- #1
endeavor
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Use the Mean Value Theorem to prove the inequality
[tex]|\sin a - \sin b| \leq |a - b|[/tex] for all a and b.
I know by the Mean Value Theorem, I can say:
[tex]\sin a - \sin b = \cos c(a - b)[/tex]
I've been trying to figure it out for awhile, but could not, so I peeked at my solution's manual. They assumed b < a, and said
[tex]|\sin a - \sin b| \leq |\cos c||b - a| \leq |a - b|[/tex]
how did they arrive at this?
[tex]|\sin a - \sin b| \leq |a - b|[/tex] for all a and b.
I know by the Mean Value Theorem, I can say:
[tex]\sin a - \sin b = \cos c(a - b)[/tex]
I've been trying to figure it out for awhile, but could not, so I peeked at my solution's manual. They assumed b < a, and said
[tex]|\sin a - \sin b| \leq |\cos c||b - a| \leq |a - b|[/tex]
how did they arrive at this?
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