maclaurin 2sin(3x)

Lösung

maclaurin

2 sin (3 x)

6 x - 9 x^{3} + \frac{81}{20} x^{5} - \frac{243}{280} x^{7} + \frac{243}{2240} x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{6}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 54}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{486}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 4374}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{39366}{9 !} x^{9} + \dots

Fasse zusammen

= 6 x - 9 x^{3} + \frac{81}{20} x^{5} - \frac{243}{280} x^{7} + \frac{243}{2240} x^{9} + \dots

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