University:
Missouri State University
Course:
MTH 261 | Analytic Geometry and Calculus I
Academic year:

2019
Views:

223

Pages:

8
Author:

vykolsinaigr

CALCULUS BC SECTION I, Part A Time-55 minutes Number of questions-28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION. Directions: Solve each of the following problems, using the available space for scratchwork. After examining the form of the chicices, decide which is the best of the choices given and fill in the corresponding oval on the answer sheet. No crodit will be given for anything written in the test book. Do not spend too much time on any one problem In this test: (1) Unless otherwise specified, the domain of a function f is assumed to be the set of all seal numbers for which (x) is a beal number, (2) The laverse of a trigonometric function / may be indicated using the inverse function notation f ^ - 1 or with the prefix "are" (e.g., sin^(- 4) x = arcsin(x) ) 1. If y=sin(3x),then (dy)/(dx) = (A) - 3cos(3x) (b) - cos(3x) (C) - 1/3 * cos(3x) (D) cos(3x) (E)3 cos(3x) y=3005(3x) 2. lim x -> 0 (e ^ x - cot x - 2x)/(x ^ 2 - 2x) * i D/D ( - 1/2 (3) 0 (D) 1 (E) nonexisicet lim x -> 0 (e ^ x + sin x - 2)/(2x - 2) = (1 + 0 - 2)/(D - 2) = - 1/- 2 = 1/2 Section Part'A Calculus BC A 3. integrate (3x + 1) ^ 5 dx = u = 3x + 1 du = 3dx (A) ((3x + 1) ^ 6)/18 + c 1/3 * integrate u ^ 5 du (B) ((3x + 1) ^ 6)/6 + c ((3x + 1) ^ 5)/2 + C 1/6 * 1/3 * (3x + 1) ^ 6 + C (D) (((3x ^ 2)/2 + x) ^ 6)/2 + C 1/18 * (3x + i) ^ 6 + C ((3x ^ 2)/2 + x) ^ 5 + C D 4. Por an object travels along an elliptical path given by the parametric equations x= exists cos tan c 0 <= t <= 13 y = 4 point where 13, the object leaves the path and travels along the line tangent to the path point. What is the slops of the line on which the object travels? = - 4/3 3 - 3/4 - (4tan 13)/3 (D) - 4/(3tan 13) (03) - 3/(4ten * 13) x = 3cos t y=4sen't t = 13 (diy)/(d ^ 2 * t) * (dic)/(dt) = (4cos t)/(- 3sin t) =.- it 3 cos t\\ t( hat s )= -it delta cos(13). t(beta) = - 4/2 * cos(13) = - 1/(3tan(13)) 5. Let y = f(x) be the solution to the differential equation d/dx (y) = x + y with the initial condition f(1) = 2 What is the approximation for f(2) if Euler's method is used, x = 1 with a step size of 0.5? (A) 3 (B) 5 16 (D) 10 (B) 12 1.5 y_{1} = 3.5 y_{1} = 2 + (3) * 0.5 ^ (Delta*x) 3.5 underline y 2 = 3.5 + (5)(0.5) =3.5+2.5 16

Calculus Exam Answers Part A

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