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(1 point) Find a function of x that is equal to the power series En= n(n...
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...
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
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. +
Find the Fourier series of the following function, and calculate the sum of rn. n=1 f(x) = 12,2 if 0<r<\ if-1< 0 f(x + 2)-f(x)
(1 point) Find a power series centered at a = 0 for the function ln(1 + x) When you have found the series, enter the sum of the first five non-zero terms of the series. Find the radius of convergence R of the power series. R= 1 Use the power series you found above, to build a power series for the function f(x) = x? ln(1 + x). Again, enter the first five non-zero terms. What is the radius of...
Consider the function x2 f(x) = 2 for -1 < x <n. Find the Fourier series of f. Argue that it is valid to differentiate the Fourier series term by term and compute the term by term derivative. Sketch the series obtained by term by term differentiation.
3. (20pts.) Find the Fourier series of the function given 0- <x<0 x. 0<x<
Find the interval of convergence. (Enter your answer using interval notation.) 27(x - 7)3n+6 n = 1 11 13 Use the equation 1 = Ï xn for 1x < 1 1 - X n = 0 to expand the function in a power series with center c = 0. 192 + 3x3 sW n = 0 Determine the interval of convergence. (Enter your answer using interval notation.) Use the formula In(1 + x) = - 1) - 1x = x...
Use the power series 1 1 + x = (-1) (-1)", IX1 < 1 no to find a power series for the function, centered at 0. g(x) = 1 9 x + 1 00 g(x) = Σ no Determine the interval of convergence. (Enter your answer using interval notation.) Submit Answer