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Question Number 110779 by ZiYangLee last updated on 30/Aug/20
If0⩽x⩽π2,Provethat2πx⩽sinx⩽xwithoutgraphicalmethod.
Answered by Her_Majesty last updated on 30/Aug/20
f1(x)=2xπf1′(x)=2πf2(x)=sinxf2′(x)=cosxf3(x)=xf3′(x)=10⩽x⩽π2:f1(0)=f2(0)=f3(0)=0∧f1′(x)⩽f2′(x)⩽f3′(x)⇒f1(x)stays⩽f2(x)f2(x)stays⩽f3(x)withinthegiveninterval
Commented by ZiYangLee last updated on 31/Aug/20
Thanks!
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