1. f(x) =2-2 (30 points) 22 + x ( x-1 ) (a) Write the rational function f(x) as a sum or difference of simpler rational expressions. That is, write a partial fraction decomposition of f. (b) Use the partial fraction decomposition of f in Part (a) to evaluate / f(x) dx. (c) Use the result in Part (b) to evaluate / f(x) dx 2. The region R is bounded by the curve y = -, the x-axis, and on the left by x = 1. 7 (30 points) (a) Sketch the region R. (b) Write an integral that represents the area of the region R. (c) Evaluate the integral in Part (b) to find the area of the region R. 3. 3 an 2n - 1 217 (40 points) (a) Write the first four terms of the sequence { an ) n=1. (b) Determine whether the sequence { an } converges or diverges. If it converges, find its limit. (c) Write the first three terms of the sequence of partial sums for the series an. n=1 (d) Determine whether the series > an converges or diverges. If it converges, find the value of an . n=1