Limit of function in $H^1(\mathbb{R}_+;\mathbb{C})$

Question

Let $H^1(\mathbb{R}_+;\mathbb{C})$ the space of function in $L^2(\mathbb{R}_+;\mathbb{C})$ with weak derivative in the same space. Show that \begin{equation} lim_{x\rightarrow \infty} f(x) = 0 \end{equation}