L'Hospital's Rule

I found the L'Hospital's rule extremely useful when I was doing process control homework tonight. So if you are not familiar with it, or can't recall it clearly, here it is.

In words, if taking limit directly doesn't work out, one thing you can do is to take derivative of the numerator and the denominator at the same time. Then take limit. Remember, after this step, if the limit still doesn't work, you can apply the L'Hospital's rule again and again until you find a way that the limit can be taken.

This can be simply applied to the initial value theorem and final value theorem in process control.

                    Initial Value Theorem

                    Final Value Theorem

                                                   
                    where F(s) is the Laplace transformation of f(t).

Hope this will help someone who are looking for a way to solve the limit problems.