At the given condition:

Demi-Leigh Barrera

Answered 2021-09-06
Author has **15378** answers

asked 2021-06-11

If \(f^{(n)}(0) = (n+1)! \text{ for } n = 0, 1, 2, \dots\), find the Maclaurin series forf and its radius of convergence.

asked 2021-05-27

Evaluate the indefinite integral as a power series.

\(\int \frac{\tan^{-1}x}{x}dx\)

\(f(x)=C+\sum_{n=0}^\infty\left( \dots \right)\)

What is the radius of convergence R?

\(\int \frac{\tan^{-1}x}{x}dx\)

\(f(x)=C+\sum_{n=0}^\infty\left( \dots \right)\)

What is the radius of convergence R?

asked 2021-09-16

Evaluate the indefinite integral as a power series.

\(\displaystyle\int{\frac{{{{\tan}^{{-{1}}}{x}}}}{{{x}}}}{\left.{d}{x}\right.}\)

\(\displaystyle{f{{\left({x}\right)}}}={C}+{\sum_{{{n}={0}}}^{\infty}}{\left(\dot{{s}}\right)}\)

What is the radius of convergence R?

\(\displaystyle\int{\frac{{{{\tan}^{{-{1}}}{x}}}}{{{x}}}}{\left.{d}{x}\right.}\)

\(\displaystyle{f{{\left({x}\right)}}}={C}+{\sum_{{{n}={0}}}^{\infty}}{\left(\dot{{s}}\right)}\)

What is the radius of convergence R?

asked 2021-02-04

a. Find the Maclaurin series of \(\cos(x)\) and find the radius of this series, without using any known power or Maclaurin series, besides geometric.

b. Find exactly the series of \(\cos(-2x)\)

asked 2021-11-06

Write out he first four terms of the Maclaurin series of f(x) if \(\displaystyle{f{{\left({0}\right)}}}={2},\ {f}'{\left({0}\right)}={3},\ {f}{''}{\left({0}\right)}={4},\ {f}{'''}{\left({0}\right)}={12}\)

asked 2021-10-24

Test the series for convergence or divergence.

\(\displaystyle{\sum_{{{n}={0}}}^{\infty}}{\frac{{{\left(-{1}\right)}^{{{n}+{1}}}}}{{\sqrt{{{n}+{4}}}}}}\)

\(\displaystyle{\sum_{{{n}={0}}}^{\infty}}{\frac{{{\left(-{1}\right)}^{{{n}+{1}}}}}{{\sqrt{{{n}+{4}}}}}}\)

asked 2020-11-20

Use the binomial series to find the Maclaurin series for the function.

\(f(x)=\frac{1}{(1+x)^4}\)