Question

how do you know when a limit does not exist?

Answer 1

kind of a broad question
can you be more specific?

Answer 2

When it doesn't exist, it just doesn't. :-)

Answer 3

if the left hand and right hand limits are not equal, then the limit doesn't exist

Answer 4

yeah maybe
but we also say the limit doesn't exist is a series diverges for example
or if the rational function has a pole
etc. kind of hard to pin down

Answer 5

If it isn't bounded \(\lim\limits_{x\rightarrow \infty} x^{2}\)

If it won't hold still \(\lim\limits_{x\rightarrow \infty} \cos(x)\)

Just to name a couple.