Answer
The quotient of two continuous functions is continuous.
Work Step by Step
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.
