taylor f(x)=cos(pix)

Lösung

taylor

f (x) = cos (π x)

1 - \frac{π ^{2}}{2} x^{2} + \frac{π ^{4}}{24} x^{4} - \frac{π ^{6}}{720} x^{6} + \frac{π ^{8}}{40320} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( cos ( π x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ( π x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ( π x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- π ^{2}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{π ^{4}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- π ^{6}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{π ^{8}}{8 !} x^{8} + \dots

Fasse zusammen

= 1 - \frac{π ^{2}}{2} x^{2} + \frac{π ^{4}}{24} x^{4} - \frac{π ^{6}}{720} x^{6} + \frac{π ^{8}}{40320} x^{8} + \dots

l a pl a ce t r an s f or m - 5 (t - 1) e^{t}

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