Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it.

lim (2x + 1)^(cot(x))
x→0+

where .

By continuity of , you have



As in the numerator, you approach ; in the denominator, you approach . So you have an indeterminate form . Provided the limit indeed exists, L'Hopital's rule can be used.



Now the numerator approaches , while the denominator approaches , suggesting the limit above is 2. This means