Question

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) ? 0.] f(x) = x^4 - 2x^2 + 2, a = 2 ? f^(n)(2)/n! (x - 2)^n = 10 + 24(x - 2) + 8(x - 2)^2 + 22(x - 2)^3 + (x - 2)^4 ? f^(n)(2)/n! (x - 2)^n = 10 + 24(x - 2) + 22(x - 2)^2 + 8(x - 2)^3 + (x - 2)^4 ? f^(n)(2)/n! (x - 2)^n = -10 + 24(x - 2) + 22(x - 2)^2 - 8(x - 2)^3 + (x - 2)^4 ? f^(n)(2)/n! (x - 2)^n = -10 - 24(x - 2) + 22(x - 2)^2 + 8(x - 2)^3 + (x - 2)^4 ? f^(n)(2)/n! (x - 2)^n = 10 + 24(x - 2) - 8(x - 2)^2 + 22(x - 2)^3 - (x - 2)^4 Find the associated radius of convergence R. R = 2 Enhanced Feedback Please try again, making sure that you use the correct formula for the Taylor expansion centered at the appropriate value (which means that you need to first find the values of the derivatives of f of all order and then use the formula for the coefficients in the Taylor expansion).

          Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) ? 0.]
f(x) = x^4 - 2x^2 + 2, a = 2
? f^(n)(2)/n! (x - 2)^n = 10 + 24(x - 2) + 8(x - 2)^2 + 22(x - 2)^3 + (x - 2)^4
? f^(n)(2)/n! (x - 2)^n = 10 + 24(x - 2) + 22(x - 2)^2 + 8(x - 2)^3 + (x - 2)^4
? f^(n)(2)/n! (x - 2)^n = -10 + 24(x - 2) + 22(x - 2)^2 - 8(x - 2)^3 + (x - 2)^4
? f^(n)(2)/n! (x - 2)^n = -10 - 24(x - 2) + 22(x - 2)^2 + 8(x - 2)^3 + (x - 2)^4
? f^(n)(2)/n! (x - 2)^n = 10 + 24(x - 2) - 8(x - 2)^2 + 22(x - 2)^3 - (x - 2)^4
Find the associated radius of convergence R.
R = 2
Enhanced Feedback
Please try again, making sure that you use the correct formula for the Taylor expansion centered at the appropriate value (which means that you need to first find the values of the derivatives of f of all order and then use the formula for the coefficients in the Taylor expansion).

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) ? 0.]
f(x) = x^4 - 2x^2 + 2, a = 2
? f^(n)(2)/n! (x - 2)^n = 10 + 24(x - 2) + 8(x - 2)^2 + 22(x - 2)^3 + (x - 2)^4
? f^(n)(2)/n! (x - 2)^n = 10 + 24(x - 2) + 22(x - 2)^2 + 8(x - 2)^3 + (x - 2)^4
? f^(n)(2)/n! (x - 2)^n = -10 + 24(x - 2) + 22(x - 2)^2 - 8(x - 2)^3 + (x - 2)^4
? f^(n)(2)/n! (x - 2)^n = -10 - 24(x - 2) + 22(x - 2)^2 + 8(x - 2)^3 + (x - 2)^4
? f^(n)(2)/n! (x - 2)^n = 10 + 24(x - 2) - 8(x - 2)^2 + 22(x - 2)^3 - (x - 2)^4
Find the associated radius of convergence R.
R = 2
Enhanced Feedback
Please try again, making sure that you use the correct formula for the Taylor expansion centered at the appropriate value (which means that you need to first find the values of the derivatives of f of all order and then use the formula for the coefficients in the Taylor expansion).

Added by Daniela W.

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