GATE Chemical 2018 | Question: 46

Question

If $y=e^{-x^{2}}$ then the value of $\underset{x\rightarrow \infty }{\lim}\frac{1}{x}\frac{dy}{dx}$ is __________

Answer 1

\[
\text{Given } y = e^{-x^2}
\]
\[
\frac{dy}{dx} = -2x e^{-x^2}
\]
\[
\frac{1}{x} \frac{dy}{dx} = \frac{1}{x}(-2x e^{-x^2}) = -2 e^{-x^2}
\]
\[
\lim_{x \to \infty} -2 e^{-x^2} = 0
\]