Find the limit L$.$

lim$$x$2($x$2+2$x$)$

L $=$

Use the $-$ definition to prove that the limit is L$.$

Given $>0$:

assume $|$f$($x$)$ L$|<,$ then$$

$($x$2+2$x$)$

$<$

x

x $+$

$<$

Assume

$3<$ x $<1,$

you can choose

$=$

$3$

$.$

Then,

if $0<|$x $(2)|<$ when $=$

$3$

$,$ you have$$

x $+$

$<$

$13$

$<$

$1|$x$|$

$$

x

x $+$

$<$

x$2+2$x $$

$<|$f$($x$)$ L$|<$