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Use the mean value theorem to prove that for 0 < a

Use the mean value theorem to prove that for 0 < a

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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COURSE: Mathematical/Real Analsys (MVT1)

TOPIC: Mean Value Theorem

**[a]** Use the mean value theorem to prove that for \(0 < a < b\) we have: \[ \frac{b-a}{2\sqrt{b}} < \sqrt{b} - \sqrt{a} < \frac{b-a}{2\sqrt{a}} \] **[b]** Use part \([a]\) to prove that: \[ 8 + \frac{1}{9} < \sqrt{66} < 8 + \frac{1}{8} \]
Transcribed Image Text:**[a]** Use the mean value theorem to prove that for \(0 < a < b\) we have: \[ \frac{b-a}{2\sqrt{b}} < \sqrt{b} - \sqrt{a} < \frac{b-a}{2\sqrt{a}} \] **[b]** Use part \([a]\) to prove that: \[ 8 + \frac{1}{9} < \sqrt{66} < 8 + \frac{1}{8} \]
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