JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f: R \rightarrow R\) is a function defined by \(f(x)=[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi,\) where \([.]\) denotes the greatest integer function, then \(f\) is
- A discontinuous at all integral values of \(x\) except at \(x=1\)
- B continuous only at \(x=1\)
- C continuous for every real \(x\)
- D discontinuous only at \(x=1\)
Answer & Solution
Correct Answer
(C) continuous for every real \(x\)
Step-by-step Solution
Detailed explanation
For \(x=n, n \in Z\) \(LHL\) \(=\lim _{x \rightarrow n^{-}} f(x)=\lim _{x \rightarrow n^{-}}[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi\) \(=0\) \(RHL =\lim _{ x \rightarrow n ^{+}} f( x )=\lim _{ x \rightarrow n ^{+}}[ x -1] \cos \left(\frac{2 x -1}{2}\right) \pi\) \(=0\)…
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