680CHAPTER 11INFINITE SERIESEXERCISES 11.6Find the Taylor polynomial of the functionffor the given valuesofaandn, and give the Lagrange form of the remainder.1.f(x)=√x;a=4,n=3.2.f(x)=cosx;a=π/3,n=4.3.f(x)=sinx;a=π/4,n=4.4.f(x)=lnx;a=1,n=5.5.f(x)=tan−1x;a=1,n=3.6.f(x)=cosπx;a=12,n=4.Expandg(x) as indicated and specify the values ofxfor whichthe expansion is valid.7.g(x)=3x3−2x2+4x+1in powers ofx−1.8.g(x)=x4−x3+x2−x+1in powers ofx−2.9.g(x)=2x5+x2−3x−5in powers ofx+1.10.g(x)=x−1in powers ofx−1.11.g(x)=(1+x)−1in powers ofx−1.12.g(x)=(b+x)−1in powers ofx−a,a= −b.13.g(x)=(1−2x)−1in powers ofx+2.14.g(x)=e−4xin powers ofx+1.15.g(x)=sinxin powers ofx−π.16.g(x)=sinxin powers ofx−12π.17.g(x)=cosxin powers ofx−π.18.g(x)=cosxin powers ofx−12π.19.g(x)=sin12πxin powers ofx−1.
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