CPM Homework Help : CALC Problem 3-12

Without your calculator, find the limits indicated below.

$\lim\limits_ { h \rightarrow 0 } \frac { ( 2 ( x + h ) - 3 ) - ( 2 x - 3 ) } { h }$
Hint (a):
There is either a hole or a vertical asymptote at $h = 0$ . If there is a hole, then the $h$ will cancel out.... and the limit will approach a finite value. If there is a vertical asymptote, then the $h$ will not cancel out... and the limit will not exist. Simplify the numerator to see if the limit exists.
Answer (a):
$\lim\limits_ { h \rightarrow 0 } \frac { ( ( x + h ) ^ { 2 } + ( x + h ) ) - ( x ^ { 2 } + x ) } { h }$

$\lim\limits_ { h \rightarrow 0 } \frac { ( ( x + h ) ^ { 2 } + ( x + h ) ) - ( x ^ { 2 } + x ) } { h }$
Hint (b):
Refer to the hint in part (a).

Compute without a calculator