Taylor Series, Radiance of Convergence, and Interval of Convergence

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7 Terms

1
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What is the Taylor Series for the function, f(x) = 1 / (1 - x)?

∑ x^n for |x| < 1

2
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What is the Taylor Series for the function, f(x) = e^x?

∑ x^n / n! for |x| < ∞

3
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What is the Taylor Series of the function, f(x) = sin(x)?

∑ [ (-1)^n x^(2 n +1) ] / [ (2 * n + 1)! ] for |x| < ∞

4
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What is the Taylor Series of the function, f(x) = cos(x)?

∑ [ (-1)^n x^(2 n) ] / [ (2n)! ] for |x| < ∞

5
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What is the Taylor Series for the function, f(x) = 1 / (1 + x)?

∑ (-1)^n x^n for |x| < 1

6
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What is the Taylor Series for the function, f(x) = lnx?

∑ [ (-1)^(n-1) (x-1)^n / n ] for 0 < x ≤ 2

7
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What is the Taylor Series for the function, f(x) = 1/x?

∑ (-1)^n (x-1)^n for 0 < x < 2