The following are well$-$known Maclaurin series with their radius of convergence $R$ for elementary functions. They can be used to find Maclaurin series of other

functions quickly.

Drag the correct answer into their placeholders.

${\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n\frac{x^{2n}}{(2n)!}$ is the Maclaurin series for

$|.$ Its radius of convergence is

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^n\frac{x}{n}$ is the Maclaurin series for $[$

$.$ Its radius of convergence is

${\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n\frac{x^{2n+1}}{(2n+1)!}$ is the Maclaurin series for

$.$ Its radius of convergence is $|,|.$

${\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n\frac{x^{2n+1}}{2n+1}$ is the Maclaurin series for $[$

$.$ Its radius of convergence is

${\displaystyle \underset{n=0}{\overset{}{}}}\frac{x^n}{n!}$ is the Maclaurin series for

$.$ Its radius of convergence ishe following are well$-$known Maclaurin series with their radius of convergence R

for elementary functions. They can be used to find Maclaurin series of other functions quickly.

Drag the correct answer into their placeholders.

$$n$=0\backslash$infty $(1)$nx$2$n$(2$n$)!$

is the Maclaurin series for Blank $1$ Question $10.$ Its radius of convergence is Blank $2$ Question $10.$

$$n$=1\backslash$infty $(1)$nxn

is the Maclaurin series for Blank $3$ Question $10.$ Its radius of convergence is Blank $4$ Question $10.$

$$n$=0\backslash$infty $(1)$nx$2$n$+1(2$n$+1)!$

is the Maclaurin series for Blank $5$ Question $10.$ Its radius of convergence is Blank $6$ Question $10.$

$$n$=0\backslash$infty $(1)$nx$2$n$+12$n$+1$

is the Maclaurin series for Blank $7$ Question $10.$ Its radius of convergence is Blank $8$ Question $10.$

$$n$=0\backslash$infty xnn$!$

is the Maclaurin series for Blank $9$ Question $10.$ Its radius of convergence is Blank $10$ Question $10.$