taylor xcos(5x)

Lösung

taylor

x cos (5 x)

x - \frac{25}{2} x^{3} + \frac{625}{24} x^{5} - \frac{3125}{144} x^{7} + \frac{78125}{8064} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( x cos ( 5 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x cos ( 5 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x cos ( 5 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 75}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{3125}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 109375}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{3515625}{9 !} x^{9} + \dots

Fasse zusammen

= x - \frac{25}{2} x^{3} + \frac{625}{24} x^{5} - \frac{3125}{144} x^{7} + \frac{78125}{8064} x^{9} + \dots