does the following function converge uniformly?

Question

Does $$f_n(x)=\frac{x^n}{n^{\frac{1}{4}}}$$ converge uniformly on [0,1]? I know it converges pointwise.

Answer 1

Hint: $$|f_n(x)-0|=\left|\frac{x^n}{n^{\frac{1}{4}}}\right| \le \frac{1}{n^{\frac{1}{4}}}$$

Answer 2

Surely $|f(x)| \leq \frac{1}{n^{1/4}}$, so yes, it converges uniformly.

Answer 3

$|f_n (x)| \le \frac {1}{n^{1/4}} $ for all $x \in [0,1] $.