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If $a, b, c$ and $d$ are positive, then
is equal
Options:
is equal
Solution:
2640 Upvotes
Verified Answer
The correct answer is:
$e^{d / b}$
$L=\lim _{x \rightarrow \infty}\left(1+\frac{1}{a+b x}\right)^{c+d x} \quad\left[\right.$ form $\left.(1)^{\infty}\right]$
$$
\begin{aligned}
&=e^{\lim _{x \rightarrow \infty} \frac{c+d x}{a+b x}}=e^{\lim _{x \rightarrow \infty} \frac{c / x+d}{a / x+b}} \\
=& e^{\frac{0+d}{0+b}}=e^{d / b}
\end{aligned}
$$
$$
\begin{aligned}
&=e^{\lim _{x \rightarrow \infty} \frac{c+d x}{a+b x}}=e^{\lim _{x \rightarrow \infty} \frac{c / x+d}{a / x+b}} \\
=& e^{\frac{0+d}{0+b}}=e^{d / b}
\end{aligned}
$$
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