Question

For a simple function like y=x
If there is a hole at x=0 would the limit as x approaches 0 exist? Or would you just round it to 0?

Answer 1

Check the limit of the function as x approaches 0 from the right and check the limit of the function as x approaches 0 from the left. If these two limits are equal, then the limit exists.

For y = x:
lim x->0+ x = 0
lim x->0- x = 0
lim x->0 x = 0

Answer 2

So despite a hole in the graph the limit would still be 0?

Answer 3

Yes, that is correct.

Answer 4

thanks!