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  • The function <img alt="\mathrm{f(x)=[x] \cos \frac{2 x-1}{2} \pi}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3D%5Bx%5D%20%5Ccos%20%5Cfrac%7B2%20x-1%7D%7B2%7D%20%5Cpi

The function \mathrm{f(x)=[x] \cos \frac{2 x-1}{2} \pi}, where [ . ] denotes the greatest integer function is discontinuous at
 

Option: 1

 all x
 


Option: 2

 all integer points
 


Option: 3

no x
 


Option: 4

x which is not integer


Answers (1)

best_answer

 If \mathrm{x \in n \in I, f(n)=n \cos \frac{2 n-1}{2} \pi=0.}

\mathrm{\lim _{x \rightarrow n+} f(x)=\lim _{x \rightarrow n^{+}} n \cos \frac{2 x-1}{2} \pi=0=\lim _{x \rightarrow n^{-}} f(x) }
If \mathrm{x \notin \mathrm{I}}, then [u] is a continuous at x and \mathrm{\cos \frac{2 u-1}{2} \pi } is also continuous. Hence f is a continuous function.

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vinayak

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