I am trying to answer the following question:
Define $f_n(s)=s^n$ where $f_n:[0,1]\rightarrow\mathbb{R}$. Is the family of functions $\{f_n\}$:
- Uniformly convergent
- Pointwise Equicontinuous
- Uniformly Equicontinuous
I think I have managed to show that they are not uniformly convergent, but am struggling with the other two. Currently, I believe the answers are No, Yes, No. But I'm not sure and I keep getting confused with all the $\epsilon$ and $\delta$. Please could someone help me answer this.