (@) lig qa () lin Tae (him “Ty kt 2 rae @ tm nae () tm ay 3 4, (25 points) The equation of motion of a particle is s(t) = t3 — 447 +5 where s(t) is in meters and t is in seconds. (a) How far from the origin does the particle start? (b) Use the Intermediate Value Theorem to show that the particle will be at the origin at some point within the first two seconds. (c) Find the velocity and the acceleration of the particle as a function of time. (d) When is the particle moving in the negative direction? 5. (25 points) Let f(z) = <2). (a) Give the definition of the derivative of a function y = f(z). (b) Use the definition of the derivative to find f(z). (c) Find the equation of the tangent line to f(z) at xz = 2. (d) Is f(e) continuous at x = 17 Why or why not? (e) Find any vertical and horizontal asymptotes of f(x). 
