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Suppose I want to construct a sequence of polynomials that converges to $|x|$ pointwise.

I am pretty good on proving that sequences of functions converge to things pointwise, but I am having trouble actually coming up with a sequence of polynomials that converges to $|x|$. Someone told me to try using the Taylor series expansion of $(1−x)^{1/2}$, but that just confused me, since I am very rusty on Taylor series. Would anyone mind explaining this to me a little?

Thanks!!

  • 0
    Maybe with an [orthogonal polynomial](http://en.wikipedia.org/wiki/Classical_orthogonal_polynomials)?2012-10-12
  • 4
    Over what domain?2012-10-12
  • 0
    The Bernstein polynomials are a nice way of approximating a continuous function over $[0,1]$. http://en.wikipedia.org/wiki/Bernstein_polynomial2012-10-12

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