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Use the power series 1/ 1+x = Summation as n=0 to infinity of (-1) n x n to determine a power series at c= 0 for the function f(x)= 1/1+x 4 Use the

  1. Use the power series 1/ 1+x = Summation as n=0 to infinity of (-1)nxn to determine a power series at c= 0 for the function f(x)= 1/1+x4
  2. Use the result in problem 1 to evaluate the indefinite integral as a power series: integration of 1/ 1+x4 dx
  3. Using the power series ex= Summation as n=0 to infinity of xn/n!= 1+x+x2/2! + x3/3! + ..., approximate(by using four terms) the value of integration of esquare root of xdx with lower limit 0 and upper limit 0.4. Round your answer to three decimal places.
  4. Use the trigonometric identity cos2x= 1+cos(2x)/2 and thepower series cos x= Summation as n=0 to infinity of (-1)nx2n/ (2n!) to find a power series for the function f(x)= cos2x.

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