Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?
88597
Improper integral from 1 to infinity $\Rightarrow$ integrated function converges towards zero?
87115
Find a continuous function $f:[1,\infty)\to\Bbb R $ such that $f(x) >0 $, $\int_1^\infty f(x)\,dx $ converges and $\int_1^\infty f(x)^2\,dx$ diverges
145233
How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?
84969
When does $\lim_{n\rightarrow \infty} a_n = 0$ imply $\sum_{n = 0}^{\infty} a_n$ converges?
57014
Existence of a power series converging non-uniformly to a continuous function
91680
Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$?
83790
Why doesn't $d(x_n,x_{n+1})\rightarrow 0$ as $n\rightarrow\infty$ imply ${x_n}$ is Cauchy?
39797
Convergence of integrals in $L^p$
123981
Is it possible to write any bounded continuous function as a uniform limit of smooth functions
91616
Existence of a $C_c^{\infty}$ function $\Phi$ s.t. $\int \nabla \Phi \neq 0.$
56867
Convergence proof that involves integral
158940
Give an example of a continuous function $f : [0, ∞) \mapsto [0, ∞)$ such that $\int_{0}^{\infty}f(x)dx$ exists but $f$ is unbounded.
90558
A question related to a convergence of an integral
85208
Is there a function with infinite integral on every interval?
52632
$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
143695
Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
63418
Show that $f_n(x) = \frac{x^2}{n}$ for $x \in \mathbb{R}$ does not converge uniformly towards $0$ for $n \rightarrow \infty$