(D) Separating variables yields so ln y = −ln cos x + C. With y =
3 when x = 0, C = ln 3. The general solution is therefore (cos x) y = 3.
When x = ,
cos x = and y = 6.
(A) Represent the coordinates parametrically as (r cos θ, r sin θ). Then
Note that sin 2θ, and evaluate at (Alternatively, write x =
cos 2θ cos θ and y = cos 2θ sin θ to find from )
(D) Note that v is negative from t = 0 to t = 1, but positive from t = 1 to t
= 2. Thus the distance traveled is given by
(A) Use parts; then u = x, dv = cos x dx; du = dx, v = sin x. Thus,
x cos x dx = x sin x − sin x dx.
(D) (A), a p-series with p = 1/2, diverges. We would like to compare (B)
to so we use the Limit Comparison Test
; since diverges, (B) diverges. For (C), we
need to use LCT for the same reason as (B), ; again
