Define the left hand limit.

The left-hand limit is a concept in calculus that describes the behavior of a function as the independent variable approaches a specific value from the left side (i.e., smaller values). It is denoted by the symbol "lim" with a subscript of "x → a^-" or "x → a-" and is read as "the limit of f(x) as x approaches a from the left" or "the limit of f(x) as x approaches a from the negative side."

Mathematically, the left-hand limit is defined as follows:

lim(x → a^-) f(x) = L

This means that if the function f(x) has a left-hand limit L as x approaches a from the left, then as x gets arbitrarily close to a from the left side, the values of f(x) approach L. In other words, the function's values converge to a specific value from the left-hand side of the point a.

To evaluate the left-hand limit of a function, you analyze the behavior of the function's values as x approaches a from the left. This involves examining the function's values for x values less than a and observing any patterns or trends that emerge.