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Question 1
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Let $f\colon\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f(0)=\frac{1}{\pi}$ and $f(x)=\frac{x}{e^{\pi x}-1}$ for $x\ne0$, then
A.
$f(x)$ is not continuous at x = 0
B.
$f(x)$ is continuous but not differentiable at x = 0
C.
$f(x)$ is differentiable at x = 0 and $f'(0) = -\frac{\pi}{2}$
D.
None of the above
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