Let $g(x) =\frac { 3 x - \sqrt { x } } { \sqrt { x ^ { 2 } - 5 } }$. This is the same function you used in the previous problem.

1. Use the previous result, but not your calculator, to find $\operatorname { lim } _ { x \rightarrow \infty } h ( x )$ where $h\left(x\right) = 2 + g\left(x\right)$.

   Hint (a):

   The limit is $2$ more than the limit for $g\left(x\right)$.

2. Without a calculator find $\lim\limits _ { x \rightarrow \infty } j ( x )$ where $j\left(x\right) = log\left(g\left(x\right)\right)$.

   Answer (b):

   $\log 3$

3. Check your answers to (a) and (b) by using both the graphing method and the table method.