Hello. I need help on two questions related to limits of indeterminate forms. I've solved at least fifty other such questions, but these just elude me...

1. $\displaystyle \lim_{x\rightarrow\infty}(\sinh(x)-x)$

2. $\displaystyle \lim_{x\rightarrow0}\frac{x-\tan^{-1}(x)}{x\sin(x)}$

Much obliged if someone can help!