query: Let $f:[0,\infty[ \rightarrow \mathbb{R}$ be differentiable on $(0,\infty)$ such that $f'(x) \to b \; as \; x \to \infty$
positive_passages.docid: 144422
positive_passages.text: How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
negative_passages.docid: 18734
negative_passages.text: Showing that a function is differentiable
negative_passages.docid: 1371
negative_passages.text: Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
negative_passages.docid: 23222
negative_passages.text: If $f(x) + f'(x) + f''(x) \to A$ as $x \to \infty$, then show that $f(x) \to A$ as $x \to \infty$
negative_passages.docid: 122003
negative_passages.text: From the limit definition of differentiability, determine where the function $f(x) = \sqrt{x}$ is differentiable?
negative_passages.docid: 68048
negative_passages.text: Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$
negative_passages.docid: 9270
negative_passages.text: Differentiable function, with $f'(x)=[f(x)]^2$
negative_passages.docid: 23186
negative_passages.text: $f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$
negative_passages.docid: 19072
negative_passages.text: $\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
negative_passages.docid: 155333
negative_passages.text: Prove that $\lim_{x\to\infty}\frac{f(x)}x=\lim_{x\to\infty}f'(x)$
negative_passages.docid: 145173
negative_passages.text: $f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
negative_passages.docid: 54321
negative_passages.text: Questions about $f: \mathbb{R} \rightarrow \mathbb{R}$ with bounded derivative
negative_passages.docid: 112285
negative_passages.text: Show that $\lim_{x\to\infty} f(x)=0 \implies \lim_{x\to\infty} f'(x)=0$
negative_passages.docid: 132824
negative_passages.text: Does $f$ monotone and $f\in L_{1}([a,\infty))$ imply $\lim_{t\to\infty} t f(t)=0$?
negative_passages.docid: 38923
negative_passages.text: What can we say about differentiability of $f$ at $c$?
negative_passages.docid: 32063
negative_passages.text: if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$
negative_passages.docid: 6417
negative_passages.text: Can a function be differentiable at the end points of its (closed interval) domain?