taylor e^{-x^3}

Lösung

taylor

e^{- x^{3}}

1 - x^{3} + \frac{1}{2} x^{6} - \frac{1}{6} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{360}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 60480}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Fasse zusammen

= 1 - x^{3} + \frac{1}{2} x^{6} - \frac{1}{6} x^{9} + \dots

\int \frac{x}{u}

a re a y = x^{3}, 0 \leq x \leq 3

t an g e n t 2 sec (x)

l a pl a ce t r an s f or m 3 sin (4 t + 2) e^{- 6 t}

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