Question

Can somebody check these limits?

Answer 1

I am not sure where I am messing up at.

Answer 2

If the one-sided limit from either side is different, then the limit from both sides simultaneously cannot exist.
\[\large\lim_{x\to c^-}f(x)\neq\lim_{x\to c^+}f(x)~~\implies~~\lim_{x\to c}f(x)~\text{doesn't exist}\]

Answer 3

So problem number 3 does not exist. Did I mess up anywhere else?

Answer 4

The fourth one is also incorrect. The function is indeed approaching some value from both sides. The fact that the function itself isn't defined for \(x=-3\) (indicated by the hole) doesn't mean the limit doesn't exist.

Answer 5

So how do you find that limit?

Answer 6

A quick way is to just figure out the \(y\) coordinate of the hole.

Answer 7

#8 and #10 are also incorrect

Answer 8

properties, and things, to know

Answer 9

Alright. I originally had most of those right, but I started second guessing myself. Thanks for the help y'all!

Answer 10

yw