Calculus Early Transcendentals

Approximate by a Taylor polynomial with degree at the number .

Find a power series representation for the function and determine the interval of convergence.

Find a power series representation for the function and determine the interval of convergence.

Find the radius of convergence and the interval of convergence of the power series.

Find the Taylor series for centered at the given value of a. Assume that f has a power series expansion. Also find the associated radius of convergence.

Find the Maclaurin series for f (x) using the definition of the Maclaurin series.

Find the Maclaurin series for using the definition of a Maclaurin serires.

Find the sum of the series.

Find a power series representation for the function and determine the interval of convergence.

Find a power series representation for the function and determine the radius of convergence.

Approximate by a Taylor polynomial with degree at the number .

Use series to approximate the definite integral to within the indicated accuracy.

Evaluate the indefinite integral as an infinite series.

Find a power series representation for the function and determine the interval of convergence.

Approximate by a Taylor polynomial with degree at the number .

Find the interval of convergence of the series.

Use the binomial series to expand the function as a power series. Find the radius of convergence.

Find the radius of convergence and the interval of convergence of the power series.

Find the Taylor polynomial for the function centered at the number .

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function.