_ x 0 2 (1+x)- (1+2 x) x^2 is equal to - Vidyadip

MCQ

$\lim _{x \rightarrow 0} \frac{2 \log (1+x)-\log (1+2 x)}{x^2}$ is equal to

A
$0$
✓
1
C
-1
D
2

✓

Answer

Correct option: B.

1

(B)
$\lim _{x \rightarrow 0} \frac{2 \log (1+x)-\log (1+2 x)}{x^2}$
$=\lim _{x \rightarrow 0} \frac{\log \left\{\frac{(1+x)^2}{1+2 x}\right\}}{x^2}$
$=\lim _{x \rightarrow 0} \frac{\log \left(1+\frac{x^2}{1+2 x}\right)}{x^2} \times \frac{1}{1+2 x}=1$

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