Q101 / 160 · AP EAMCET 2022 (05 Jul Shift 2) · Mathematics

$\lim _{n \rightarrow \infty} \frac{A+e^{n x}}{x+A e^{n x}}=$

  • Correct answer
    A
    $\frac{A}{x}$, when $x < 0$
  • B
    1 , when $\mathrm{x}>0$
  • C
    0 , when $\forall \mathrm{x} \in \mathbf{R}$
  • D
    $A$, when $x=0$

Solution

when $x < 0$ $\begin{aligned} & n x < 0 \\ & \lim _{n \rightarrow \infty} n x \rightarrow-\infty \\ & \lim _{n \rightarrow \infty} e^{n x}=e^{-\infty}=0\end{aligned}$ $\lim _{n \rightarrow \infty} \frac{A+e^{n x}}{x+A e^{n x}}=\lim _{n \rightarrow \infty} \frac{A+0}{x+A \cdot 0}$ $=\frac{A}{x}$

Hence, the correct answer is option: 'A'.

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