taylor sin(x),(pi/4)

Lösung

taylor

sin (x), (\frac{π}{4})

\frac{2}{2} + \frac{1}{2} (x - (\frac{π}{4})) - \frac{1}{2 2} (x - (\frac{π}{4}))^{2} - \frac{1}{6 2} (x - (\frac{π}{4}))^{3} + \frac{1}{24 2} (x - (\frac{π}{4}))^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{2}{2} + \frac{\frac{d}{d x} ( sin ( x ) ) ( ( \frac{π}{4} ) )}{1 !} (x - (\frac{π}{4})) + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( x ) ) ( ( \frac{π}{4} ) )}{2 !} (x - (\frac{π}{4}))^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( x ) ) ( ( \frac{π}{4} ) )}{3 !} (x - (\frac{π}{4}))^{3} + \dots

Evaluate Derivatives

= \frac{2}{2} + \frac{\frac{2}{2}}{1 !} (x - (\frac{π}{4})) + \frac{- \frac{2}{2}}{2 !} (x - (\frac{π}{4}))^{2} + \frac{- \frac{2}{2}}{3 !} (x - (\frac{π}{4}))^{3} + \frac{\frac{2}{2}}{4 !} (x - (\frac{π}{4}))^{4} + \dots

Fasse zusammen

= \frac{2}{2} + \frac{1}{2} (x - (\frac{π}{4})) - \frac{1}{2 2} (x - (\frac{π}{4}))^{2} - \frac{1}{6 2} (x - (\frac{π}{4}))^{3} + \frac{1}{24 2} (x - (\frac{π}{4}))^{4} + \dots