L'Hopitals rule really doesn't help in this situation. How would you determine this? As x approaches infinity, the limit of cosine is indefinite. Also as x approaches infinity, e^x approaches infinity.

So basically, are you supposed to look at it from the perspective that no matter what is going on with cosine, e^x becomes so massive that the numerator is negligible?....or how should you approach this limit?

Thank you.