taylor 3/(1+3x)

Lösung

taylor

\frac{3}{1 + 3 x}

3 - 9 x + 27 x^{2} - 81 x^{3} + 243 x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 3 + \frac{- 9}{1 !} x + \frac{54}{2 !} x^{2} + \frac{- 486}{3 !} x^{3} + \frac{5832}{4 !} x^{4} + \dots

Fasse zusammen

= 3 - 9 x + 27 x^{2} - 81 x^{3} + 243 x^{4} + \dots

\int x 5 + 2 x d x

y^{^{''}} - 4 y^{^{'}} + 3 y = 10 e^{3 t}

\frac{d y}{d x} = \frac{sin ( x )}{cos ( y )}

\int_{0}^{\infty} (e^{- x}) d x

x \to 1 lim (\frac{x ^{2}}{x ^{2} - 1})