Use the mean value theorem to prove that v1+ x < 1 + x for x > 0 *Hint*: Apply to mean value theorem to f(x) = /1+x on the interval [0, x]
Use the mean value theorem to prove that v1+ x < 1 + x for x > 0 *Hint*: Apply to mean value theorem to f(x) = /1+x on the interval [0, x]
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 (MVT3)
TOPIC: Mean Value Theorem
![**Problem Statement:**
Use the mean value theorem to prove that \(\sqrt{1+x} < 1 + \frac{1}{2}x\) for \(x > 0\).
**Hint:** Apply the mean value theorem to \(f(x) = \sqrt{1+x}\) on the interval \([0, x]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbaa9c753-6b68-41b4-8837-61aa8aa0a19b%2F5b61792d-8714-492e-8bfd-b66a4ab42f80%2Fcnl492s_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Use the mean value theorem to prove that \(\sqrt{1+x} < 1 + \frac{1}{2}x\) for \(x > 0\).
**Hint:** Apply the mean value theorem to \(f(x) = \sqrt{1+x}\) on the interval \([0, x]\).
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