MATH 221 Final: MATH 221 KSU Final Exam f98
15 Feb 2019
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The point value of each problem is given in the margin. Show your work clearly. cos2 x = sin2 x = Find the derivatives. (do not try to simplify your answers!) page 2 (a) e(ex) (b) tan 1(ln(2x)) (c) xsin x (12) 2. Evaluate the limits. (a) lim x 0 ex x 1. 2x (b) lim x x(cid:16)e1/x 1(cid:17) (20) 3. Evaluate the integrals. (don"t simplify your answers. ) page 3 (a) z sin2(4x) dx (b) z x ln x dx (c) z dx x(2x + 1) (d) z dx. Find the volume obtained by revolving the region between the graph of y = e x , the x -axis, and the vertical lines x = 0 and x = b , around the x -axis. page 4 (10) 5. Immediately after an accident at a nuclear power plant, the radioactivity level is 10 times the safe limit. After 6 months the radioactivity drops to 8 times the safe limit.
