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Question
The function
Options
3
6
9
12
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Solution
\[f\left( x \right) = \binom{\frac{\sin 3x}{x}}{\frac{k}{2}, x = 0}, x \neq 0\]
If \[f\left( x \right)\] is continuous at \[x = 0\] , then
\[\Rightarrow \lim_{x \to 0} \frac{\sin 3x}{x} = f\left( 0 \right)\]
\[ \Rightarrow 3 \lim_{x \to 0} \frac{\sin 3x}{3x} = \frac{k}{2}\]
\[ \Rightarrow 3 \times 1 = \frac{k}{2}\]
\[ \Rightarrow \frac{k}{2} = 3\]
\[ \Rightarrow k = 6\]
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