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