## Definition 6.1.8: One-Sided Limits of a Function

If

*f*is a function with domain*and***D***c closure(*. Then:*)***D***f*has a**left-hand limit***L*at*c*if for every*> 0*there exists*> 0*such that if*x*and**D***c - < x < c*then*| f(x) - L | <*. We write*f(x) = L**f*has a**right-hand limit***L*at*c*if for every*> 0*there exists*> 0*such that if*x*and**D***c < x < c +*then*| f(x) - L | <*. We write*f(x) = L*