19.5.8 Compactness

Condition: Are the following sets of functions in the space \( C[0,1]: \) a) \( \left\{t^{n}: n \in \mathbb{N}\right\} \) b) \( \left\{n\left(1-\cos) \left(\frac{1}{n} t\right)\right): n \in \mathbb{N}\right\} \)