Question

what are three cases where a limit does not exist? (& can you give ex of functions of graphs that represent these cases)

Answer 1

*or graphs

Answer 2

The limit doesn't exist when (for example) the limit from one direction is different than the limit from another direction. Or if the function never settles anywhere..

For example, the limit of sin(x) as x goes to infinity does not exist. the sine function will continue to oscillate between -1 and 1, forever.

Answer 3

BAsically the cases are summed up into when you have a discontinuity in the function. This can be shown as you suggested better with a graph

Answer 4

1.) Jump discontinuities - Any line that jumps at a point
2.) Infinite discontinuities (y = 1/|x|
3.) Oscillating discontinuities (sinx as polpak suggested)