maclaurin x-sin(x)

Lösung

maclaurin

x - sin (x)

\frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{1}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 1}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{1}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 1}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Fasse zusammen

= \frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \dots

y^{^{''}} + 6 y^{^{'}} - 16 y = - 272 sin (8 x)

\frac{d}{d x} (\frac{ln ( cos ( 2 x ) )}{x})

\frac{d}{d x} (cos (3 x))

\frac{d}{d x} (arcsin (x) + arccos (x))

\int 8 x + 1 d x