The limit of a function or a sequence in mathematics is the number the function or sequence approaches as the independent variable (x) approaches a particular number. The definition is as follows: If f(x) becomes arbitrarily close to a unique number L as x approaches c from either side, the limit of f(x) as x approaches c is L. This is often expressed lim x c f(x) = L.

There are three major areas where the limit of a function or sequence does not exist. In order for a function or sequence to have a limit, the function or sequence must be approaching the said value of the function or sequence from the left and right sides of x. Left and right hand behavior must agree. If it does not, the function does not have a limit. The behavior of the function or sequence cannot approach...