Let a be a real number such that $0$Find the second Taylor polynomial

T$2($x$)$

for

f$($x$)=$ex$2$

based at

b$=0$

$.$

T$2($x$)=$

For values of x near $0,$

T$2($x$)$ ex$2.$

Approximate the value of

$1$ex$20$

$$dx

by computing

$1$T$2($x$)0$

$$dx

$.$

$1$ex$20$

dx$$