4146 If f is increasing on an interval [0, b), then it followsfrom Definition 4.1.1 that
Chapter 4, Problem 45(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.
(a) Show that \(\ln (x+1) \leq x \text { if } x \geq 0\).
(b) Show that \(\ln (x+1) \geq x-\frac{1}{2} x^{2} \text { if } x \geq 0\).
(c) Confirm the inequalities in parts (a) and (b) with a graphing utility.
Equation Transcription:
if
if
Text Transcription:
f
[0, b)
f(0) < f(x)
x
(0, b)
ln (x+1) leq x if x geq 0
ln (x+1) geq x - frac{1}{2} x^2 if x geq 0
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