If $f(x) = \left\{ \begin{array}{r} \log_{(1 - 3x)}{(1 + 3x),\ for\ x
eq 0} \ k,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ for\ x = 0 \end{array} ight.\$ is continuous at $x = 0$, then $k$ is equal to

Question

If $f(x) = \left\{ \begin{array}{r} \log_{(1 - 3x)}{(1 + 3x),\ for\ x 
eq 0} \ k,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ for\ x = 0 \end{array} ight.\$ is continuous at $x = 0$, then $k$ is equal to

Dr. Abubacker · Accepted Answer

(d)
Given, $f(x) = \left\{ \begin{array}{r}
\log_{(1 - 3x)}{(1 + 3x),\ for\ x 
eq 0} \
k,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ for\ x = 0
\end{array} ight.\$
$\lim_{x ightarrow 0}\ \ f(x) = \lim_{x ightarrow 0}\frac{\log{(1 + 3x)}}{\log{(1 - 3x)}}$
$= - \lim_{x ightarrow 0}\frac{\log{(1 + 3x)}}{3x}.\frac{( - 3x)}{\log{(1 - 3x)}}$
$= - 1$
And $f(0) = k$
$\because f(x)$ is continuous at $x = 0$
$	herefore\ \ \ \ k = - 1$

Q. If $f(x) = \left\{ \begin{array}{r} \log_{(1 - 3x)}{(1 + 3x),\ for\ x \neq 0} \\ k,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ for\ x = 0 \end{array} \right.\$ is continuous at $x = 0$, then $k$ is equal to

Explanation

Reviewed by Dr. Abubacker

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