# Maclaurin series questions with answers

Recent questions in Maclaurin Series
garkochenvz 2022-08-13

### Find Maclaurin series for this$f\left(x\right)={x}^{3}{\mathrm{tan}}^{-1}\left(2x\right);\phantom{\rule{1em}{0ex}}|x|<\frac{1}{2}$

Yair Valentine 2022-08-12

### find the Maclaurin series for $\mathrm{ln}\sqrt{\frac{1+x}{1-x}}$. I found it is $\frac{{x}^{2n+1}}{2n+1}$ ,is it correct? I got the $1/2$ outside and solved the maclaurin for the normal log. If it is okay how can I find a relationship between this and the maclaurin series artg.I know it is $\left(-1{\right)}^{n}$n of my series but how can I write it?

Jazmin Clark 2022-08-11

### So for $f\left(z\right)=\frac{1}{z+1}-\frac{1}{z+4}$, I am supposed to find the Maclaurin Series and give the region which it converges. Also, I am supposed to find ${f}^{\left(17\right)}\left(0\right)$ without computing the derivatives.I know how to find the Maclaurin series, I am just struggling with finding the region it converges and how to compute the $17$th derivative.

cottencintu 2022-08-10

### Solve this limit.$\underset{x\to 0}{lim}\frac{\left({e}^{x}\mathrm{sin}x-\left(x+1\right)\mathrm{tan}x\right)}{\left(x\mathrm{log}\mathrm{cos}\left(x\right)\right)}$

Databasex3 2022-08-09

### How to expand that function below into Maclaurin series? Is it even possible?$f\left(x\right)={x}^{2}+\mathrm{ln}\left(\frac{2x-3}{5-3x}\right)$

Ibrahim Rosales 2022-07-23

### Find the Maclaurin series for $f\left(x\right)=\left({x}^{2}+4\right){e}^{2x}$ and use it to calculate the 1000th derivative of $f\left(x\right)$ at $x=0$. Is it possible to just find the Maclaurin series for e2x and then multiply it by $\left({x}^{2}+4\right)$?

Leila Jennings 2022-07-21

### From Rogawski $ET$ $2e$ section $10.7$, exercise $4$.Find the Maclaurin series for $f\left(x\right)=\frac{{x}^{2}}{1-8{x}^{8}}$.$\frac{{x}^{2}}{1-8{x}^{8}}=\sum _{n=0}^{\mathrm{\infty }}\left[\text{_______________}\right]$

Kenya Leonard 2022-07-19

### find $\int p\left(x\right)dx$ where:$p\left(x\right)=\frac{{e}^{\frac{-{x}^{2}}{2}}}{\sqrt{2\pi }}.$

acsuvaic9 2022-07-18