MAC 2311 Midterm: MAC2311 F05 Test 4
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December 5, 2005 (1) (10 pts. ) (a) if f (x) = esin x, nd z . 0 f (x) dx. (b) if f (x) = z x. 0 ln (t + et) dt, nd f (x). (2) (10 pts. each) integrate the following. (a) z (cid:18)5 + 2 x sin x + sec2 x + x(cid:19) dx (b) z 1. Test 4 page 2 (c) z (1 2x)(x2 + 1) dx (d) z /4. Test 4 page 3 (3) (10 pts. each) di erentiate. (a) y = tan x x (b) y = (1 + x7)e x (4) (10 points) integrate: z x(cid:0)2 x2(cid:1)3/2 dx. Find f (x) if f (x) = sin x, f (0) = 0 and f (0) = 2. (7) (10 pts. ) Find the limit: x (cid:19)x x (cid:18) x + 1 lim. Sketch the graph of f (x) = 8 x3 on the interval 0 x 2 and.
