1. Evaluate the following: ( a ) e" ( Vi tex ) dic TT / 2 (b) esin(z) cos(x) dx (c) lim (In(x))/x I -+ 00 2. Differentiate the following: (a) y= x2x sin x ( b) f (2) = / (+2 - 1) at3. Evaluate the following: (a) feda: D (b) f xe'mdx 700 4. Determing whether the following series are absolutely convergent, conditionally convergent, or diver gent. Explain your decision. (a) Find the interval of convergence for the following: 2% 11:0 (b) Determine whether the alternating series converges or diverges by using the alternating series test: (c) Use the ratio test to determine whether the series is absolutely convergent, conditionally conver n! gent, or divergent: Z(1)\"' 11:1 ((1) Determine whether the alternating series converges or diverges by using the alternating series test: 00 Z(-1)\"n+1 13:1 DC (e) Determine Whether the following series converges or diverges by using the comparison test: 2% n=0 . Compute f \"mim2 da: . Find an equation of the tangent line to the curve at the indicated point: 550?) = toos(t), y(t) = tsin(t) at t = 7r. . Find the exact length of the curve: a:(t) = 2t, y(t) = 2t, 0 S t S 1 . Graph the curve and nd the area. that it enclosed: 'r = 2.305(6). . Find 35 if 3(t) = t + sin(t), and y(t) = t c0506). 10. Find a Maclaurin series which represents cos(:c) for every real number :5 around the point a = 0