Question on uniform convergence

  • Thread starter malachia
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  • #1
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Probably is a silly question, but how could I prove that the function (expressed in polar coordinates)

[tex]
\left(\rho^4\cos^2{\theta} + \sin^3{\theta}\right)^{\frac{1}{3}} - \sin{\theta}
[/tex]

converges to 0 as rho->0 uniformely in theta (if it is true, of course)?
 

Answers and Replies

  • #2
mathman
Science Advisor
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It should be straightforward enough, since |sin|≤ 1 and the angle domain is a finite interval.
 
  • #3
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Ok well your functions are continuous. So show that inside goes to sin^3(theta), then the cubed root is going to equal sin(theta), then subtract to get 0.

But this is assuming you have defined or can assume x^(1/3) is defined and is continuous.
 

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