WBJEE · Maths · Continuity and Differentiability
The function \(f(x)=\frac{\tan \left\{\pi\left[x-\frac{\pi}{2}\right]\right\}}{2+[x]^{2}},\) where \([x]\) denotes the greatest integer \(\leq x\), is
- A continuous for all values of \(x\)
- B discontinuous at \(x=\frac{\pi}{2}\)
- C not differentiable for some values of \(x\)
- D discontinuous at \(x=-2\)
Answer & Solution
Correct Answer
(A) continuous for all values of \(x\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\frac{\tan \left\{\pi\left[x-\frac{\pi}{2}\right]\right\}}{2+[x]^{2}}\) Since. \(\left[x-\frac{\pi}{2}\right]\) is an integer for all \(x\), therefore \(\pi\left[x-\frac{\pi}{2}\right]\) is an integral multiple of \(\pi\) for all \(x\). Hence,…
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