Recent questions in Maclaurin Series

Calculus 2Answered question

sf2or5eek8 2023-01-07

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

Calculus 2Answered question

vedentst9i 2022-11-18

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

Calculus 2Answered question

Rihanna Bentley 2022-11-04

Find maclaurin series using the first few terms for:

$\frac{1}{{x}^{2}}(\frac{\mathrm{sin}x}{\mathrm{cos}x}-x)$

$\frac{1}{{x}^{2}}(\frac{\mathrm{sin}x}{\mathrm{cos}x}-x)$

Calculus 2Answered question

Diego Barr 2022-10-22

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

Calculus 2Answered question

Paloma Sanford 2022-10-18

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

$\frac{1+x}{1+{x}^{2}}$

$\frac{1+x}{1+{x}^{2}}$

Calculus 2Answered question

Ryder Ferguson 2022-10-14

What is the Maclaurin series of

${z}^{3}\mathrm{sin}({z}^{2})$

${z}^{3}\mathrm{sin}({z}^{2})$

Calculus 2Answered question

Hope Hancock 2022-10-03

Say$f(x)=\mathrm{ln}(1+2x+2{x}^{2})$ or $g(x)=\mathrm{tan}(2{x}^{4}-x)$.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

Calculus 2Answered question

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.

Calculus 2Answered question

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?

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?

Calculus 2Answered question

skilmarka8j 2022-09-26

calculate a 3rd order Maclaurin series

$f(x)=(1+x{)}^{1/x},$

$f(x)=(1+x{)}^{1/x},$

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 $f(x)=\frac{1}{1-x}$.

What do they mean by differentiation formula and how do I get it using Maclaurin series?

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 $\frac{1}{(1-x)}$ after finding the Maclaurin series for $(1+x{)}^{n}$ which is $\sum _{k=0}^{\mathrm{\infty}}\frac{{f}^{k}(0)}{k!}\ast {x}^{k}$.

Calculus 2Open question

Nina Perkins 2022-08-22

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

Calculus 2Open question

garkochenvz 2022-08-13

Find Maclaurin series for this

$f(x)={x}^{3}{\mathrm{tan}}^{-1}(2x);\phantom{\rule{1em}{0ex}}|x|<\frac{1}{2}$

$f(x)={x}^{3}{\mathrm{tan}}^{-1}(2x);\phantom{\rule{1em}{0ex}}|x|<\frac{1}{2}$

Calculus 2Answered question

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 $(-1{)}^{n}$n of my series but how can I write it?

Calculus 2Answered question

Jazmin Clark 2022-08-11

So for $f(z)=\frac{1}{z+1}-\frac{1}{z+4}$, I am supposed to find the Maclaurin Series and give the region which it converges. Also, I am supposed to find ${f}^{(17)}(0)$ 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.

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.

Calculus 2Answered question

cottencintu 2022-08-10

Solve this limit.

$\underset{x\to 0}{lim}\frac{({e}^{x}\mathrm{sin}x-(x+1)\mathrm{tan}x)}{(x\mathrm{log}\mathrm{cos}(x))}$

$\underset{x\to 0}{lim}\frac{({e}^{x}\mathrm{sin}x-(x+1)\mathrm{tan}x)}{(x\mathrm{log}\mathrm{cos}(x))}$

Calculus 2Answered question

Databasex3 2022-08-09

How to expand that function below into Maclaurin series? Is it even possible?

$f(x)={x}^{2}+\mathrm{ln}\left(\frac{2x-3}{5-3x}\right)$

$f(x)={x}^{2}+\mathrm{ln}\left(\frac{2x-3}{5-3x}\right)$

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When it comes to math, one of the most important things to understand are intervals of increase and decrease. This is because they can help you solve a variety of questions and equations. Luckily, we have a **maclaurin series calculator** that can help you with this. All you need to do is input the formula, and it will provide you with the expansion. Additionally, if you are having trouble understanding the concept, there are a variety of known maclaurin series that can help you out. And finally, if you still have questions, our resource can help you find the answers you need.