# How do you know when to use L'hospital's rule twice?

##### 1 Answer

As soon as you try substitution and see you're in the form

#L = lim_(x->0) (e^x- x - 1)/x^2#

Try substitution on this and you will get

#L = lim_(x->0) (e^x - 1)/(2x)#

Now try substitution again to get

#L = lim_(x-> 0) (e^x)/2#

Now we can evaluate directly and see that the limit is

However there will be times when you may not use l'hospitals more than once. Take the following.

#L = lim_(x->0) (e^x - 1)/x^2#

Try substitution and it'll yield

#L = lim_(x->0) e^x/(2x)#

Now try substitution and you will get

Hopefully this helps!