A) 3
B) 0
C) -3
D) -1
Correct Answer: A
Solution :
For f(x) to be continuous, \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=f(0)\]\[f(0)=k\] \[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\underset{x\to 0}{\mathop{\lim }}\,=\frac{\sin 3x}{\sin x}=\underset{x\to 0}{\mathop{\lim }}\,\frac{3.\frac{\sin 3x}{3x}}{\frac{\sin x}{x}}=3\]\[\left[ \because \underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \theta }{\theta }=1 \right]\] \[\Rightarrow k=3\]
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