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!!