taylor 1/((x+2))

Lösung

taylor

\frac{1}{( x + 2 )}

\frac{1}{2} - \frac{1}{4} x + \frac{1}{8} x^{2} - \frac{1}{16} x^{3} + \frac{1}{32} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{2} + \frac{- \frac{1}{4}}{1 !} x + \frac{\frac{1}{4}}{2 !} x^{2} + \frac{- \frac{3}{8}}{3 !} x^{3} + \frac{\frac{3}{4}}{4 !} x^{4} + \dots

Fasse zusammen

= \frac{1}{2} - \frac{1}{4} x + \frac{1}{8} x^{2} - \frac{1}{16} x^{3} + \frac{1}{32} x^{4} + \dots

\int \frac{1}{4 x + 2} d x

\int \frac{3}{x ^{2} ( x ^{2} + 25 )} d x

\int \frac{1}{36 + x ^{2}} d x

\frac{\partial}{\partial x} (- 2 e^{4 y - x^{2} - y^{2}} x)

x \to \infty lim (x - 6)