taylor f(x)=e^{x^4}

Lösung

taylor

f (x) = e^{x^{4}}

1 + x^{4} + \frac{1}{2} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{x^{4}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{x^{4}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{x^{4}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{20160}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Fasse zusammen

= 1 + x^{4} + \frac{1}{2} x^{8} + \dots

\frac{\partial}{\partial x} (\frac{1}{x + y + z})

\int \frac{1}{x ^{4} x ^{2} + 4} d x

s im pl i f y (x - 3)^{- 2}

y^{^{'}} = - y (1 + x y^{2})

x \to 2 lim (\frac{x ^{3} - 2 x ^{2}}{10 x - 20})