How do you use l'Hopital's Rule to evalute #lim_(xrarroo) (x+sin(x))/x#?
L'Hopital's Rule only applies if the limit is the indeterminate
There is one error and an additional explanation is needed for why it won't work even if we correct the error. I have added a second edit .
We apply l"Hopital's Rule for
This limit does not exist and is neither
In order to use
we must have one of the appropriate initial indeterminate forms (
and also we must have
In this question,
It occurs to me that there may be a typographic error in the question.
It may be that the intended question involved
Is so, then the derivative stated in the question is correct, but the explanation of why l'Hopital fails is the same.
In order to get an anwer from l'Hopital we must have
Therefore l'Hopital's rule offers us no help for evaluating this limit.
(Note: This example shows the l'Hopital will not give answers for every indeterminate limit. Sometimes it fails.)
Finally, note that we can evaluate the limit without l'Hopital using