For a real number y, let [y] denotes the greatest integer less than or equal to y. Then…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
For a real number y, let [y] denotes the greatest integer less than or equal to y. Then, the function
\(f(x)=\frac{\tan (\pi[x-\pi])}{1+[x]^{2}}\) is
- discontinuous at some x
- continuous at all x, but the derivative f'(x) does not exist for some x
- f '(x) exists for all x, but the derivative f''(x) does not exist for some x
- f'(x) exists for all x
Answer
(D) f'(x) exists for all x
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