Evaluate the following limits.

1. $\lim \limits _ { x \rightarrow 2 } \frac { x ^ { 2 } - 4 } { x - 2 }$ 

   Hint (a):

   Factor first. The denominator might 'cancel out.'

2. $\lim \limits _ { h \rightarrow 0 } \frac { ( 1 + h ) ^ { 2 } - 1 } { h }$ 

   Hint (b):

   This is Hana's definition of a derivative at a point.

   $f'(a)=\lim \limits_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h}$

   What is $f\left(x\right)$?
   What is $a$?
   What is $f^\prime\left(x\right)$?
   What is $f^\prime\left(a\right)$?

   Answer (b):

   $f\left(x\right) = x^{2}$
   $a = 1$
   $f ^\prime\left(x\right) = 2x$
   $f ^\prime\left(a\right) = 2$
   Therefore the limit as $h→0 = f^\prime \left(a\right) = 2$