query: Find a continuous function , Riemann integrable on $\mathbb{R}_+$ which does not tend to zero
positive_passages.docid: 58361
positive_passages.text: Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?
negative_passages.docid: 21269
negative_passages.text: Bijective continuous function between $(0 ,\infty)$ and $\mathbb{R}$.
negative_passages.docid: 30036
negative_passages.text: Function in $H^1$, but not continuous
negative_passages.docid: 82210
negative_passages.text: Analytic continuation of function continuous on boundary
negative_passages.docid: 80643
negative_passages.text: Show that f(x) defined on [0,infinity) R to is continuous at 0.
negative_passages.docid: 88240
negative_passages.text: Two functions discontinuous, but sum continuous
negative_passages.docid: 91398
negative_passages.text: Continuous function on R which tends to infinity on open interval must have a minimum
negative_passages.docid: 131992
negative_passages.text: A problem on continuous functions
negative_passages.docid: 96729
negative_passages.text: Changing the values of an integrable function $f:[a,b] \to \mathbb R$ countably infinitely many points not a dense subset of $[a,b]$
negative_passages.docid: 58816
negative_passages.text: Existence of a continuous function which does not achieve a maximum.
negative_passages.docid: 103241
negative_passages.text: A function that is continuous at the origin but not differentiable there
negative_passages.docid: 64797
negative_passages.text: Does an absolutely integrable function tend to $0$ as its argument tends to infinity?
negative_passages.docid: 53841
negative_passages.text: Function always continuous in a Sobolev Space?
negative_passages.docid: 33488
negative_passages.text: A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
negative_passages.docid: 68165
negative_passages.text: Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
negative_passages.docid: 74950
negative_passages.text: Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$
negative_passages.docid: 54797
negative_passages.text: Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$