taylor sin(x)2

Lösung

taylor

sin (x) 2

2 x - \frac{1}{3} x^{3} + \frac{1}{60} x^{5} - \frac{1}{2520} x^{7} + \frac{1}{181440} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 2 x - \frac{1}{3} x^{3} + \frac{1}{60} x^{5} - \frac{1}{2520} x^{7} + \frac{1}{181440} x^{9} + \dots

\int e^{5 x} sin (2 x) d x

\int \frac{x}{x ( x ^{2} + 1 )} d x

d er i v a t i v e \frac{e ^{x}}{7 x ^{2}}

\frac{\partial}{\partial x} ((x + y) (2 x + y)^{2})

x \to + 0 lim (\frac{e ^{- 1 x} - 1}{x})