Given $x,y\in\mathbb{C}^n$ s.t. $f(x,y)=\sup_{\theta,\phi}\{\|e^{i\theta}x-e^{i\phi}y\|^2,\theta,\phi\in\mathbb{R}\}$
68409
Consider $f(x,y)=\sup_{θ,φ}\{||e^{i θ }x+ e^{i φ }y||^2: θ,φ∈R\}$ in which $x,y\in\mathbb C^n$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
79281
Let $f : X \to Y$ be a function and $E \subseteq X$ and $F \subseteq X$. Show that in general
86635
Optimizing $(X_{n}+c)^{2}$ to show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
143200
$f(r,\theta)=(r\cos\theta,r\sin\theta)$ Then
91251
$n$th derivative of $e^{ax}\sin(bx+c)$
149634
$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
45342
Generalization of Mean Value Theorem to functions, $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$
79307
How to analyze $\sup_{x>0}|e^xf(x)| < \infty$ and $\sup_{n\in\mathbb{N}} |f^{(n)}(0)|< \infty$?
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
34077
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
38923
What can we say about differentiability of $f$ at $c$?
127449
Uniform continuous of $f(x,y) = \sin(x^2+y)$
125723
Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
26602
Continuity and existence of directional derivatives at all directions of a $f:\mathbb{R}^{2} \to \mathbb{R}$ given by $f(x,y)=\frac{2x^2y}{x^2+y^2}$