taylor cos(x),pi

Lösung

taylor

cos (x), π

- 1 + \frac{1}{2} (x - π)^{2} - \frac{1}{24} (x - π)^{4} + \frac{1}{720} (x - π)^{6} - \frac{1}{40320} (x - π)^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= - 1 + \frac{1}{2} (x - π)^{2} - \frac{1}{24} (x - π)^{4} + \frac{1}{720} (x - π)^{6} - \frac{1}{40320} (x - π)^{8} + \dots

\int 8 x^{3} (2 x^{4} + 4) d x

\frac{d}{d x} (cos (x) - \frac{1}{2})

\int_{0}^{1} x e^{3 x} d x

\int 9 x (1 - x) d x

\int_{0}^{π} - cos (x) d x