(C)
[We rewrite so do 3x and 4x; the fraction
approaches 1 · 1 · .]
(B)
[We can replace 1 − cos x by 2 sin^2 , getting
(D)
approaches 0, the original
fraction approaches π · 1 · = π.]
(C) The limit is easiest to obtain here if we rewrite:
(B) Since x − 3 = 2 sin t and y + 1 = 2 cos t,
(x − 3)^2 + (y + 1)^2 = 4.
This is the equation of a circle with center at (3,−1) and radius 2. In the
domain given, −π ≤ t ≤ π, the entire circle is traced by a particle moving
counterclockwise, starting from and returning to (3, −3).
(C) Use L’Hôpital’s Rule; then
