Prove that $f$ defined by $f(x)=1$ if $x \in \mathbb{Q}$, $f(x)=0$ if $x \in \mathbb{R}\setminus \mathbb{Q}$, is not integrable
71095
Is Dirichlet function Riemann integrable?
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
144322
Prove for bounded $f$, if $f:[a,r] \to \mathbb{R}$ is Riemann-Integrable for $r \in [a,b)$ then $f:[a.b] \to \mathbb{R}$ is Riemann-Integrable
110395
Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
102943
$f(x)=1/q$ for $x=p/q$ is integrable
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
43733
$|f'(x)| \le g(x)$ implies $|f(b) - f(a)| \le \int_a^b g(x) dx$, without assuming $f'$ to be integrable.
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
145573
How to show that $f$ is a zero function?
47856
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
107727
$m\{x\in [0,1]:f'(x)=0\}>0$