taylor x^7e^x5

Lösung

taylor

x^{7} e^{x} 5

5 x^{7} + 5 x^{8} + \frac{5}{2} x^{9} + \frac{5}{6} x^{10} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( x ^{7} e ^{x} \cdot 5 ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{7} e ^{x} \cdot 5 ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{7} e ^{x} \cdot 5 ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{25200}{7 !} x^{7} + \frac{201600}{8 !} x^{8} + \frac{907200}{9 !} x^{9} + \frac{3024000}{10 !} x^{10} + \dots

Fasse zusammen

= 5 x^{7} + 5 x^{8} + \frac{5}{2} x^{9} + \frac{5}{6} x^{10} + \dots

x \to 0 lim (\frac{sin ^{2} ( x )}{x})

2 y^{^{'}} + 3 y = 5

d er i v a t i v e g (t) = \frac{1}{t}

\int_{1}^{\infty} \frac{2}{e ^{x}} d x

\frac{\partial}{\partial x} (6 y^{2} - 6 x^{2})