Prove that $f(\overline A) \subseteq \overline{f(A)}$
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
32063
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$
135751
Show that $Int(A)=X\setminus\overline{X\setminus A}$.
40604
Is this proof correct for : Does $F(A)\cap F(B)\subseteq F(A\cap B) $ for all functions $F$?
104263
How to show that $f'(x)<2f(x)$
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
79281
Let $f : X \to Y$ be a function and $E \subseteq X$ and $F \subseteq X$. Show that in general
117502
Proving that a certain continuous function is surjective.
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
80421
Show that $a - b \mid f(a) - f(b)$
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
83311
Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
150554
proof that $f'$ is continuous at $a$
132971
Prove that $|a| < b \iff -b<a<b$
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $