taylor 1/(x-1),21

Lösung

taylor

\frac{1}{x - 1}, 21

\frac{1}{20} - \frac{1}{400} (x - 21) + \frac{1}{8000} (x - 21)^{2} - \frac{1}{160000} (x - 21)^{3} + \frac{1}{3200000} (x - 21)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{20} + \frac{\frac{d}{d x} ( \frac{1}{x - 1} ) ( 21 )}{1 !} (x - 21) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{x - 1} ) ( 21 )}{2 !} (x - 21)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{x - 1} ) ( 21 )}{3 !} (x - 21)^{3} + \dots

Evaluate Derivatives

= \frac{1}{20} + \frac{- \frac{1}{400}}{1 !} (x - 21) + \frac{\frac{1}{4000}}{2 !} (x - 21)^{2} + \frac{- \frac{3}{80000}}{3 !} (x - 21)^{3} + \frac{\frac{3}{400000}}{4 !} (x - 21)^{4} + \dots

Fasse zusammen

= \frac{1}{20} - \frac{1}{400} (x - 21) + \frac{1}{8000} (x - 21)^{2} - \frac{1}{160000} (x - 21)^{3} + \frac{1}{3200000} (x - 21)^{4} + \dots

\int_{0}^{\frac{1}{6}} \frac{3}{1 - 9 x ^{2}} d x

\frac{d x}{d t} = x t

y^{^{''}} - 2 y^{^{'}} + 1 y = 0, y (0) = 8, y^{^{'}} (0) = 2

\int - 8 x^{2} d x

in v erse l a pl a ce \frac{e ^{- π (s)}}{s ^{3} + s}