taylor x-1-0.5sin(x)

Lösung

taylor

x - 1 - 0.5 sin (x)

- 1 + 0.5 x + 0.08333 \dots x^{3} - 0.00416 \dots x^{5} + 0.00009 \dots x^{7} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= - 1 + \frac{\frac{d}{d x} ( x - 1 - 0.5 sin ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x - 1 - 0.5 sin ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x - 1 - 0.5 sin ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= - 1 + \frac{0.5}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0.5}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 0.5}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0.5}{7 !} x^{7} + \dots

Fasse zusammen

= - 1 + 0.5 x + 0.08333 \dots x^{3} - 0.00416 \dots x^{5} + 0.00009 \dots x^{7} + \dots

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