question: what is lim x→+∞ s(x)? s(x)=4ex10x2 select the correct answer below: 0 5/2 2/5 +∞ -∞

Explanation:

Step1: Apply L'Hopital's rule

Since $\lim_{x\rightarrow+\infty}\frac{10x^{2}}{4e^{x}}$ is in the $\frac{\infty}{\infty}$ - form, by L'Hopital's rule, $\lim_{x\rightarrow+\infty}\frac{10x^{2}}{4e^{x}}=\lim_{x\rightarrow+\infty}\frac{20x}{4e^{x}}$.

Step2: Apply L'Hopital's rule again

The limit $\lim_{x\rightarrow+\infty}\frac{20x}{4e^{x}}$ is still in the $\frac{\infty}{\infty}$ - form. So, $\lim_{x\rightarrow+\infty}\frac{20x}{4e^{x}}=\lim_{x\rightarrow+\infty}\frac{20}{4e^{x}}$.

Step3: Evaluate the limit

As $x\rightarrow+\infty$, $e^{x}\rightarrow+\infty$. Then $\lim_{x\rightarrow+\infty}\frac{20}{4e^{x}} = 0$.

Answer:

$0$