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b) Prove that tan-1 x < x for all x > 0 (Using mean value theorem on {o,x} for tan-1x)


Question asked by: varsijith

Asked on: 14 Apr 2010

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By: knowitall
Replied at: 03 May 2010
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Let g(x)=x-tan-1x g'(x)=1-1/(1+x^2). This is>0 if x>0 By MVT g(x)-g(0)/(x-0)= 1-1/(1+x^2) Hence g(x)-g(0)= x-x/(1+x^2) which is >0 if x>0 so g(x)>g(0) x-tan-1x> 0 Hence the result
By: IsaacN

Date of comment: Mon, Jun 7th 2010

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Next question: Find the area of the region included between the circle: x2 + y2 + 2 x + 10y + 27 = 0 and the parabola y2 + 10y x + 23 = 0 Find the area of the region included between the circle: x2 + y2 + 2 x + 10y + 27 = 0


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Question Keywords

value  mean  theorem  tan1x  prove  tan1  

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