The function h is defined by the power series h(x) = x+1+1+140+ Part A: Determine the...

  

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The function h is defined by the power series h(x) = x+1+1+140+ Part A: Determine the interval of convergence of the power series for h. (10 points) x+2 2n+1 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) 3. (10.01, 10.09 HC) 8 8 The power series for f(x)= == 1 is defined as 1+x+x + x + ... = x", and the power series for -sinx is defined as x+ 1-x n=0 3! 5! 7! -x2n-1 (-1). n=0 (2n-1)! Part A: Find the general term of the power series for g(x)=- 4 x-4 and evaluate the infinite sum when x = 1. Justify your solution. (15 points) Part B: Find an upper bound for the error of the approximation sin(0.4) = 0.4 (0.4) Round your final answer to five decimal places. (15 points) 3! Part C: Find a power series for h(x) = In(1 + x) centered at x = 0 and show the work that leads to your conclusion. (10 points) The function h is defined by the power series h(x) = x+1+1+140+ Part A: Determine the interval of convergence of the power series for h. (10 points) x+2 2n+1 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) 3. (10.01, 10.09 HC) 8 8 The power series for f(x)= == 1 is defined as 1+x+x + x + ... = x", and the power series for -sinx is defined as x+ 1-x n=0 3! 5! 7! -x2n-1 (-1). n=0 (2n-1)! Part A: Find the general term of the power series for g(x)=- 4 x-4 and evaluate the infinite sum when x = 1. Justify your solution. (15 points) Part B: Find an upper bound for the error of the approximation sin(0.4) = 0.4 (0.4) Round your final answer to five decimal places. (15 points) 3! Part C: Find a power series for h(x) = In(1 + x) centered at x = 0 and show the work that leads to your conclusion. (10 points)