16: You should get

There is an indeterminate product in the denominator. Algebra does not seem to help, so the standard procedure tells you to change this product into a ratio; this time you will be "putting something up". However, none of the terms looks exactly appealing. If you put the sine on the top, it will become even more nasty: Imagine differentiating sine of 1/x and the power ⁻¹ on the top of it. The term with the root looks equally unappetizing. Still, one of these two options is slightly better. Try to guess and do it.

Remark: Is there any way to avoid this work? It depends. If you are lucky and the original difference on the top has limit zero, then you can apply the l'Hospital rule to the original fraction, which is somewhat easier (it does not have the reciprocals in it). How do you find out whether the numerator goes to zero? Just like what we did above, just ignore the sine.

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