4146 If f is increasing on an interval [0, b), then it followsfrom Definition 4.1.1 that

Chapter 4, Problem 44

(choose chapter or problem)

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

Use a graphing utility to make a conjecture about the relative sizes of \(1-x^{2} / 2\) and \(\cos x \text { for } x \geq 0\), and prove your conjecture. [Hint: Use the result of Exercise 43.]

Equation Transcription:

 for

Text Transcription:

f

[0, b)

f(0) < f(x)

x

(0, b)

1 - x^2/2

cos x for x geq 0