The Rule
L’Hospital’s Rule states if the limit as x approaches a of f(x) over g(x) results in types of indeterminate form then, the limit as x approaches a of f(x) over g(x) is equal to the limit as x approaches a of f’(x) over g’(x). In simpler terms, the limit of a quotient of functions resulting in indeterminate form is equal to the limit of the quotient of their derivatives. The reason this is true is when we apply the definition of a derivative of the quotient of the derivatives we see it equals the original quotient of the function. (Stewart)