44: After the l'Hospital you should get

This indeterminate ratio is way better than the one before and l'Hospital would handle it, but it would have to be used twice. Since this is a textbook example of a ratio of polynomials, it will definitely be easier to identify leading powers and factor them out (see the box "polynomials and ratios with powers").

If you went for the e^c-form, you should have done

Note that (e²)^∞ = ∞ follows from the fact that e² > 1 and the limit algebra. If you got the same result and did not think of this, you missed an important point. To see it, try to figure out the same problem, but with "+" and "-" switched in the fraction. You should get 0 as the answer, at one point you will use the fact that |e⁻²| < 1.

Next hint
Answer