taylor e^{(x^2)}

Lösung

taylor

e^{(x^{2})}

1 + x^{2} + \frac{1}{2} x^{4} + \frac{1}{6} x^{6} + \frac{1}{24} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{x^{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{x^{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{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{12}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{120}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{1680}{8 !} x^{8} + \dots

Fasse zusammen

= 1 + x^{2} + \frac{1}{2} x^{4} + \frac{1}{6} x^{6} + \frac{1}{24} x^{8} + \dots

\int \frac{x ^{2} - 400}{x} d x

\frac{\partial}{\partial x} (- e^{y} sin (x) + 4 y + 7 y x)

x \to 3 lim (\frac{5}{( x - 3 ) ^{2}})

x \to 2 lim (3 x^{2} - 5 x + 2)

e^{y} d x - e^{- x} d y = 0, y (0) = 0