L'Hospital's rule:

Suppose f(x) and g(x) be two provided functions differentiable in the neighbourhood of the point 'a', excluding at the point 'a' itself. If  f(x)=g(x) = 0. Or,  f(x) = g(x) = ∞. Thenf(x)/g(x) = f'(x)/g'(x) given that the limit on the right exists as a finite number or is ±∞.

Problem: If  then calculate the value of a.

Solution:  Since the applying limit is in the form of 0/0, we may use  L' Hospital's  principle

                              It is fulfilled only when a = 1.

Remark:

• L'Hospitals principle is not always useful. Suppose the example,  .

            Here, if we apply L' Hospital's Principle, then 

            Now, each the N^r and the D^r are undefined because  cos x doesn't exist.

            We may calculate this limit as follows:

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