Section 11.3 – Power Series

THE RATIO TEST 10.3

10.5

Find the radius of convergence of Therefore, the radius of convergence is 3 Therefore, the radius of convergence is 1

Find the radius of convergence of Therefore, the radius of convergence is infinite.

Find the Maclaurin series for and determine its radius of convergence Radius of Convergence Is ½

The Taylor series about x = 0 for a certain function f converges for all x in the interval of convergence. The nth derivative of f at x = 1 is given by a. Write the third degree Taylor polynomial for f about x = 0 b. Find the radius of convergence for the Taylor series about x = 0 Radius of Convergence is 3

The Taylor series about x = 0 for a certain function f converges for all x in the interval of convergence. The nth derivative of f at x = 1 is given by a. Write the third degree Taylor polynomial for f about x = 0 b. Find the radius of convergence for the Taylor series about x = 0 Radius of Convergence is infinite

Let f be the function defined by a. Find for n = 1 to n = 3, where is the nth derivative of f. Write the first three nonzero terms and the general term for the Taylor series expansion of f(x) about x = 1

Determine the radius of convergence for the series. Show your reasoning The radius of convergence is 1