In the statements below, select the best answer from each dropdown menu. The functions are chosen from the list below:

f$($x$)=$ex

g$($x$)=$sin$($x$)$

h$($x$)=$cos$($x$)$

i$($x$)=11$x

j$($x$)=$log$(1+$x$)$

k$($x$)=$arctanx

The function $?$ f$($x$)$ g$($x$)$ h$($x$)$ i$($x$)$ j$($x$)$ k$($x$)$ is equal to its Taylor series $$n$=0$xnn$!$ when x is $?$ any real number between $-1$ and $1.$

The function $?$ f$($x$)$ g$($x$)$ h$($x$)$ i$($x$)$ j$($x$)$ k$($x$)$ is equal to its Taylor series $$n$=0$$(1)$n$1(2$n$)!$x$2$n when x is $?$ any real number between $-1$ and $1.$

The function $?$ f$($x$)$ g$($x$)$ h$($x$)$ i$($x$)$ j$($x$)$ k$($x$)$ is equal to its Taylor series $$n$=0$$(1)$n$1(2$n$+1)!$x$2$n$+1,$ when x is $?$ any real number between $-1$ and $1.$

The function $?$ f$($x$)$ g$($x$)$ h$($x$)$ i$($x$)$ j$($x$)$ k$($x$)$ is equal to its Taylor series $$n$=0$$(1)$nxn$+1$n$+1,$ when x is $?$ any real number between $-1$ and $1.$

The function $?$ f$($x$)$ g$($x$)$ h$($x$)$ i$($x$)$ j$($x$)$ k$($x$)$ is equal to its Taylor series $$n$=0$xn$,$ when x is $?$ any real number between $-1$ and $1.$

The function $?$ f$($x$)$ g$($x$)$ h$($x$)$ i$($x$)$ j$($x$)$ k$($x$)$ is equal to its Taylor series $$n$=0$$(1)$nx$2$n$+12$n$+1,$ when x is $?$ any real number between $-1$ and $1.$