The function is $f(x)= \frac{tan(\pi[x-\pi])}{1+[x]^2}$, where $[x]$ is the greatest integer function. I have four options. One or more are correct. They are - 1) $f(x)$ is discontinuous at some $x$, 2)$f’(x)$ exists for all $x$, 3)$f’(x)$ exists for all $x$ but $f’’(x)$ doesn’t exist, 4)$f(x)$ is continuous for all $x$ but $f’(x)$ doesn’t exist for some $x$
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Hint: You have $\tan(k\pi)$ for some integer $k$ in the numerator. – bjorn93 Jan 06 '20 at 14:40
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Okay,so the numerator will always approach 0,and hence the function is continuous at all points,since it will always take the value 0. Am I correct? What about differentiability? – user733666 Jan 06 '20 at 14:42
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It doesn't just approach $0$. It is $0$ for all $x$. What's the derivative of a constant? – bjorn93 Jan 06 '20 at 14:45
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....Oh. I’m sorry,yeah,the greatest integer function ensures that it is equal to 0. Okay,so it’s differentiable as well and the derivative is 0 at all points? – user733666 Jan 06 '20 at 14:47
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Sounds like you can take it from here. – bjorn93 Jan 06 '20 at 14:49
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Thank you for all the help! – user733666 Jan 06 '20 at 14:50