taylor (1+x)^2

Lösung

taylor

(1 + x)^{2}

1 + 2 x + x^{2}

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 1 + 2 x + x^{2}

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

n = 0 \sum \infty \frac{2 ^{n}}{5 ^{n}}

x \to \infty - lim (\frac{1}{x})

x y^{^{'}} = x e^{- 2 x} - (2 x + 1) y

x \to 8 - lim (4 x)