Uniform convergent sequences of functions?
Calculus
Level
pending
Which of the following sequences of functions \(\{f_n\}_{n=1}^{\infty}\) is/are uniformly convergent on its/their domain?
(A): \(f_n(x) = \cos^{n}(x)\) on \(\left[-\dfrac \pi2, \dfrac \pi2\right]\).
(B): \(f_n(x) = \dfrac{x}{n}\) on \(\mathbb{R}\).
(C): \(f_n(x) = \dfrac{\sin(nx)}{n}\) on \(\mathbb{R}\).
Notation: \(\mathbb R \) denotes the set of real numbers.
by
Ognjen Vukadin