Mississippi Mu Alpha Theta 2014
Calculus Written Test
Mississippi Mu Alpha Theta 2014
Calculus Written Test
1. Evaluate limx→4x- 3x+44-x
A. Does not exist B. 0 C. 58 D. -58 E. 85
2. Find the average rate of change of f(x) = 3x2- x over the interval [1, 4].
A. 6x-1 B. 21 C. 14 D. 114 E. 44
3. Which of the following is an equation of the normal line to y = sin x + cos x at x = π?
A. y = -x + π – 1 B. y = x – π – 1 C. y = x – π + 1
D. y = x + π + 1 D. y = x + π – 1
4. π4π2cosxsinx dx
A. ln 2 B. ln π4 C. ln 3 D. ln 32 E. ln e
5. Which of the following functions has exactly two local extrema on its domain?
A. f(x) = |x – 2| B. f(x) = tan x C. f(x) = x3 – 6x + 5 D. f(x) = x3 + 6x – 5 E. f(x) = x + lnx
6. The sides of a right triangle with legs x and y and hypotenuse z increase in such a way that dz/dt = 1 and dx/dt = 3 dy/dt. At the instant when x = 4 and y = 3, what is dx/dt?
A. 13 B. 1 C. 2 D. 5 E. 5
7. The function f given by f(x) = 2x3 – 3x2 – 12x has a relative minimum at x =
A. -3 B. -1 C. 0 D. 2 E. 12
8. If f(x) = cos3 (4x), then f ’(x) =
A. 3cos2 (4x) B. -4 sin3 (4x) C. -3 cos2 (4x) sin (4x)
D. 12 cos2 (4x) sin (4x) E. -12 cos2 (4x) sin (4x)
9. The area of the region bounded by the curve y = e2x, the x-axis, the y-axis, and the line x = 2 is equal to
A. e42- e B. e42- 1 C. e42- 12 D. 2e4 – e E. 2e4 – 2
10. The position of a particle moving along a straight line at any time t is given by s(t) = t2 + 4t + 4. What is the acceleration of the particle when t = 4?
A. 0 B. 2 C. 4 D. 8 E. 12
11. The x-coordinates of the points of inflection of the graph of y = x5 – 5x4 + 3x + 7 are
A. 0 only B. 1 only C. 3 only D. 0 and 3 E. 0 and 1
12. Let f(3) = 6, f ’(3) = 5, g(3) = 1, and g’ (3) = 23 . Find h’ (3) if h(x) = f(x)g(x).
A. 23 B. 6 C. 0 D. 1 E. Undefined
13. If f(x) = e-x, find all solutions for f’(x) = -1.
A. no solutions B. 0 C. 1 D. 0 and 1 E. –e
14. Find f’(2) if limh→01x+h-1xh .
A. -12 B. 12+h C. 14 D. 14+h E. -14
15. A solid is generated by rotating the region enclosed by the graph of y = x , the lines x = 1, x = 2, and y = 1, about the x-axis. Which of the following integrals gives the volume of the solid?
A.
B.
C.
D.
E.
16. Explain why the Mean Value Theorem cannot be applied to the function f(x) = |x-1| on the interval [-2, 2].
A. The function is not continuous on the interval [-2, 2].
B. The function is not differentiable at the endpoint.
C. The function is not differentiable at a point on the interval (-2, 2).
D. Both A and C explain why the Mean Value Theorem cannot be applied.
E. The Mean Value Theorem can be applied.
17. Find the total area of the region bounded by the graph of y = sin x, the x-axis,
x = -π4 , and x= π2.
A. 0 B. 4- 22 C. 22 D. 4+ 22 E. -1 - 22
18. How many of the following functions have the property that f’’(x) = -f(x)?
(i) f(x) = sin x
(ii) f(x) = cos x
(iii) f(x) = e-x
(iv) f(x) = ln x
A. 0 B. 1 C. 2 D. 3 E. 4
19. ddx 7x2wsinw dw=
A. cos x2 B. x2cos x2 + sin x2 C. 49 cos 49 + sin 49
D. x2 sin x2 E. 2x3 sin x2
20. -22xdx.
A. 4 B. 1 C. 0 D. ½ E. 8