taylor sin(x),(2pi)/3

Lösung

taylor

sin (x), \frac{2 π}{3}

\frac{3}{2} - \frac{1}{2} (x - \frac{2 π}{3}) - \frac{3}{4} (x - \frac{2 π}{3})^{2} + \frac{1}{12} (x - \frac{2 π}{3})^{3} + \frac{1}{16 3} (x - \frac{2 π}{3})^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= \frac{3}{2} - \frac{1}{2} (x - \frac{2 π}{3}) - \frac{3}{4} (x - \frac{2 π}{3})^{2} + \frac{1}{12} (x - \frac{2 π}{3})^{3} + \frac{1}{16 3} (x - \frac{2 π}{3})^{4} + \dots

\int (4 x - sin (x)) d x

\int_{5}^{1} (- 4 x + 1) d x

x \to 3 - lim (2)

f^{^{'}} = f^{3}

\frac{d}{d x} (x^{- 2} ln (x))