Basic Real Analysis 1 4. Use the inequality | sin x|< |x| for x ER to show that the sine function is continuousat x = 0. Use this fact and the identitysin x - sin u =2 sinCoS|to prove that the sine function is continuous at any point of u E R.

Sine function and it's continuity at 0

Answered: 4. Use the inequality | sin r|< |x| for…

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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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.