taylor 1/(2+7x)

Lösung

taylor

\frac{1}{2 + 7 x}

\frac{1}{2} - \frac{7}{4} x + \frac{49}{8} x^{2} - \frac{343}{16} x^{3} + \frac{2401}{32} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{2} + \frac{\frac{d}{d x} ( \frac{1}{2 + 7 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{2 + 7 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{2 + 7 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{2} + \frac{- \frac{7}{4}}{1 !} x + \frac{\frac{49}{4}}{2 !} x^{2} + \frac{- \frac{1029}{8}}{3 !} x^{3} + \frac{\frac{7203}{4}}{4 !} x^{4} + \dots

Fasse zusammen

= \frac{1}{2} - \frac{7}{4} x + \frac{49}{8} x^{2} - \frac{343}{16} x^{3} + \frac{2401}{32} x^{4} + \dots

\frac{d}{d x} (x^{3} ln ∣ 1 + x ∣)

\int \frac{x ^{2} - 4 x + 9}{x ^{2} - 6 x + 9} d x

d er i v a t i v e arctan (9 x)

\int sin^{3} (3 x) cos^{3} (3 x) d x

x \to 0 lim (cot (3 x))