# 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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