$h(x)={f(x)\over x}$ is decreasing or increasing or both over $[0,\infty)$
86305
A secant inequality for convex functions
142637
If $f \in \mathcal{L}^1(\mathbb{R})$ then $\lim_{h\rightarrow 0}\int_{-\infty}^\infty |f(x+h)-f(x)|dx\rightarrow 0$
132824
Does $f$ monotone and $f\in L_{1}([a,\infty))$ imply $\lim_{t\to\infty} t f(t)=0$?
3387
Derivative of $f(x)=|x|$
144422
How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
21954
A question about $f(x)\equiv 0$
91852
A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
105658
Show that a function that is locally increasing is increasing?
104263
How to show that $f'(x)<2f(x)$
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
154264
$f \in C[-1,1]$, Prove ${\lim_{h \to 0^+}}{\int_{-1}^1 \frac{h}{h^2+x^2}f(x)\,dx} = \pi f(0)$
108060
Suppose $f:[0,\infty]\rightarrow$ to R and has continuous $f'(x)$ and $f''(x)$ f(x) → 0 as x → ∞. Show that f′(x)→0 as x→∞
113871
Prove $f(x) = \sqrt x$ is uniformly continuous on $[0,\infty)$
66531
$\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open
35091
How can I prove this sequence is decreasing?
78754
Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x
50472
If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$