# Maclaurin Series Explained: In-Depth Examples, Equations, and Expert Insights

Recent questions in Maclaurin Series
crubats4b5p 2023-03-15

## Give the Maclaurin series for sin x.

sf2or5eek8 2023-01-07

## Find the Maclaurin series for this function: $f\left(x\right)={x}^{5}\mathrm{cos}\left(\pi x\right)$.

vedentst9i 2022-11-18

## Calculate this limit using Maclaurin series: $\underset{x\to \mathrm{\infty }}{lim}\left(\left({x}^{3}-{x}^{2}+\frac{2}{x}\right){e}^{\frac{1}{x}}-\sqrt{{x}^{3}+{x}^{6}}\right)$

Rihanna Bentley 2022-11-04

## Find maclaurin series using the first few terms for:$\frac{1}{{x}^{2}}\left(\frac{\mathrm{sin}x}{\mathrm{cos}x}-x\right)$

Diego Barr 2022-10-22

## Maclaurin series for $\frac{\mathrm{cos}2x-1}{{x}^{2}}$ using Maclaurin series for $\mathrm{cos}2x$

Paloma Sanford 2022-10-18

## Using the Maclaurin series for $\frac{1}{1-x}$, compute the Maclaurin series for:$\frac{1+x}{1+{x}^{2}}$

Ryder Ferguson 2022-10-14

## What is the Maclaurin series of${z}^{3}\mathrm{sin}\left({z}^{2}\right)$

Hope Hancock 2022-10-03

## Say$f\left(x\right)=\mathrm{ln}\left(1+2x+2{x}^{2}\right)$ or $g\left(x\right)=\mathrm{tan}\left(2{x}^{4}-x\right)$.Using the definition leads to messy derivatives almost immediately.If it was some simple rational function,for example,i would try to use Maclaurin Series of $\frac{1}{1+x}$ or $\frac{1}{1-x}$ and then manipulate it to get result

Bergsteinj0 2022-09-30

## using standard Maclaurin series (e.g. ${e}^{x}=1+x+\frac{{x}^{2}}{2!}+...$ , we can substitute $x$ with other functions such as $z={x}^{2}$ to transform the standard Maclaurin series into ${e}^{{x}^{2}}=1+{x}^{2}+\frac{{x}^{4}}{2!}+...$ Why doesn't this require a $\frac{dz}{dx}=2x$ component in the expansion since the standard Maclaurin series are derived from differentiation of the original term.

ghulamu51 2022-09-27

## Maclaurin series for $\frac{1}{|1+x|}$However, would it be appropriate for me to refer $\frac{1}{|1+x|}$ as 'not a smooth' curve (discontinuity at $x=1$) hence the non-existence of a Maclaurin or in any case a Taylor Series?

skilmarka8j 2022-09-26

## calculate a 3rd order Maclaurin series$f\left(x\right)=\left(1+x{\right)}^{1/x},$

Calculus 2Open question
dejanimaab 2022-08-28

## So knowing that the power series may be differentiated term by term inside the interval of convergence, using the Maclaurin series you can derive the differentiation formula for the function $f\left(x\right)=\frac{1}{1-x}$.What do they mean by differentiation formula and how do I get it using Maclaurin series?

Calculus 2Open question
hannahb862r 2022-08-22

## Is there a way to derive the Maclaurin series for $\frac{1}{\left(1-x\right)}$ after finding the Maclaurin series for $\left(1+x{\right)}^{n}$ which is $\sum _{k=0}^{\mathrm{\infty }}\frac{{f}^{k}\left(0\right)}{k!}\ast {x}^{k}$.

Calculus 2Open question
Nina Perkins 2022-08-22

## Find the Maclaurin series for $\mathrm{ln}\left(1+{x}^{2}+x\right)$

Calculus 2Open question
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