31: After substituting in the limit point you should get
In fact the type is "infinity over infinity", but it needs some work. In the numerator it is a bit ore difficult (it is best investigated by factoring out the dominant term, then one l'Hospital), but fortunately it is not necessary since we ave the more general version of l'Hospital's rule. It is enough to prove that the denominator goes to infinity, which is quite clear since we know that for x large the sine is irrelevant there. Formally it can be proved using comparison,
This confirms the infinity in the denominator, so we can use the l'Hospital rule.