A) R
B) \[\left\{ n\pi \pm \frac{\pi }{3},n\in I \right\}\]
C) \[\left\{ n\pi \pm \frac{\pi }{6},n\in I \right\}\]
D) None of these
Correct Answer: C
Solution :
[c] We have, \[f(x)=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{(2\,\sin \,x)}^{2n}}}{-{{(2\cos \,x)}^{2n}}}\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{(2\,\,\sin \,\,x)}^{2n}}}{{{(\sqrt{3})}^{2n}}-{{(2\,\cos \,x)}^{2n}}}\] \[f(x)\] is discontinuous when \[{{(\sqrt{3})}^{2n}}-{{(2\,\,\cos \,\,x)}^{2n}}=0\] i.e. \[\cos \,\,x=\pm \frac{\sqrt{3}}{2}\Rightarrow x=n\pi \pm \frac{\pi }{6}(n\in I)\]You need to login to perform this action.
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