[a] Use the mean value theorem to prove that for 0
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 (MVT2)
TOPIC: Mean Value Theorem
![### Mean Value Theorem and Inequalities
**[a]** Use the mean value theorem to prove that for \(0 < a < b\) we have:
\[
\left(1 - \frac{a}{b}\right) < \ln\left(\frac{b}{a}\right) < \left(\frac{b}{a} - 1\right)
\]
**[b]** Use part [a] to prove that:
\[
\frac{1}{6} < \ln(1/2) < \frac{1}{5}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbaa9c753-6b68-41b4-8837-61aa8aa0a19b%2Fb7aa8458-a952-4dab-a09d-2aa19e6c8beb%2Fz4t7dfc_processed.png&w=3840&q=75)
Transcribed Image Text:### Mean Value Theorem and Inequalities
**[a]** Use the mean value theorem to prove that for \(0 < a < b\) we have:
\[
\left(1 - \frac{a}{b}\right) < \ln\left(\frac{b}{a}\right) < \left(\frac{b}{a} - 1\right)
\]
**[b]** Use part [a] to prove that:
\[
\frac{1}{6} < \ln(1/2) < \frac{1}{5}
\]
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