1Xn=0cn(x a)nddx(f(x)+g(x)) =ˆ(f(x)+g(x)) dx =1Xn=0cn(x a)nr1Xn=1cnn(x a)n1r1Xn=0cn(x a)nf(x)1Xn=1cnn(x a)n1ˆ 1Xn=0cn(x a)n!dx rf(x)=1Xn=0xnn!f0(x)ˆf(x) dx f(x)f(x)=11+x2f(x) = arctan xx⇡4f(x)=x2(1 + x)2f(x)=x3 x1Xn=1nxng(x)=x +12x2+13x3+14x4+ ··· +1nxn+ ···
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