For the function $f(x)=\frac{\log _8(1+x)-\log _3(1-x)}{x}$ be continuous at x=0, the value of f(0) should be
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For the function $f(x)=\frac{\log _8(1+x)-\log _3(1-x)}{x}$ be continuous at $x=0$, the value of $f(0)$ should be

(A) -1

(B) 0

(C) -2

(D) 2

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Best answer

SOLUTION —

Here, $f(0)=\lim _{x \rightarrow 0} f(x)$

$\begin{array}{l}=\lim _{x \rightarrow 0} \frac{\log _e(1+x)-\log _e(1-x)}{x} \\=\lim _{x \rightarrow 0} \frac{\frac{1}{1+x}+\frac{1}{1-x}}{1}=2\end{array}$

So, The correct option will be (D).

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