lim-n-0-1-1-sin-pit-2-n-dt-1-n-

Question Number 160825 by qaz last updated on 07/Dec/21

\lim_{n \to \infty} {[\int_{0}^{1} {(1 + \sin \frac{π t}{2})}^{n} dt]}^{\frac{1}{n}} = ?

Answered by mnjuly1970 last updated on 07/Dec/21

a n s w e r : Ω := {s u p}_{[0, 1]} (1 + s i n (\frac{π t}{2}))

\underset{i s c o m p a c t s e t}{\overset{[0, 1]}{=}} 2