# How do you use l'Hopital's Rule to evalute #lim_(xrarroo) (x+sin(x))/x#?

##### 2 Answers

L'Hopital's Rule only applies if the limit is the indeterminate

#### Explanation:

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** .

#### Explanation:

**Error**

**Corrected version**

We apply l"Hopital's Rule for

This limit does not exist **and** is neither

**Explanation**

In order to use

we must have one of the appropriate initial indeterminate forms (

**and also** we must have

In this question,

**Second Edit**

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

But

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