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4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0. Use this fact and the identity sin x sin u = 2 sin u) cos %3D to prove that the sine function is continuous at any point of u E R.

4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0. Use this fact and the identity sin x sin u = 2 sin u) cos %3D to prove that the sine function is continuous at any point of u E R.

Advanced Engineering Mathematics
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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Basic Real Analysis 1

4. Use the inequality | sin x|< |x| for x ER to show that the sine function is continuous at x = 0. Use this fact and the identity sin x - sin u = 2 sin CoS | to prove that the sine function is continuous at any point of u E R.
Transcribed Image Text:4. Use the inequality | sin x|< |x| for x ER to show that the sine function is continuous at x = 0. Use this fact and the identity sin x - sin u = 2 sin CoS | to prove that the sine function is continuous at any point of u E R.
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