If the question is in several parts, carefully label the answer to each part. Do all of your work on the examination paper; scratch paper is not permitted. If you continue a problem on the back of the page, please write continued on back . d. Problem 1: calculate g(1) and g(cid:48)(1), where g(x) is the inverse of f (x) = x + ln x. Problem 2: evaluate the integral using trigonometric substitution. (cid:90) (cid:112) x. Problem 3: evaluate the integral (cid:90) x5 + 2 x2(x + 1) dx. Problem 4: evaluate the integral (cid:90) sin(ln x)dx. Problem 5: determine whether or not the improper integral converges. x ln x. Problem 6: use the error bound for taylor polynomials to nd a value of n for which. | ln 2 tn(2)| 10 6, where tn is the nth taylor polynomial for f (x) = ln x centered at 1. Problem 8: find the interval of convergence of the power series.
