Consider functions $f_n$, $f : \mathbb{R} \rightarrow \mathbb{R}$ such that the sequence $\{f_n\}$ is uniformly convergent to $f$ and every $f_n$ has property $W$. Determine whether $f$ must have $W$ property as well when:
- a)$W$ = continuity
- b)$W$ = differentiability
- c)$W$ = concavity
- d)$W$ = even/odd
- e)$W$ = strict monotonicity
For a) answer is of course yes. How about other ones?