6. Use the Mean Value Theorem to prove that Isin x sin yl < x - y| for all x, y in R. 7. Use the Mean Value Theorem to prove that (x-1)/x < In x 1. [Hint: Use the fact that D In x 1/x for x> 0.]
6. Use the Mean Value Theorem to prove that Isin x sin yl < x - y| for all x, y in R. 7. Use the Mean Value Theorem to prove that (x-1)/x < In x 1. [Hint: Use the fact that D In x 1/x for x> 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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Question
q6 and 7
![at 1 and a/b.)
6. Use the Mean Value Theorem to prove that Isin x- sin yl < x- y| for all x, y in R.
7. Use the Mean Value Theorem to prove that (x 1)/x < In x <x-1 for x > 1. [Hint: Use the
fact that D In x 1/x for x > 0.]
%3D
8. Letf : [a, b] → Rbe continuous on [a, b] and differentiable in (a, b). Show that if lim f'(r)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8aa4bdda-f4ef-498e-a4e2-3c943a0d75f7%2Fa113051a-9f8b-4f65-8ef3-5a5593311a0f%2Fsbihvab_processed.jpeg&w=3840&q=75)
Transcribed Image Text:at 1 and a/b.)
6. Use the Mean Value Theorem to prove that Isin x- sin yl < x- y| for all x, y in R.
7. Use the Mean Value Theorem to prove that (x 1)/x < In x <x-1 for x > 1. [Hint: Use the
fact that D In x 1/x for x > 0.]
%3D
8. Letf : [a, b] → Rbe continuous on [a, b] and differentiable in (a, b). Show that if lim f'(r)
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