Question

Could someone help me with this problem?

Answer 1

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

Answer 2

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

Answer 3

Woah! Thank you, @gaberen!

Answer 4

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

Answer 5

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

Answer 6

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