Let $V$ be the linear span of the set of vectors $\{1, \sqrt{2}\cos 2\pi x, \sqrt{2}\sin 2\pi x\}$ where $0\leq x\leq 1$. Recall that $V$ is equipped with the inner product: $\langle u, v \rangle=\int_0^1u(x)v(x)\, dx$ whenever $u, v\in V$.

The nearest vector $f$ in $V$ to the vector $g(x)=e^x$ is