I was wondering if someone could help me with the problems within the picture:
I am in dire need of a step by step explanation as I answered this as Not enough info for #8 and -8 for #9 and both were incorrect
well # 2 should be 8 since h(x) approaches 5, which causes g(x) to approach 8
#1 is a piece wise function which is not continous since approaching the value from the right and left yield two different values
i dont think you can answer this with the information your given
$\displaystyle \lim_{x \rightarrow p} g(h(x)) = g\left( \lim_{x \rightarrow p} h(x) \right)$
(provided certain conditions are met)
$\displaystyle = g(5)$.
However, $\displaystyle \lim_{u \rightarrow p} g(u) = g(5)$ only if g is continuous at $\displaystyle u = 5$. Since you have not been told whether or not this is the case, there is insufficient information to determine the given limit since the value of $\displaystyle g(5)$ is not known.