A) \[1,-1\]
B) \[0,\,\,\,1\]
C) \[1,\,\,\,2\]
D) \[0,\,\,\,\pi \]
Correct Answer: A
Solution :
Given that, \[\underset{x\to 0}{\mathop{\lim }}\,\,\,kx\,\text{cosec (x)=}\underset{x\to 0}{\mathop{\text{lim}}}\,x\,\text{cosec (kx)}\] \[\Rightarrow \] \[k\,\underset{x\to 0}{\mathop{\lim }}\,\,\frac{x}{\sin \,\,x}=\,\underset{x\to 0}{\mathop{\lim }}\,\,\frac{x}{\sin \,kx}\times \frac{k}{k}\] \[\Rightarrow \] \[k=\frac{1}{k}\] \[\Rightarrow \] \[{{k}^{2}}=1\] \[\Rightarrow \] \[k=\pm 1\]
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