Express the integrand as a sum of partial fractions and evaluate the integral.
A. -12 ln 
+ 8ln
+ C
B. -4 ln 
+ 8ln
- 4ln
+ C
C. - 
+ 8ln
+ 4ln
+ C
D. -12 ln 
+ 8ln
+ 4ln
+ C
Answer: D
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Find the average value of 
over the given region.
over the rectangular solid in the first octant bounded by the coordinate planes and the planes 
, 
, 
A. 
B. 
C. 
D. 
Find the slope of the graph and they y -intercept. Then sketch the graph for values of x between -10 and 10.y = -4x - 1
A. slope = -4; y intercept = (-1, 0)
B. slope = - 
; y intercept = (0, -1)
C. slope = - 
; y intercept = (-1, 0)
D. slope = -4; y intercept = (0, -1)
Determine the intervals on which the function is increasing, decreasing, and constant.
A. Increasing on (-?, 4); Decreasing on (-4, ?); Constant on (4, ?) B. Increasing on (4, ?); Decreasing on (-4, ?); Constant on (-4, 4) C. Increasing on (-?, 4); Decreasing on (-?, -4); Constant on (4, ?) D. Increasing on (4, ?); Decreasing on (-?, -4); Constant on (-4, 4)
An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up.a = 7;
T = 4 seconds
A. d = -7 cos 
B. d = -7 cos 
C. d = -4 cos 
D. d = -7 sin 