21 a) Consider the function arctan(x²).Write a partial sum for the power series which represents this function consisting of the first 4nonzero terms. For example, if the series were Σ0 3" x ², you would write 1 + 3x² + 3²x² + 3³×6.Also indicate the radius of convergence.Partial Sum:Radius of Convergence:=0b) Use part a) to write the partial sum for the power series which represents arctan(x²)dx.Write the first 4 nonzero terms. Also indicate the radius of convergence.Partial Sum:Radius of Convergence:0.7c) Use part b) to approximate the integral for arctan(x²)dx.☐

Question

21 a) Consider the function arctan(x²).Write a partial sum for the power series which represents this function consisting of the first 4nonzero terms. For example, if the series were Σ0 3&#34; x ², you would write 1 + 3x² + 3²x² + 3³×6.Also indicate the radius of convergence.Partial Sum:Radius of Convergence:=0b) Use part a) to write the partial sum for the power series which represents arctan(x²)dx.Write the first 4 nonzero terms. Also indicate the radius of convergence.Partial Sum:Radius of Convergence:0.7c) Use part b) to approximate the integral for arctan(x²)dx.☐

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