Could someone help me with this problem?

Question

anonymous · Answer

attachment

anonymous · Answer

I know that I can't use substitution, but the other two methods are giving me trouble.

gaberen · Answer

$$\lim_{x \rightarrow 4}\frac{ x^2-16 }{ x+4 }=\lim_{x \rightarrow 4}\frac{ (x+4)(x-4) }{ (x+4) }=\lim_{x \rightarrow 4}(x-4)=(4-4)=0$$

anonymous · Answer

Woah! Thank you, @gaberen!

anonymous · Answer

But wait, if it's zero, does that mean it doesn't exist?

gaberen · Answer

No problem! And, no, it just means the graph approaches 0 as x approaches 4. You can plot the equation here for a more visual explanation: https://www.desmos.com/calculator

gaberen · Answer

Situations a limit doesn't exist:
1. The limit from the right doesn't equal the limit from the left
2. The function is unbounded e.g. goes to +/- infinity
3. Some oscillating functions