$f(x) = \left\{ \begin{array}{r} \frac{\sin{3x}}{\sin x},\ \ \ x
eq 0 \ k,\ \ \ \ \ \ \ \ \ \ x = 0 \end{array} ight.\$ is continuous, if $k$ is

Question

$f(x) = \left\{ \begin{array}{r} \frac{\sin{3x}}{\sin x},\ \ \ x 
eq 0 \ k,\ \ \ \ \ \ \ \ \ \ x = 0 \end{array} ight.\$ is continuous, if $k$ is

Dr. Abubacker · Accepted Answer

(a)
For continuity, $\lim_{x \rightarrow 0}\ f(x) = k$
$\Rightarrow \ \ \ \lim_{x \rightarrow 0}\ \ \ \frac{\sin{3x}}{\sin x} = k\ \  \Rightarrow \ \underset{x \rightarrow 0}{lim}\ \ \frac{\sin{3x}}{3x}.\frac{3x}{\sin{3x}} = k$
$\Rightarrow \ \ \ 3 = k$

Q. $f(x) = \left\{ \begin{array}{r} \frac{\sin{3x}}{\sin x},\ \ \ x \neq 0 \\ k,\ \ \ \ \ \ \ \ \ \ x = 0 \end{array} \right.\$ is continuous, if $k$ is

Explanation

Reviewed by Dr. Abubacker

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