The first one is correct, but be careful with "inverse" - formally, is the inverse of , not .

The second one is also correct but your reasoning is faulty - checking a few values does not show what the limit is.

To formally prove each limit, show that the numerator of the function does not tend to 0 as x tends to infinity. Then, since the denominator does tend to 0, the function will tend to positive or negative infinity, depending on which side the limit is taken from (a few details are left out for you to complete)