I'm trying to figure out how to prove this inequality

  • Thread starter minifhncc
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  • #1
minifhncc
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I'm trying to figure out how to prove this inequality:

I know it's true (by graphing), but what's an algebraic way to prove it?

[tex]1+\frac{1}{3x^2}< x \tan \frac{1}{x} < \frac{1}{\sqrt{1-\frac{2}{3x^2}}}[/tex]

Thanks
 

Answers and Replies

  • #2
mathman
Science Advisor
8,056
539


You need to specify the range for x. Let y=1/x, it will be easier to handle.
 
  • #3
minifhncc
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I guess it's for 'large enough x' ie. for x>N for some N.

It's actually Euler's limit that I'm trying to prove...
 
  • #4
disregardthat
Science Advisor
1,866
34


Try to differentiate the differences.
 

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