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Beliebt Rechnen >

taylor 2sin(x^2)

Lösung

taylor

2 sin (x^{2})

Lösung

2 x^{2} - \frac{1}{3} x^{6} + \frac{1}{60} x^{10} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{4}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 240}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{60480}{10 !} x^{10} + \dots

Fasse zusammen

= 2 x^{2} - \frac{1}{3} x^{6} + \frac{1}{60} x^{10} + \dots

Beliebte Beispiele

integral of 2sec^2(x)tan(x)

\int 2 sec^{2} (x) tan (x) d x

laplacetransform t^3e^{-2t}

l a pl a ce t r an s f or m t^{3} e^{- 2 t}

derivative of x*e^{-1/(x^2})

\frac{d}{d x} (x \cdot e^{- \frac{1}{x ^{2}}})

(e^{- 5 x})^{^{'}}

integral of (x+4)/x

\int \frac{x + 4}{x} d x