Left hand limit is denoted by following symbol:
lim x- >a-
Here a- (negative symbol). This left hand side limit is used for calculating the left hand side area of particular function like f(x) = x2 is a function and we want to calculate area around x - > 0, then left side area of f(x) is calculated by left hand side limit and right hand side area is calculated by right hand side limit. Basically left hand limit is define that value of x is slightly lower than 0 in above case. For checking the continuity or discontinuity we use left hand limit.
Limit of a function is used to describe the behavior of the function near a particular point. If a function has ordinary limits at a point x = a then definitely it will have the approximate limit at the same value. Means if the ordinary limit exists, then the left and right hand limits are same.