Chapter 4.1, Problem 44ES

If $f$ is increasing on an interval $\left[0,b\right),$ then it follows from Definition $\mathrm{4.1.1}$ that $f\left(0\right)<f\left(x\right)$ for each $x$ in the interval $\left(0,b\right)$ . Use this result in these exercises.

Use a graphing utility to make a conjecture about the relative sizes of $1-x^2/2$ and $\cos x$ for $x\ge 0$ , and prove your conjecture.