MAC 2311 Midterm: MAC2311 F04 Test 4
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Calculus 1, test 4g (1) (10 pts. ) (a) if f (x) = csc (x4 + 4x), nd z f (x) dx. December 3, 2004 (b) if f (x) =z x. 0 ln(cid:0)sin (et)(cid:1) dt, nd f (x). (2) (10 pts. each) integrate the following. (a) z (cid:0) x + x 1 + ex + x + 5(cid:1) dx (b) z. 0 x 1 x dx (e) z 2. 1 t2 1 t4 dt (3) (10 pts. each) di erentiate. (a) y = sin (3x + 1) 2x + 5 (b) y = e2+3x tan 2x. The velocity function is v(t) = 1 2. Find the limit lim x e 5x + x2. Find the area under the curve y = 1 x2 , 1 x 10. (8) (10 pts. ) If f is continuous and f (0) = 1 and f (x) =(x if x < 0. Nd a similar piecewise formula for f (x).
