Question

How do you determine one sided limits numerically?

Answer 1

if either of the one-sided limits fails to exist, or if the one-sided limits exist but do not agree, then the limit as x approaches a of f(x) does not exist. Examples: In the case of f(x) = sqrt(x - 2), the left-hand limit at x=2 does not exist, so the limit at x=2 does not exist.