A left hand limit for f(x) as x approaches a is the value that f(x) approaches as x gets closer and closer to a but x is always less than (to the left of) a.
A lright hand limit for f(x) as x approaches a is the value that f(x) approaches as x gets closer and closer to a but x is always greater than (to the right of) a.
The limit of f(x) as x approaches a exists (notice there is no mention of lh or rh limit) only when the lh limit equals the rh limit.
