Homework Answers
Use the power series 1 1 + X = Ë (-1)^x), 1x! < 1 n=0 to...
Use the power series 1 1 + X = Ë (-1)^x), 1x! < 1 n=0 to find a power series for the function, centered at 0. 1 g(x) x + 1 00 g(x) = Σ n=0 Determine the interval of convergence. (Enter your answer using interval notation.)
Use the power series itxË (-1)"X", Ixl < 1 -n=0 to determine a power series for...
Use the power series itxË (-1)"X", Ixl < 1 -n=0 to determine a power series for the function, centered at 0, 14 02 7 f(x) (x + 1) dx2 ( x + 1 00 f(x) no Determine the interval of convergence. (Enter your answer using interval notation.) 3. [-17.69 Points] DETAILS LARCALC11 9.2.061. Find all values of x for which the series converges. (Enter your answer using interval notation.) 00 (8x)" n=1 For these values of x, write the sum...
3. [0/10 Points] DETAILS LARCALC11 9.9.026. 1/2 Submissions Used Use the power series 1 | (-13240,...
3. [0/10 Points] DETAILS LARCALC11 9.9.026. 1/2 Submissions Used Use the power series 1 | (-13240, Ixl <1 1 + x n=0 to find a power series for the function, centered at 0. f(x) = In(x4 + 1) 00 f(x) X n0 Determine the interval of convergence. (Enter your answer using interval notation.) I X Submit Answer
Use the equation 1,- Σ x for x < 1 1 - x n = 0...
Use the equation 1,- Σ x for x < 1 1 - x n = 0 to expand the function in a power series with center c = 0. f(x) = 2 + 9x į n=0 Determine the interval of convergence. (Enter your answer using interval notation.) eBook -/1 Points] DETAILS ROGACALCET3 10.6.055. Find all values of x such that 9.22 2(n!) mel converges. (Enter your answer using interval notation.)
4. Use the power series representaion f(t) = In(1 - 1) =- for -1 <<1, k=1...
4. Use the power series representaion f(t) = In(1 - 1) =- for -1 <<1, k=1 to find the power series representation for the following function(centered at 0). Give the interval of convergence of the new series. p(r) = 2.r" ln(1-2) 5. Find the power series representation for g centered at 0 by differentiating or integrating the power series of f(perhaps more than once). Give the interval of convergence for the resulting series. 1 using (3) 1-
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)!...
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
1 Problem 7 We know that we can expand as a power series for -1 <...
1 Problem 7 We know that we can expand as a power series for -1 < < 1. 1+2 Follow the given steps to manipulate this power series to derive the power series representation for f(x) = tan-(2) centered at a = 0. • Make the appropriate substitution to find a power series for g(x) 1/(1 + x2). • Either integrate or differentiate the previous power series to find a power series for f(x) = tan-'(x). Has the radius of...
Use the equation 1 1x = Ž for 1x1 <1 1 - X n = 0...
Use the equation 1 1x = Ž for 1x1 <1 1 - X n = 0 to expand the function in a power series with center c = 0. 1 f(x) 5 + x3 00 Σ n = 0 Determine the interval of convergence. (Enter your answer using interval otation.)
1 6. Using the power series = Σ c" |x | < 1, find a power...
1 6. Using the power series = Σ c" |x | < 1, find a power series about O for 1 х n=0 1 and state the radius of convergence. (2 - x)2
Find a power series representation centered at O for the following function using known power series....
Find a power series representation centered at O for the following function using known power series. Give the interval of convergence for the resulting series. 9 f(x) 9 + x Which of the following is the power series representation for f(x)? oo 0 OA. (-9x)" OB. (-xº)* k=0 k=0 0 00 х Ο C. Σ OD. Σ 9x* 9 k=0 k= 0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.)
Use the power series 1 1 + X = Ë (-1)^x), 1x! < 1 n=0 to find a power series for the function, centered at 0. 1 g(x) x + 1 00 g(x) = Σ n=0 Determine the interval of convergence. (Enter your answer using interval notation.)
Use the power series itxË (-1)"X", Ixl < 1 -n=0 to determine a power series for the function, centered at 0, 14 02 7 f(x) (x + 1) dx2 ( x + 1 00 f(x) no Determine the interval of convergence. (Enter your answer using interval notation.) 3. [-17.69 Points] DETAILS LARCALC11 9.2.061. Find all values of x for which the series converges. (Enter your answer using interval notation.) 00 (8x)" n=1 For these values of x, write the sum...
3. [0/10 Points] DETAILS LARCALC11 9.9.026. 1/2 Submissions Used Use the power series 1 | (-13240, Ixl <1 1 + x n=0 to find a power series for the function, centered at 0. f(x) = In(x4 + 1) 00 f(x) X n0 Determine the interval of convergence. (Enter your answer using interval notation.) I X Submit Answer
Use the equation 1,- Σ x for x < 1 1 - x n = 0 to expand the function in a power series with center c = 0. f(x) = 2 + 9x į n=0 Determine the interval of convergence. (Enter your answer using interval notation.) eBook -/1 Points] DETAILS ROGACALCET3 10.6.055. Find all values of x such that 9.22 2(n!) mel converges. (Enter your answer using interval notation.)
4. Use the power series representaion f(t) = In(1 - 1) =- for -1 <<1, k=1 to find the power series representation for the following function(centered at 0). Give the interval of convergence of the new series. p(r) = 2.r" ln(1-2) 5. Find the power series representation for g centered at 0 by differentiating or integrating the power series of f(perhaps more than once). Give the interval of convergence for the resulting series. 1 using (3) 1-
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
1 Problem 7 We know that we can expand as a power series for -1 < < 1. 1+2 Follow the given steps to manipulate this power series to derive the power series representation for f(x) = tan-(2) centered at a = 0. • Make the appropriate substitution to find a power series for g(x) 1/(1 + x2). • Either integrate or differentiate the previous power series to find a power series for f(x) = tan-'(x). Has the radius of...
Use the equation 1 1x = Ž for 1x1 <1 1 - X n = 0 to expand the function in a power series with center c = 0. 1 f(x) 5 + x3 00 Σ n = 0 Determine the interval of convergence. (Enter your answer using interval otation.)
1 6. Using the power series = Σ c" |x | < 1, find a power series about O for 1 х n=0 1 and state the radius of convergence. (2 - x)2
Find a power series representation centered at O for the following function using known power series. Give the interval of convergence for the resulting series. 9 f(x) 9 + x Which of the following is the power series representation for f(x)? oo 0 OA. (-9x)" OB. (-xº)* k=0 k=0 0 00 х Ο C. Σ OD. Σ 9x* 9 k=0 k= 0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.)
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