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The function \mathrm{f(x)=\frac{\cos x-\sin x}{\sin 4 x}} is not defined at \mathrm{x=\pi / 4.} The value which should be assigned to f at \mathrm{x=\pi / 4}\mathrm{x=\pi / 4}, so that it is continuous there, is

Option: 1

0


Option: 2

1


Option: 3

1


Option: 4

none of these

 


Answers (1)

best_answer

If \mathrm{f} is continuous at \mathrm{\mathrm{x}=\pi / 4,} then

\mathrm{ F(\pi / 4)=\lim _{x \rightarrow \frac{\pi}{4}} \frac{\cos x-\sin x}{\sin 4 x}=\lim _{x \rightarrow \frac{\pi}{4}} \frac{1}{2 \sin 2 x \cdot(\cos x+\sin x)}=\frac{1}{2 \sqrt{2}} }

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Devendra Khairwa

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