-11 Points] DETAILS MY NOTES SCALCET9 2.XP.6.007. Find the limit. (If the limit is infinite, enter ' \( \infty \) ' or ' \( -\infty \) ', as appropriate. If the limit does not otherwise exist, enter DNE \( \lim _{t \rightarrow \infty} \frac{\sqrt{t}+t^{2}}{6 t-t^{2}} \)

Calculate the limit \( \lim_{t\rightarrow \infty} \frac{\sqrt{t}+t^{2}}{6t-t^{2}} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{t\rightarrow +\infty}\left(\frac{\sqrt{t}+t^{2}}{6t-t^{2}}\right)\) - step1: Rewrite the expression: \(\lim _{t\rightarrow +\infty}\left(\frac{\left(\sqrt{t^{-3}}+1\right)t^{2}}{\left(\frac{6}{t}-1\right)t^{2}}\right)\) - step2: Reduce the fraction: \(\lim _{t\rightarrow +\infty}\left(\frac{\sqrt{t^{-3}}+1}{\frac{6}{t}-1}\right)\) - step3: Rewrite the expression: \(\frac{\lim _{t\rightarrow +\infty}\left(\sqrt{t^{-3}}+1\right)}{\lim _{t\rightarrow +\infty}\left(\frac{6}{t}-1\right)}\) - step4: Calculate: \(\frac{1}{\lim _{t\rightarrow +\infty}\left(\frac{6}{t}-1\right)}\) - step5: Calculate: \(\frac{1}{-1}\) - step6: Divide the terms: \(-1\) The limit of the expression \( \frac{\sqrt{t}+t^{2}}{6t-t^{2}} \) as \( t \) approaches infinity is -1.