taylor 1/(x-1),x=7

Lösung

taylor

\frac{1}{x - 1}, x = 7

\frac{1}{6} - \frac{1}{36} (x - 7) + \frac{1}{216} (x - 7)^{2} - \frac{1}{1296} (x - 7)^{3} + \frac{1}{7776} (x - 7)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{6} + \frac{\frac{d}{d x} ( \frac{1}{x - 1} ) ( 7 )}{1 !} (x - 7) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{x - 1} ) ( 7 )}{2 !} (x - 7)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{x - 1} ) ( 7 )}{3 !} (x - 7)^{3} + \dots

Evaluate Derivatives

= \frac{1}{6} + \frac{- \frac{1}{36}}{1 !} (x - 7) + \frac{\frac{1}{108}}{2 !} (x - 7)^{2} + \frac{- \frac{1}{216}}{3 !} (x - 7)^{3} + \frac{\frac{1}{324}}{4 !} (x - 7)^{4} + \dots

Fasse zusammen

= \frac{1}{6} - \frac{1}{36} (x - 7) + \frac{1}{216} (x - 7)^{2} - \frac{1}{1296} (x - 7)^{3} + \frac{1}{7776} (x - 7)^{4} + \dots

t an g e n t y = x^{3} - 2 x^{2} + x + 7

\frac{\partial}{\partial x} (tan (x) y)

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