University:
Missouri State University
Course:
MTH 138 | Pre-Calculus Mathematics
Academic year:

2020
Views:

358

Pages:

12
Author:

Makhi Crane

CALCULUS SECTION I, Part A Time-55 minutes Number of questions-28 KEY A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM. Directions: Solve each of the following problems, using the available space for scratch work. After examining the form of the choices, decide which is the best of the choices given and fill in the corresponding circle on the answer sheet. No credit will be given for anything written in the exam book. Do not spend too much time on any one problem. In this exam: (1) Unless otherwise specified, the domain of a function is assumed to be the set of all real numbers x for which f(x) is a real number. (2) The inverse of a trigonometric function ƒ may be indicated using the inverse function notation f ^ - 1 or with the prefix "arc" (e.g., arcsin(x) = arc * sin x ) 1. If y=x sin x t then d/dx (y) = (A) sin x + cos x x * cos x + sin x - t (B) inx + x * cos x (C) sin x - x * cos x (D) x(sin x + cos x) (E) x(sin x - cos x) 2. Let f be the function given by f(x) = 300x - x ^ 3 On which of the following intervals is the function f increasing? (A) (- ∞, - 10] and [10, 0) f' = 300 - 3x ^ 2 = 0 (B)[10.10] x=±10 (C) [0,10] only 10 (D) [0,10√3] only (E) [0,00) 3. integrate sec(x) * tan x dx = (A) sec x + C (B) tan x + C (C) (sec^2 x)/2 + c (D) (tan^2 x)/2 + C (E) (sec^2 x * tan^2 x)/2 + C 4. If f(x) = 7x - 3 + ln(x) then f' * (1) = (A) 4 (B) 5 f' * (x) = 7 + 1/x (C) 6 (D) 7 6 5 4 9 2- 1 5. The graph of the function f is shown above. Which of the following statements is false? (A) lim x -> 2 f(x) exists. (B) lim x -> 3 f(x) exists. lim x -> 4 f(x) exists. (D) lim x -> 5 f(x) exists. (E) The function f is continuous at x = 3 이 1 2 3 4 5 6 Graph of f 6. A particle moves along the x-axis. The velocity of the particle at time is 6t - t ^ 2 What is the total distance traveled by the particle from time t = 0 t =3? (A) 3 (B) 6 (C) 9 (D) 18 (E) 27 6k - k ^ 2 = 0 b(6 - 6) = 0 integrate 6t - t ^ 2 dt from 0 to 3 3t^ 2 - 1/3 * t ^ 3 | 0 ^ 3 27-9 7. If dot y = (x ^ 3 - cos x) ^ 3 , then y' = (A) 5 * (x ^ 3 - cos x) ^ 4 5 * (x ^ 3 - cos lambda) ^ 11 (3x ^ 2 + 56ax) (B) 5 * (3x ^ 2 + sin x) ^ 4 (C) s(3x ^ 2 + sin x) (D) 5 * (3x ^ 2 + sin x) ^ 4 * (6x + cos x) (B) 5 * (x ^ 3 - cos x) ^ 4 * (3x ^ 2 + sin x) Graph of f' 85. The graph of f' the derivative of f, is shown in the figure above. The function f has a local maximum at x = (A) -3 (B) -1 (D) 3 (B) 4 f'chayet to 86. If f' * (x) > 0 for all real numbers x and function f integrate f(t) dt from 4 to 7 = 0 which of the following could be a table of values for the (A) x f(x) 4-4 5 -3 7 0 (C) x f(x) 4 5 7 -4 6 3 ( D) x f(x) 4 5 7 0 0 0 (B)) x f(x) 4 5 7 5 -4 -2 (E) x f(x) 4 5 0 4 76 87. The graph of f ^ prime prime , the second derivative of f, is shown above for - 2 < = x <= 4 What are all intervals on which the graph of the function f is concave down? (A) - 1 < x < 1 F40 (B) 0 < x < 2 (C) 1< x< 3 only (D) -2x-1 only ((E)) - 2 < x < - 1 and 1 < x < 3 AV -210 1 2 3

Calculus Exam Part A B

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