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6. Prove the following inequalities. (a) | sin(x) – sin(y)| < |æ – y| for x, Y E R (b) -1 < log(x) < x – 1 for x > 1

6. Prove the following inequalities. (a) | sin(x) – sin(y)| < |æ – y| for x, Y E R (b) -1 < log(x) < x – 1 for x > 1

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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6. Prove the following inequalities. (a) |sin(x) – sin(y)| < |x – y| for x, y E R (b) - - x-1 < log(x) < x – 1 for x > 1 -
Transcribed Image Text:6. Prove the following inequalities. (a) |sin(x) – sin(y)| < |x – y| for x, y E R (b) - - x-1 < log(x) < x – 1 for x > 1 -
Expert Solution
Step 1

To prove the following inequalities.

  1. sinx−siny≤x−y for x,y∈R
  2. x−1x<logx<x−1 for x>1
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