Find a power series representation for the function. (Center your power series representation at x = 0.) f(x) = 00 Σ n = 0 f(x) = 1 3 + x Determine the interval of convergence. (Enter your answer using interval notation.)
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Hello, please answer the following question and show all your work. Thank you
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- Find a power series representation for the function. (Give your power series representation centered at x = 0.) 2x2 F(x) D= Determine the interval of convergence. (Enter your answer using interval notation.)Find all values of x for which the series converges. (Enter your answer using interval notation.) X - 6 n = 0 For these values of x, write the sum of the series as a function of x. 1 f(x) = 15 - nFind a power series representation for the function. (Give your power series representation centered at x = 0.) 2 17 + X f(x): = f(x): n = 0 = Determine the interval of convergence. (Enter your answer using interval notation.)
- Find a power series representation for the function. (Center your power series representation at x = 0.) 1 f(x) : 5 + x 00 f(x) = E( n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)Find all values of x for which the series converges. (Enter your answer using interval notation.) (²) For these values of x, write the sum of the series as a function of x. f(x) =Now use the method of completing the square to express the function as a power series and give the natural center and open interval of convergence. ∞ f(x) = Σ n=0 The center is: The open interval of convergence is: Give your answer in interval notation. f(x) = = x² 17 + 1x - 72
- Find a power series representation for the function. f(x) = X 8 - x³Find a power series representation for the function. (Center your power series representation at x = 0.) 1 f(x) 7 + x 00 E((-x- 6)" ) f(x) %D n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)Find a power series representation for the function. (Give your power series representation centered at x = 0.) X - 1 f(x) x + 6 00 f(x) = 1 + n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)
- Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) 49 + x2 f(x) = Determine the interval of convergence. (Enter your answer using interval notation.)Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 7- x f(x) = n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x): = n = 0 f(x) = 7 1- x x + 34 Determine the interval of convergence. (Enter your answer using interval notation.) (7,1)