• Math Archive: Questions from 2023-08-28

    Find a power series representation for the function and determine the radius of convergence. f(x) = arctan(x/3)

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    Find the Taylor series for f(x) centered at the given value of a. Assume that f has a power series expansion. Also find the associated radius of convergence. f(x) = x^4 - 3x^2 + 1, a = 1

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    Find the sum of the series. summation n = 0 infinity 5^n/(6^n n!)

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    Find the sum of the series. n = 2 to infinity 2n(n-1)x^(n+1) |x| < 1

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    Find the Taylor series for f(x) centered at the given value of a. Assume that f has a power series expansion. Also find the associated radius of convergence. f(x) = e^5x, a = 4

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    Find the Taylor series for f(x) centered at the given value of a. Assume that f has a power series expansion. f(x) = 1/4-x, a = 8

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    Evaluate the indefinite integral as an infinite series. integration 5(e^x - 1)/x dx
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    Find the first three nonzero terms in the Maclaurin series for f(x) = e^x (1+x)^17.
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