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OpenStudy (anonymous):
Taylor series question: Why is the 2 that is in a red block there? where did it come from?
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OpenStudy (anonymous):
OpenStudy (phi):
the cos2x is expanded to 1-4x^2/2!+ ... multiply by e^(-x)= 1 - x +x^2/2! -x^3/3! ... the 1 from cos 2x times e^-x gives 1 - x +x^2/2! -x^3/3! the -4x^2/2! times e^-x gives -4x^2/2! +4x^3/2! -4x^4/2! 2! .... you get 2 x^3 terms -x^3/3! + 4x^3/2! or (4/2! - 1/3!)x^3 = (2 - 1/3!)x^3
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