taylor e^{x^2+x}

Lösung

taylor

e^{x^{2} + x}

1 + x + \frac{3}{2} x^{2} + \frac{7}{6} x^{3} + \frac{25}{24} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{3}{2 !} x^{2} + \frac{7}{3 !} x^{3} + \frac{25}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + x + \frac{3}{2} x^{2} + \frac{7}{6} x^{3} + \frac{25}{24} x^{4} + \dots

\frac{d}{d x} (y^{2} - x)

s im pl i f y e^{l n (s i n (x^{2}))} 2 x + 1

x \to 0 lim (\frac{ln ( x + 1 )}{x})

\int cos^{2} (10 x) d x

\frac{d}{d x} ((x^{4} + 2)^{c o s (x)})