Homework Statement
I want to prove that the span of $\{x^{2n}:n \geq0\}$ is dense in $C([0,1])$.
Furthermore, that the closure of the span of $\{x^{2n+1}:n \geq0\}$ is $\{f \in C([0,1]):f(0) = 0\}$.Homework Equations
Is my solution correct?
Now I do not know how to tackle the second part...