taylor 1+x^2

Lösung

taylor

1 + x^{2}

1 + x^{2}

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 1 + x^{2}

d er i v a t i v e - \frac{1}{4} (x^{- 4} - x^{8})

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

\int e^{\frac{1}{2} x^{2}} \cdot x^{3} d x

\frac{d}{d x} ((4 + x^{2})^{- 1})

\int (x^{8} - \frac{2 x ^{5}}{7} - 5) d x