## Calculus (3rd Edition)

We are given the function $f(x)=\frac{x^{2}-\cos x}{3+\cos x}$. By Theorem 2 and 3, $x^2$ and $\cos x$ are continuous functions. We know that $3+\cos x$ can not be zero for any $x\in R$, so by using the basic laws of continuity the quotient of two continuous functions is continuous; that is $$f(x)=\frac{x^{2}-\cos x}{3+\cos x}$$ is continuous.