(A) cos and thus cos x. From the equation given, y = esinx.
(D) If f (x) = x cos x, then f ′(x) = −x sin x + cos x, and
(C) If y = ex ln x, then ln x, which equals e when x = 1. Since
also y = 0 when x = 1, the equation of the tangent is y = e(x − 1).
(B) v = 4(t − 2)^3 and changes sign exactly once, when t = 2.
(C) Evaluate .
(C).
(C) Since v = 3t^2 + 3, it is always positive, while a = 6t and is positive for
t > 0 but negative for t < 0. The speed therefore increases for t > 0 but
decreases for t < 0.
(A) Note from the figure that the area, A, of a typical rectangle is
