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Taylor, Maclaurin, & Power series challenge


Let  g(x)=sin(2xπ2)  and let  T3(x)  be the third-degree Taylor polynomial for  g  centered at  x=0. Determine the sum of the coefficients of  T3.
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4