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.

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