taylor sin(x),pi

Lösung

taylor

sin (x), π

- (x - π) + \frac{1}{6} (x - π)^{3} - \frac{1}{120} (x - π)^{5} + \frac{1}{5040} (x - π)^{7} - \frac{1}{362880} (x - π)^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{- 1}{1 !} (x - π) + \frac{0}{2 !} (x - π)^{2} + \frac{1}{3 !} (x - π)^{3} + \frac{0}{4 !} (x - π)^{4} + \frac{- 1}{5 !} (x - π)^{5} + \frac{0}{6 !} (x - π)^{6} + \frac{1}{7 !} (x - π)^{7} + \frac{0}{8 !} (x - π)^{8} + \frac{- 1}{9 !} (x - π)^{9} + \dots

Fasse zusammen

= - (x - π) + \frac{1}{6} (x - π)^{3} - \frac{1}{120} (x - π)^{5} + \frac{1}{5040} (x - π)^{7} - \frac{1}{362880} (x - π)^{9} + \dots

\frac{d P}{d t} = P (850 - P)

\frac{d y}{d x} = - y

y^{^{'}} + \frac{5}{x} y = 0

\int_{- \infty}^{0} x e^{x} d x

\frac{d}{d x} ((x + h)^{3})