3 Suppose that e(x) and f(x) are differentiable on [0, 1] and that 0 < |e'(x)| < |f'(x)| for all x € (0, 1). Show that |e(x) – e(y)| < |f(x) – f(y)| for all æ, y E [0, 1].
3 Suppose that e(x) and f(x) are differentiable on [0, 1] and that 0 < |e'(x)| < |f'(x)| for all x € (0, 1). Show that |e(x) – e(y)| < |f(x) – f(y)| for all æ, y E [0, 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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![3 Suppose that e(x) and f(x) are differentiable on [0, 1] and that 0 < |e'(x)| < |f'(x)| for
all x € (0, 1). Show that |e(x) – e(y)| < |f(x) – f (y)| for all x, y E [0, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6915687c-4f06-4661-ac02-aefc88931b4a%2F554cf4d8-8840-4c0f-ab97-0e3ed64e28f6%2F2dy8n1s_processed.png&w=3840&q=75)
Transcribed Image Text:3 Suppose that e(x) and f(x) are differentiable on [0, 1] and that 0 < |e'(x)| < |f'(x)| for
all x € (0, 1). Show that |e(x) – e(y)| < |f(x) – f (y)| for all x, y E [0, 1].
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