Theory and ExamplesThe series converges to sec x for a.

Chapter 10, Problem 58E

(choose chapter or problem)

Problem 58E

Theory and Examples

The series

converges to sec x for

a. Find the first five terms of a power series for the function For what values of x should the series converge?

b. Find the first four terms of a series for sec x tan x. For what values of x should the series converge?

c. Check your result in part (b) by multiplying the series for sec x by the series given for tan x in Exercise 53.

Reference: Exercise 53

Theory and Examples

The series

converges to tan x for

a. Find the first five terms of the series for For what values of x should the series converge?

b. Find the first five terms of the series for sec2 x. For what values of x should this series converge?

c. Check your result in part (b) by squaring the series given for sec x in Exercise 54.