Find the limit as x approaches infinity (sqrt(t)+t^2)/(2t-t^2).

We are asked to evaluate (sqrt(t)+t^2)/(2t-t^2) as t approches infinity. In this case, when infinity is substituted, the answer is infinity/infinity which is an indeterminate number. Using L'hopital's rule, we differentiate separately the tems in the numerator and denominator. This is equal to [0.5t^-0.5 + 2t] / [2 - 2t]. In this case, 1/infinity is equal to zero but still the quotient is equal to infinity over infinity. We derive again. [0.25t^-1.5 + 2] / [-2]. Substituting, the final answer is -1.