taylor (sin(x)), pi/2

Lösung

taylor

(sin (x)), \frac{π}{2}

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

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

n = 1 \sum \infty \frac{2 n}{3 n}

d er i v a t i v e 1 + x^{2}

\int_{0}^{9} 4 x - \frac{4 x}{3} d x

\frac{\partial}{\partial x} (3 x^{3} y^{2} z)

l a pl a ce t r an s f or m 0.03 (1 - cos (2 t))