Maximal ideal of $C(\mathbb{R})$

Question

Is the ideal $I$ defined as follows a maximal ideal in $C(\mathbb{R})$? $$I=\{f\in C(\mathbb{R}):\exists N\in {R} , f(x)=0 \forall x>N\}$$.

Where $C(\mathbb{R})$ is ring of all real valued continuous function. Is $I $ a maximal ideal?

Answer 1

No. For instance, $1\notin\langle I,\sin \rangle\supsetneq I$.