Answer
$$1$$
Work Step by Step
Given $$ \lim _{t\rightarrow \infty}\frac{\sqrt{t}+t^2}{2t-t^2}$$
Then
\begin{aligned}
\lim _{t\rightarrow \infty}\frac{\sqrt{t}+t^2}{2t-t^2} &=
\lim _{t\rightarrow \infty}\frac{\frac{\sqrt{t}}{t^2}+\frac{t^2}{t^2}}{\frac{2t}{t^2}-\frac{t^2}{t^2}} \\
&= \lim _{t\rightarrow \infty}\frac{\frac{1}{t^{3/2}}+1}{\frac{2 }{t }-1} \\
&= \lim _{x\rightarrow \infty}\frac{0+1 }{0-1}\\
&=1
\end{aligned}
