How to find the MacLaurin polynomial of degree 5 for F(x) ?

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Answer 1 · 2016-05-31T04:13:43

#-(2/5)x^5#

The power series for the integrand

#f(t)=e^(-2t^4) = 1+(-2t^4)+(-2t^4)^2/2!+ O(t^12)#

Now, after term by term integration, the given definite integral

#F(x)=x-2/5x^5+O(x^13)#

The MacLaurin 5th degree polynomial for F(x) is

#F(0)+xF'(0)+... +(x^5/(5!))F'''''(0)#

F(0) = 0 and the first non-zero derivative at x = 0 is #F'''''(0)=-(2/5)(5!))#

#=0+0+0+0+0+(x^5/5!)(-(2/5)(5!))#

#=-(2/5) x^5#