Q73 / 150 · MHT CET 2011 · Mathematics

If $a, b, c$ and $d$ are positive, then is equal

  • Correct answer
    A
    $e^{d / b}$
  • B
    $e^{c / a}$
  • C
    $e^{(c+d) /(a+b)}$
  • D
    $\underline{e}$

Solution

$L=\lim _{x \rightarrow \infty}\left(1+\frac{1}{a+b x}\right)^{c+d x} \quad\left[\right.$ form $\left.(1)^{\infty}\right]$ $$ \begin{aligned} &=e^{\lim _{x \rightarrow \infty} \frac{c+d x}{a+b x}}=e^{\lim _{x \rightarrow \infty} \frac{c / x+d}{a / x+b}} \\ =& e^{\frac{0+d}{0+b}}=e^{d / b} \end{aligned} $$

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

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