Question

Why does the limit as x->5 of (x^2 -6x+5)/(x-5) exist but the limit as x->5 of (x^2 -5x+6)/(x-5) does not?

Answer 1

What happens in the denominator if you allow x to = 5 in the second example?

Answer 2

This is the key to understanding the problem.

Answer 3

both of them approach infinity, don't they? D:

Answer 4

however the limits of the numerators differ