Mathematics

(1) The length of a 12-foot by 8-foot rectangle is increasingat a rate of 3 feet per second and the

width is decreasing at 2 feet per second (see figure

below).

(a) How fast is the perimeter changing?

(b) How fast is the area changing?

(c) find all critical points and localextremes of the following function on the given intervals.

f (x) = 2-x^3 on [-2, 1]

(d) calculate the limits of the following

lim┬(x→0)〖(x+5)/x^2 〗

(e) evaluate A'(x) at x = 1, 2, and 3.

A(x) = ∫_(-3)^x▒〖 2t dt〗

(f) . Let A(x) represent the area bounded by the graph and the horizontal axis and verticallines at t=0 and t=x for the graph in Fig. 25. Evaluate A(x) for x = 1, 2, 3, 4, and 5.