Use the mean value theorem to prove that for 0 < a
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:
\[
8 + \frac{1}{9} < \sqrt{66} < 8 + \frac{1}{8}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbaa9c753-6b68-41b4-8837-61aa8aa0a19b%2F94826a35-6025-4811-a4d0-896e10a51f0d%2Fy9ekizr_processed.png&w=3840&q=75)
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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