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 ? 3x^2 + 5, a = 1 ?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = 2 + 3(x ? 1) + 3(x ? 1)^2 + 4(x ? 1)^3 + (x ? 1)^4 ?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = 3 ? 2(x ? 1) + 3(x ? 1)^2 + 4(x ? 1)^3 + (x ? 1)^4 ?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = 2 + 3(x ? 1) + 4(x ? 1)^2 + 3(x ? 1)^3 + (x ? 1)^4 ?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = 3 ? 2(x ? 1) + 4(x ? 1)^2 + 3(x ? 1)^3 + (x ? 1)^4 ?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = ?3 ? 2(x ? 1) + 3(x ? 1)^2 + 4(x ? 1)^3 + (x ? 1)^4

          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 ? 3x^2 + 5, a = 1
?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = 2 + 3(x ? 1) + 3(x ? 1)^2 + 4(x ? 1)^3 + (x ? 1)^4
?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = 3 ? 2(x ? 1) + 3(x ? 1)^2 + 4(x ? 1)^3 + (x ? 1)^4
?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = 2 + 3(x ? 1) + 4(x ? 1)^2 + 3(x ? 1)^3 + (x ? 1)^4
?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = 3 ? 2(x ? 1) + 4(x ? 1)^2 + 3(x ? 1)^3 + (x ? 1)^4
?_{n=0}^? (f^(n)(1) / n!)(x ? 1)^n = ?3 ? 2(x ? 1) + 3(x ? 1)^2 + 4(x ? 1)^3 + (x ? 1)^4

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 ? 3x^2 + 5, a = 1
?n=0^? (f^(n)(1) / n!)(x ? 1)^n = 2 + 3(x ? 1) + 3(x ? 1)^2 + 4(x ? 1)^3 + (x ? 1)^4
?n=0^? (f^(n)(1) / n!)(x ? 1)^n = 3 ? 2(x ? 1) + 3(x ? 1)^2 + 4(x ? 1)^3 + (x ? 1)^4
?n=0^? (f^(n)(1) / n!)(x ? 1)^n = 2 + 3(x ? 1) + 4(x ? 1)^2 + 3(x ? 1)^3 + (x ? 1)^4
?n=0^? (f^(n)(1) / n!)(x ? 1)^n = 3 ? 2(x ? 1) + 4(x ? 1)^2 + 3(x ? 1)^3 + (x ? 1)^4
?n=0^? (f^(n)(1) / n!)(x ? 1)^n = ?3 ? 2(x ? 1) + 3(x ? 1)^2 + 4(x ? 1)^3 + (x ? 1)^4

Added by Greg B.

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