A two-sided limit exists if the left-hand limit and the right-hand limit of a function are the same. A shorthand notation is used to describe the limit of a function according to the form lim x → a f ( x ) = L , which indicates that as x approaches a , both from the left of x = a and the right of x = a , the output…

A function has a left-hand limit if f ( x ) approaches L as x approaches a where x < a . A function has a right-hand limit if f ( x ) approaches L as x approaches a where x > a

left-hand limit — the limit of values of f ( x ) as x approaches from a the left, denoted lim x → a - f ( x ) = L . The values of f ( x ) can get as close to the limit L as we like by taking…. limit — when it exists, the value, L , that the output of a function f ( x ) approaches as the input x gets closer and closer to a but does not equal a . The value of the output, f ( x )…. right-hand limit — the limit of values of f ( x ) as x approaches a from the right, denoted lim x → a + f ( x ) = L . The values of f ( x ) can get as close to the limit L as we like by taking…. two-sided limit — the limit of a function f ( x ) , as x approaches a , is equal to L , that is, lim x → a f ( x ) = L if and only if lim x → a - f ( x ) = lim x → a + f ( x ) . lim x → a - f ( x….