Let $g\left(x\right)$ be the function $\frac { 2 ^ { x } - 2 } { 3 ^ { x } - 3 }$.

1. Below is a table of values for $g\left(x\right)$ for $x$ near $1$. Estimate $\lim\limits _ { x \rightarrow 1 } g(x)$.

   Hint (a):

   Check at $x = 0.9999$ and at $x = 1.0001$. What do you notice?

   x	g(x)
   $0.9$	$0.4291$
   $0.95$	$0.4249$
   $0.99$	$0.4215$
   $0.999$	$0.4207$
   $0.9999$	$0.42063$

   x	g(x)
   $1.1$	$0.4120$
   $1.05$	$0.4164$
   $1.01$	$0.4198$
   $1.001$	$0.42053$
   $1.0001$	$0.42061$

2. Use a graph to decide if you can get a better estimate of the limit for $g\left(x\right)$ as $x → 1$.