Application of the Uniform limit theorem
Calculus
Level
3
For \(n\in \mathbb{N}\), let \(f_n:[0, \pi]\to \mathbb{R}\) be defined by
\[ f_n(x):= \sin^n (x) \]
Is the sequence \(\{f_n\}_{n=1}^{\infty}\) uniformly convergent?
Hint: is the limit function continuous?
This problem is often posed in calculus textbooks.
by
Ognjen Vukadin