15: The exponential can be ignored first, the fraction is a ratio of polynomials and it is of the type . What should one do? The "+1" and "−1" parts can be ignored when x is large, what is left is x/x = 1. So the guess for the limit should be e¹ = e. To prove it, there are two options.

The easier way is to determine leading terms in the fraction and factor them out, even easier is to cancel the leading term.

An alternative would be to pull the exponential out of the limit and apply l'Hospital's rule to the resulting limit of the type .

Next hint
Answer