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.

×

Problem Loading...

Note Loading...

Set Loading...