Do there exist functions $f$, where $\lim_{x \rightarrow \infty} f(x) = 0$ and $\lim_{x \rightarrow \infty} \frac{df(x)}{dx} \neq 0$?
Limit of a function and its derivative
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calculus
limits
functions
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1If $\lim_{x \to \infty}f'(x)$ exists, there is no such function. – 2012-12-23