Why $C_c^\infty(\mathbb{R})$ can be dense in different Banach space?

Question

As we know $C_c^\infty(\mathbb{R})$ is dense in $L^p(\mathbb{R}), W^{k,p}(\mathbb{R}),C_0(\mathbb{R}), \infty>p\geq 1.$ Why this space can be dense in different Banach space? Is there some deep reason?