Let $f:[0,\infty)\to \mathbb R$ be Continuous and strictly decreasing function such that : $\lim_{x\to \infty}f(x)=0$
13674
Divergence of an improper integral
91398
Continuous function on R which tends to infinity on open interval must have a minimum
36248
A classical problem about limit of continuous function at infinity and its connection with Baire Category Theorem
45806
Finding $\lim\limits_{n \rightarrow \infty}\left(\int_0^1(f(x))^n\,\mathrm dx\right)^\frac{1}{n}$ for continuous $f:[0,1]\to[0,\infty)$
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
5371
If a function has a finite limit at infinity, does that imply its derivative goes to zero?
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
96273
Is a continuous function $ f\colon(0,\infty)\to R$, such that $f(x)\leq f(nx)$ increasing?
132738
Showing $\lim_{n \to \infty} m(E_n) = 0$, assuming $f > 0$ a.e. and $\lim_{n \to \infty} \int_{E_n}f \,dm =0$
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
144422
How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
65033
Prove inverse of strictly monotone increasing function is continuous over the range of original function
81
$\lim_{n\to \infty}f(nx)=0$ implies $\lim_{x\to \infty}f(x)=0$
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous