query: Can the derivative of a $C^1$ function vanish at the infinity imply it has a limit at the infinity?
positive_passages.docid: 143874
positive_passages.text: Limit of derivative is zero. Does it imply a limit for f(x)?
negative_passages.docid: 12556
negative_passages.text: A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
negative_passages.docid: 91310
negative_passages.text: Does a limit point always exist?
negative_passages.docid: 91616
negative_passages.text: Existence of a $C_c^{\infty}$ function $\Phi$ s.t. $\int \nabla \Phi \neq 0.$
negative_passages.docid: 2129
negative_passages.text: Showing that the derivative operator is not bounded on $L^2 (\mathbb{R})$
negative_passages.docid: 79368
negative_passages.text: Can a limit of an integral be moved inside the integral?
negative_passages.docid: 142329
negative_passages.text: Limit of reciprocal function is the reciprocal of its limit
negative_passages.docid: 5625
negative_passages.text: Entire function with vanishing derivatives?
negative_passages.docid: 113888
negative_passages.text: Behavior of derivative near the zero of a function.
negative_passages.docid: 123945
negative_passages.text: Every absolutely continuous function with integrable derivative tends to zero at infinity
negative_passages.docid: 69845
negative_passages.text: Construct a real function with is exactly $C^2$ such that its first derivative does not vanish everywhere
negative_passages.docid: 131444
negative_passages.text: Local maximum implies derivative is $0$
negative_passages.docid: 13150
negative_passages.text: If the derivative of $f$ is never zero, then $f$ is one-to-one
negative_passages.docid: 35264
negative_passages.text: Must a monotone function have a monotone derivative?
negative_passages.docid: 10428
negative_passages.text: Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist
negative_passages.docid: 33486
negative_passages.text: Negation of the Definition of Limit of a Function
negative_passages.docid: 50472
negative_passages.text: If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$