Let f(x) = x sin x. a. Compute f'(x). b. Show that for every M > 0 and every k > 1, there is xo > M such that f' (æ) > k, Væ E [x0, x0 + 1/k]. c. Show that f(x) is NOT uniformly continuous on [0, +∞).
Let f(x) = x sin x. a. Compute f'(x). b. Show that for every M > 0 and every k > 1, there is xo > M such that f' (æ) > k, Væ E [x0, x0 + 1/k]. c. Show that f(x) is NOT uniformly continuous on [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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![Let f(x) = x sin x.
a. Compute f'(x).
b. Show that for every M > 0 and every k > 1, there is xo > M such that
f' (æ) > k, Væ E [x0, x0 + 1/k].
c. Show that f(x) is NOT uniformly continuous on [0, +∞).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b2ad9d7-a90a-421a-bb74-2feb16faebe3%2F1a6b043f-d234-49d3-aab6-e928dcc3233a%2Fmxtekb8_processed.png&w=3840&q=75)
Transcribed Image Text:Let f(x) = x sin x.
a. Compute f'(x).
b. Show that for every M > 0 and every k > 1, there is xo > M such that
f' (æ) > k, Væ E [x0, x0 + 1/k].
c. Show that f(x) is NOT uniformly continuous on [0, +∞).
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