Recent content by PonyBarometer

Definition of this orthogonality goes like this: ## x, y \in X##, where ##X## - normed space and ##X^*## - its dual space. Then ##x## is orthogonal ##y##, if $$ \sup\{f(x)g(y)-f(y)g(x)|, \, f,g\in X^*, \|f\|,\|g\|≤1\}=\|x\|\|y\| $$ From what I understand ##f## and ##g## are linear...

Oh, I new I had made some mistakes writing the post. It was meant to be n -> infinity. And I can't see how can the fundamental theorem of calculus help.

Homework Statement Given:lim_{n\rightarrow ∞} \int^{a^n}_{1} \frac{t^{1/n}}{(1+t)t} dt=\int^{∞}_{1} \frac{1}{(1+t)t} dt a - Natural number. I need to prove that I can bring limit under the integral sign. Homework Equations The Attempt at a Solution I've got this so far: | \int^{a^n}_{1}...