e4-sample - power series on its interval of convergence....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 170, Section 01, Exam 4, Sample Monday, November 30th, 2009 Name (PRINT clearly): You will receive full credit only if you show all work and explain all steps. 1. Find the radius and interval of convergence of the following power series. (a) n =1 2 n +1 x n (b) n =1 n ! n n x n (c) n =1 x n 2 n + 1 2. Find a power series expansion (centered at the origin) for the function f ( x ) = 2 + x 2 - x . Compute the radius of convergence and determine the interval of convergence of the power series. 3. Find the radius and interval of convergence of the power series n =0 n 1 + n 2 x n . Let f denote the function defined by this
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: power series on its interval of convergence. Find a power series representation f ( x ). Let F ( x ) denote an anti-derivative of f , find the power series representation for F and f Compute their radius and interval of convergence. 4. Let f ( x ) = sin(2 x ). Find the 8th degree Taylor polynomial for f centered at the origin. Estimate the error in approximating sin(1) using this Taylor polynomial. How large a degree is required in order to approximate sin(1) to within 4 decimal places. 1...
View Full Document

This document was uploaded on 10/29/2011 for the course MATH 170 at Vanderbilt.

Ask a homework question - tutors are online