Evaluation of Limits by Using DE 'L' Hospital's Rule

If f(x0 and g(x) are two functions of x and

(i) lim (x→a) f(x) = lim (x→a) g(x) = 0

both functions are continuous and differentiable at x = a

Then lim (x→a) f(x)/g(x) = lim (x→a) f'(x)/g'(x)

Provided g(a)≠ 0 and f'(x) and g'(x) are continuous at x=a.