Prove the statement using the $,$ definition of a limit$.$

$$lim$$x $1$

$10+2$x$3$

$=4$

Given $>0,$ we need $---$Select$--->0><0<$ such that if $0<|$x $1|<,$ then

$10+2$x$3$

$4$

$---$Select$--->><<.$

But

$10+2$x$3$

$4$

$<$

$2$x $23$

$<$

$23$

$|$x $1|<|$x $1|<---$Select$---(3/2)44.$

So if we choose

$=---$Select$---4(3/2)3/24,$

then

$0<|$x $1|<$

$$

$10+2$x$3$

$4$

$<.$

Thus,

lim$$x $1$

$10+2$x$3$

$=4$

by the definition of a limit$.$