Proving f(x)=0 for all x in [a,b] when we only know that f is continuous and f(x)=0 when x is rational.
2321
Can there be two distinct, continuous functions that are equal at all rationals?
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
121771
Proof $f(x)\equiv 0$
158888
Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$.
67020
Proving that for a smooth function if $f(\frac 1 k)=0 :\forall k\in \mathbb N$ then $f(x)=0 :\forall x\in[-1,1]$
78834
if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
97316
Let $F : X → X$ be continuous. Prove that the set $\{x ∈ X : F(x) = x\}$ of fixed points of F is closed in X
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
13927
Values of $a$ s.t. for all continuous $f$ with $f(0)=f(1)$ there exists $x$ s.t. $f(x+a) = f(x)$
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
88690
$\int_a^b f(x)\mathrm dx=0$ for all $-\infty<a<b<\infty$ a,b rational implies $f=0$ a.e