maclaurin cos(3x)

Lösung

maclaurin

cos (3 x)

1 - \frac{9}{2} x^{2} + \frac{27}{8} x^{4} - \frac{81}{80} x^{6} + \frac{729}{4480} x^{8} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 9}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{81}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 729}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{6561}{8 !} x^{8} + \dots

Fasse zusammen

= 1 - \frac{9}{2} x^{2} + \frac{27}{8} x^{4} - \frac{81}{80} x^{6} + \frac{729}{4480} x^{8} + \dots

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