A) 1
B) ?1
C) \[\pm 1\]
D) \[\pm \,2\]
Correct Answer: C
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\,kx\cos ec\,x=\underset{x\to 0}{\mathop{\lim }}\,x\cos ec\,\,kx\] \[\Rightarrow \,\,k\,\,.\,\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{x}{\sin x}=\frac{1}{k}\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{kx}{\sin \,kx}\]\[\Rightarrow \,\,k=\frac{1}{k}\,\,\Rightarrow \,\,k=\pm \,1\] .
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