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Question Number 5525 by sanusihammed last updated on 17/May/16
Expand f(z) = cos(z) about point z = Π/3
Expandf(z)=cos(z)aboutpointz=Π/3
Commented by Yozzii last updated on 18/May/16
Taylor expansion of f(z) near z=π/3: f(z)=Σ_(i=0) ^∞ {((f^((i)) (π/3)(x−(π/3))^i )/(i!))} f^((0)) (z)=cosz f^1 (z)=−sinz f^((2)) (z)=−cosz f^((3)) (z)=sinz f^((4)) (z)=cosz f^((5)) (z)=−sinz f^((2n−1)) (z)=(−1)^n sinz f^((2n)) (z)=(−1)^n cosz
Taylorexpansionoff(z)nearz=π/3:f(z)=∑∞i=0{f(i)(π/3)(x−π3)ii!}f(0)(z)=coszf1(z)=−sinzf(2)(z)=−coszf(3)(z)=sinzf(4)(z)=coszf(5)(z)=−sinzf(2n−1)(z)=(−1)nsinzf(2n)(z)=(−1)ncosz

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