1. ## Help Needed with Advanced Limits

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

2. 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

3. Well #2 seems to be right, but if anyone could reword it, I'd be thankful. #1 can't be Not enough info because my proffesor said that that was the wrong answer. Any suggestions???

4. Originally Posted by TheUnfocusedOne
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
The right hand limit is (1)(4) = 4. The left hand limit is (-2)(-2) = 4. Left hand limit = right hand limit therefore the limit exists and is equal to

Spoiler:
*gasp* I can't believe it ...... 4

5. Originally Posted by TheUnfocusedOne
well # 2 should be 8 since h(x) approaches 5, which causes g(x) to approach 8
I don't understand. It should approach -8 right? That's what I had thought but I was incorrect

6. Originally Posted by Some1Godlier
I don't understand. It should approach -8 right? That's what I had thought but I was incorrect
$\lim_{x \rightarrow p} g(h(x)) = g\left( \lim_{x \rightarrow p} h(x) \right)$

(provided certain conditions are met)

$= g(5)$.

However, $\lim_{u \rightarrow p} g(u) = g(5)$ only if g is continuous at $u = 5$. 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 $g(5)$ is not known.