let $g:[0,1] \rightarrow R$ be a continuous function. Let $\epsilon >0$. Prove that there is a real analytic function $h: [0,1] \rightarrow R$ such that $|g(x)-h(x)| < \epsilon$ for all $x \in [0,1]$.
let $g:[0,1] \rightarrow R$ be a continuous function. Let $\epsilon >0$. Prove that there is a real analytic function $h: [0,1] \rightarrow R$ such that $|g(x)-h(x)| < \epsilon$ for all $x \in [0,1]$.