These problems deal with the Taylor series $f$ at the point $a$ which is $\sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x-a)^n$ and let $A\subset \Bbb{R}$ be an interval, $a\in A$ and $f : A \rightarrow \Bbb{R}$
For question 1. We need to prove that the Taylor series converges to $f(x)$ if and only if $E_N(x) \rightarrow 0$ as $N \rightarrow \infty$ For this we need to use the definition of pointwise convergence of a series.
For question 2. Let $B\subset A$ Prove that the Taylor series converges uniformly to $f$ on $B$ if and only if $E_N(x) \rightarrow 0$ uniformly on $B$ as $N \rightarrow \infty$. For this we need to use the definition of uniform convergence of a series.
I am confused on how to start these proofs in either direction since I am new to Taylor series and especially error terms of Taylor polynomials. Any help would really be appreciated.