The value of limx→∞ 1+3×2+3×1−x1+x , is

The value of $lim_{x \to \infty} {(\frac{1 + 3 x}{2 + 3 x})}^{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}}$ , is

A
0
B
-1
C
$e$
D
1

Solution:

$lim_{x \to \infty} {(\frac{1 + 3 x}{2 + 3 x})}^{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}} = 1$ , because

$\frac{1 + 3 x}{2 + 3 x} \to 1$ and $\frac{1 - \sqrt{x}}{1 + \sqrt{x}} \to 1$ as $x \to \infty$

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