31: The expression in the numerator is of the type
∞ − ∞,
another infinity is in the
denominator. One could try to use the general version of l'Hospital's rule,
but check that it would not help at all, since exponentials do not change
when differentiated.
The right approach is to use the factoring out of dominant powers
(see the box
"polynomials and ratios with
powers").
Next hint
Answer