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  • The value of  <img alt="\mathrm{\lim _{x \rightarrow \frac{\pi}{2}}\left[\frac{[\sin x]-[\cos x]+1}{3}\right]=}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7Bx

The value of  \mathrm{\lim _{x \rightarrow \frac{\pi}{2}}\left[\frac{[\sin x]-[\cos x]+1}{3}\right]=} (where \mathrm{[.]} denotes the greatest integer function)
 

Option: 1

0


Option: 2

1


Option: 3

-1


Option: 4

2


Answers (1)

best_answer

\mathrm{\begin{aligned} & \lim _{x \rightarrow \frac{\pi^{+}}{2}}\left[\frac{[\sin x]-[\cos x]+1}{3}\right]=\left[\frac{0-(-1)+1}{3}\right]=0 \\ & \lim _{x \rightarrow \frac{\pi^{-}}{2}}\left[\frac{[\sin x]-[\cos x]+1}{3}\right]=\left[\frac{0-0+1}{3}\right]=0 \\ & \therefore \lim _{x \rightarrow \frac{\pi}{2}}\left[\frac{[\sin x]-[\cos x]+1}{3}\right]=0 \end{aligned}}

Hence option 1 is correct.

Posted by

himanshu.meshram

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