Finding the limit $\lim_{t \to \infty} \frac{t-t\sqrt{t}}{2t^{3/2}+3t-5} $ Can someone help me solve this limit?
$$\lim_{t \to \infty} \frac{t-t\sqrt{t}}{2t^{3/2}+3t-5} $$
 A: Hint: $$t\sqrt t = t^{3/2}$$
Then divide numerator and denominator by $t^{3/2}$ and evaluate to get a limit of $-1/2$.
A: \begin{align}
\lim_{t \to \infty} \frac{t-t\sqrt{t}}{2t^{3/2}+3t-5}&=\lim_{t \to \infty} \frac{-t^{3/2}+t}{2t^{3/2}+3t-5}\\
&=\lim_{t \to \infty} \frac{-\frac{t^{3/2}}{t^{3/2}}+\frac{t}{t^{3/2}}}{2\frac{t^{3/2}}{t^{3/2}}+3\frac{t}{t^{3/2}}-\frac{5}{t^{3/2}}}\\
&=\frac{-1+0}{2+0-0}\\
&=-\frac{1}{2}
\end{align}
A: General rule with polynomials or terms with radical roots: divide by the term with the highest order. If there's one term of this order, the limit is its coefficient, if two - the ratio of their coefficients. All other terms tend to $0$.
A: Thx @amWHy
$$\lim_{t \to \infty} \frac{t-t\sqrt{t}}{2t^{3/2}+3t-5}
\implies 
\lim_{t \to \infty} \frac{t-t^{3/2}}{2t^{3/2}+3t-5} 
\implies 
\lim_{t \to \infty} \frac{\frac{t}{t^{3/2}}-\frac{t^{3/2}}{t^{3/2}}}{\frac{2t^{3/2}}{t^{3/2}}+\frac{3t}{t^{3/2}}-\frac{5}{t^{3/2}}}
\implies
\lim_{t \to \infty} \frac{0-1}{2+0-0}
\implies
\lim_{t \to \infty}-\frac{1}{2}$$
