Search any question & find its solution
Question:
Answered & Verified by Expert
$\lim _{n \rightarrow \infty} \frac{A+e^{n x}}{x+A e^{n x}}=$
Options:
Solution:
1509 Upvotes
Verified Answer
The correct answer is:
$\frac{A}{x}$, when $x < 0$
when $x < 0$
$\begin{aligned} & n x < 0 \\ & \lim _{n \rightarrow \infty} n x \rightarrow-\infty \\ & \lim _{n \rightarrow \infty} e^{n x}=e^{-\infty}=0\end{aligned}$
$\lim _{n \rightarrow \infty} \frac{A+e^{n x}}{x+A e^{n x}}=\lim _{n \rightarrow \infty} \frac{A+0}{x+A \cdot 0}$
$=\frac{A}{x}$
$\begin{aligned} & n x < 0 \\ & \lim _{n \rightarrow \infty} n x \rightarrow-\infty \\ & \lim _{n \rightarrow \infty} e^{n x}=e^{-\infty}=0\end{aligned}$
$\lim _{n \rightarrow \infty} \frac{A+e^{n x}}{x+A e^{n x}}=\lim _{n \rightarrow \infty} \frac{A+0}{x+A \cdot 0}$
$=\frac{A}{x}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.