Homework SourseUse a Maclaurin series derived in the text to derive the Mac
Use a Maclaurin series derived in the text to derive the Maclaurin series for the function f(x)=e^(?x/4) . Find the first 4 nonzero terms in the series, that is write down the Taylor polynomial with 4 nonzero terms.
Solution
In general, f(x) = f(0) + f\'(0)x + f\'\'(0)x^2/2! + f\'\'\'(0)x^3/3! + ....... f(x) = e^(-x/6)..........f(0) = 1 f\'(x) = -1/6 e^(-x/6)......f\'(0) = -1/6 f\'\'(x) = 1/36 e^(-x/6).........f\'\'(0) = 1/36 f\'\'\'(x) = - 1/216 e^(-x/6)..........f\'\'\'(0) = - 1/216 First four non zero terms are e^(-x/6) = 1 - x/6 + x^2/72 - x^3/1296
