# 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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### Comments and other answers:

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

By: IsaacN

*Date of comment: Mon, Jun 7th 2010***Ask a New Question**

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Next question: Find the area of the region included between the circle:
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Find the area of the region included between the circle:
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