(a) Divide the power series in Exercise 42 by 4x³ to obtain a power series for h(x) = 1/(1 − x⁴)² and use the Ratio Test to show that the radius of convergence is 1.

Data From Exercise 42

Differentiate the power series in Exercise 40 to obtain a power series for

Data From Exercise 40

Use Eq. (2) to expand the function in a power series with center c = 0 and determine the interval of convergence.

(b) Another way to obtain a power series for h(x) is to square the power series for ƒ(x) in Exercise 40. By multiplying term by term, determine the terms up to degree 12 in the resulting power series for (ƒ(x))² and show that they match the terms in the power series for h(x) found in part (a).

Data From Exercise 40

Use Eq. (2) to expand the function in a power series with center c = 0 and determine the interval of convergence.

(b) Another way to obtain a power series for h(x) is to square the power series for ƒ(x) in Exercise 40. By multiplying term by term, determine the terms up to degree 12 in the resulting power series for (ƒ(x))² and show that they match the terms in the power series for h(x) found in part (a).

Transcribed Image Text:

g(x): = 4x³ (1-x4)²*