taylor ((e^x-1))/x

Lösung

taylor

\frac{( e ^{x} - 1 )}{x}

e - 1 + (x - 1) + \frac{e - 2}{2} (x - 1)^{2} + \frac{- 2 e + 6}{6} (x - 1)^{3} + \frac{9 e - 24}{24} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= e - 1 + \frac{1}{1 !} (x - 1) + \frac{e - 2}{2 !} (x - 1)^{2} + \frac{- 2 e + 6}{3 !} (x - 1)^{3} + \frac{9 e - 24}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= e - 1 + (x - 1) + \frac{e - 2}{2} (x - 1)^{2} + \frac{- 2 e + 6}{6} (x - 1)^{3} + \frac{9 e - 24}{24} (x - 1)^{4} + \dots

\int \frac{- 3}{x ^{2}} d x

y^{^{'}} = y cos (x)

y^{^{'}} + \frac{y}{x} = y^{2}

\frac{\partial}{\partial y} (50 x + 400 - 50 y)

d er i v a t i v e 8 e^{- x} + 1