MATH 1552 : Math 1552 Final Spring 2010
Document Summary
Answer any 10 questions: use integration by parts to evaluate the following integrals (a) Z (2x + 1)e3xdx: (a) use a suitable trigonometric substitution to evaluate the integral. 25 + x2 (b) evaluate the integral r tan3 x sec3 xdx. 0: use partial fraction decomposition to evaluate. 1 (x 1)(2x + 1)(x + 3) dx: (a) evaluate the geometric series or state that it diverges (i) (cid:1)k (b) use the integral test to show that the series. 1 k(lnk)4 is convergent: use either the comparison test or the limit comparison test to determine if the following series converge or diverge (a) 3n(n2 + 5n 1: find the radius of convergence and the interval of convergence of the power series. 2: (a) find the taylor series for the function f (x) = e2x about the value a = 3. (b). Use the binomial series to expand the function: sketch the graph of the hyperbola (1 3x)5 as a power series.
