University:
Florida Gateway College
Course:
MAC 2311 | Calculus I
Academic year:

2020
Views:

148

Pages:

15
Author:

Viapianara

KEY Sample Examination I Section I Part A 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. Do not spend too much time on any one problem. Calculators may NOT be used on this part of the exam. In this exam: (1) Unless otherwise specified, the domain of a function fis 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 f may be indicated using the inverse function notation f or with the prefix "arc" (e.g., sinx = arcsin x) [x²+bx for x ≤5 5 sin(x) for x > 5 f(x) = 1. Let f be the function defined above, where b is a constant. If f is a continuous function, what is the value of b? (A) -6 (B) -5 (C)) -4 (D) 4 (E) 5 5²+56=50m (5) 25 +56 = 5 (5) 25 56 5 56-20 b=-4 Answer C 2 Sample Examination I 2. The graph of y=3x²-x has a relative maximum at (A) (0,0) only (B) (1,2) only ((C)) (2,4) only (D) (4,-16) only (E) (0,0) and (2,4) 1= 6x-3x² y y'= 3x (2-x)=0 x=0, x=2 + 2 Answer C 3. A particle moves in the xy-plane so that its velocity vector at time t is v (t) = (r², sin (xt)) and the particle's position vector at time = 0 is (1, 0). What is the position vector of the particle when t=37 (A) (9.) (B) (10.) = t (C) (6,-2) (D) (10,2π) (E) (10,2) St² dt = ++C Som Int) dt = cos(at). C -105 -cos(0)+c=0 +c=0 뉴 2 3 3 s(t)= < 1,-10s()+ 5(3)=1, -105(30)+뉴> < 10 > < 10, > Answer B 20. Shown above is the slope field for which of the following differential equations? (A) dy dx 1-x (B) d=x-y (C) x y (D)=1+y² only has + slopes (E)=1-y 12 Sample Examination I 21. The power series 1+2x+4x²+8x+2x+converges for what values of x ? (A) x = 0 only Geometria! r= 2x (B)- < x < only Converges when /r/24, 00 (C) -1 < x < 1 only 12x11 (D)-2 < x < 2only -122x21 (E) All real numbers x Answer B 22. The Taylor series for sin (x²) centered at x = 0 is x² (A)(-1)+1 (2k+1)! Create the seris: sin x = 3 x-x 3! + x7 5! (日) (C) Σ (-1)+1 (2k)! 10 nx²= x²x + xx 2 2 X 6 3! (D) (2k+1)! sis-x? 2 -X 4 3! 8 +x 5! 12 -X + (E) + (-1)x2-1 (2k-1) Wheit matches up with D Answer D Sample Examination I 13 23. If the length of a curve y = f(x) from x x = a to x = b is given by L = [√o² + 2e* +2 dx, then f(x) could equal b (A) 2e2+2e (B)²+2e²+2x Are Length = SVI + G')" dx b =√1+ (ex+2x+1) da (C) e-x+3 (D) +1 (E) e+x-2 2 Answer Do it f') ext then flix)=ex+x+C E 3 (x) + 1 23 2 3 5 24. The functions f and g are piecewise linear functions whose graphs are shown above. If h(x) = f(x) g(x), then h'(3) = (A) 8 (B) (C) 0 (D) (E) 8 h'(x)=f(x) •g'(x) + g(x) f '(x) Product Roule h'(3)=f(3).g(3)+ g(3). f' (3) 1 1 +3 = = 0 Answer C

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