L'Hospital's Rule states that a limit if the limit is indeterminate, that is,

Here, if we substitute x=1 into the function , we get . Notice that if the numerator is NOT zero, then the limit will run off to . Therefore, it is necessary that A=1 so the limit is indeterminate, otherwise the limit will not converge at all. Apply L'Hospital's Rule...

Now , so repeat the process to find B. Keep going and you can get A,B,C, and also the final value of the limit L.