cyr

### Questions (8)

 5 $f,g$ analytic on $I\subset \mathbb{R}$. If exist $a\in I$ such that $f=g$ and $f^{(n)}=g^{(n)}$then we have $f(x)=g(x)$ for every $x \in I$. 3 Give $f:\mathbb{R} \rightarrow \mathbb{R}$ such that $|f'(x)|<1$ $f(x) \neq x$ for all $x \in \mathbb{R}$ 1 Show that $\lim \limits_{|P|\rightarrow 0} \sum \limits^n_{i=1}f(\zeta_i)g(\eta_i)(t_i-t_{i-1})=\int^{b}_{a}f(x)g(x)dx$ [duplicate] 1 If $f(0)=0$ and for every $x\in \mathbb{R}$ we have $f'(x)=[f(x)]^2$, show $f(x)=0$ $\space$ for every $x\in \mathbb{R}$ 1 Set of distance between elements of Cantor set is equal to [0,1]

### Reputation (167)

This user has no recent positive reputation changes

This user has not answered any questions

### Tags (10)

 0 real-analysis × 8 0 riemann-integration 0 cantor-set 0 proof-verification 0 calculus 0 analyticity 0 functions 0 analytic-functions 0 limits 0 derivatives

### Accounts (7)

 Mathematics 167 rep 99 bronze badges Physics 13 rep 33 bronze badges Philosophy 1 rep 11 bronze badge English Language Learners 1 rep 11 bronze badge MathOverflow 1 rep 11 bronze badge