Let f be a function that satisfies f(x) > 0, f'(x) > 0 for all x 2 0, and suppose n> 1 is some integer. (i) Explain why f(n - 1) < f(x) dx < f(n) n-1 By considering areas bounded by the y-axis, evaluate L in In x dx n-1 i) Hence show that n-1
Let f be a function that satisfies f(x) > 0, f'(x) > 0 for all x 2 0, and suppose n> 1 is some integer. (i) Explain why f(n - 1) < f(x) dx < f(n) n-1 By considering areas bounded by the y-axis, evaluate L in In x dx n-1 i) Hence show that n-1
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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![(c) Let f be a function that satisfies f(x) > 0, f'(x) > 0 for all x 2 0, and suppose n >1 is some
integer.
(i) Explain why
f(n – 1) <
f (x) dx < f(n)
1/-
(ii) By considering areas bounded by the y-axis, evaluate
In x dx
n-1
(iii) Hence show that
n
n-1
くe<
n - 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7a736a9-b3d2-4a38-a3ba-aa09cfe77d1b%2F32e441ce-58f9-4492-9ef1-cee9b1b6720a%2Fg6rtwli_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(c) Let f be a function that satisfies f(x) > 0, f'(x) > 0 for all x 2 0, and suppose n >1 is some
integer.
(i) Explain why
f(n – 1) <
f (x) dx < f(n)
1/-
(ii) By considering areas bounded by the y-axis, evaluate
In x dx
n-1
(iii) Hence show that
n
n-1
くe<
n - 1
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