The function h is defined by the power series h(x)= x + 3 x5 x6 +~+~+~+=...

 

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The function h is defined by the power series h(x)= x² + 3 x5 x6 +~+~+~+= Σ 7 9 5 ∞ xn+2 n=0 2n+1 Part A: Determine the interval of convergence of the power series for h. (10 points) Part B: Find h'(-1) and determine if the new series converges or diverges. Justify your response and discuss the relationship between the radius of convergence and interval of convergence of h(x) and h'(x). (10 points) Part C: Determine if the power series h(x2) has any points of inflection. Justify your answer. (10 points) The function h is defined by the power series h(x)= x² + 3 x5 x6 +~+~+~+= Σ 7 9 5 ∞ xn+2 n=0 2n+1 Part A: Determine the interval of convergence of the power series for h. (10 points) Part B: Find h'(-1) and determine if the new series converges or diverges. Justify your response and discuss the relationship between the radius of convergence and interval of convergence of h(x) and h'(x). (10 points) Part C: Determine if the power series h(x2) has any points of inflection. Justify your answer. (10 points)