Question

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 2020-11-20

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

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

asked 2021-04-24

Find the second partial derivatives for the function \(\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{{4}}}-{3}{x}^{{{2}}}{y}^{{{2}}}+{y}^{{{2}}}\) and evaluate it at the point(1,0).

asked 2021-06-13

Use derivatives to show that f is increasing and its graph is concave down for all x>0.