taylor 8/(3x+2),5

Lösung

taylor

\frac{8}{3 x + 2}, 5

\frac{8}{17} - \frac{24}{289} (x - 5) + \frac{72}{4913} (x - 5)^{2} - \frac{216}{83521} (x - 5)^{3} + \frac{648}{1419857} (x - 5)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{8}{17} + \frac{\frac{d}{d x} ( \frac{8}{3 x + 2} ) ( 5 )}{1 !} (x - 5) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{8}{3 x + 2} ) ( 5 )}{2 !} (x - 5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{8}{3 x + 2} ) ( 5 )}{3 !} (x - 5)^{3} + \dots

Evaluate Derivatives

= \frac{8}{17} + \frac{- \frac{24}{289}}{1 !} (x - 5) + \frac{\frac{144}{4913}}{2 !} (x - 5)^{2} + \frac{- \frac{1296}{83521}}{3 !} (x - 5)^{3} + \frac{\frac{15552}{1419857}}{4 !} (x - 5)^{4} + \dots

Fasse zusammen

= \frac{8}{17} - \frac{24}{289} (x - 5) + \frac{72}{4913} (x - 5)^{2} - \frac{216}{83521} (x - 5)^{3} + \frac{648}{1419857} (x - 5)^{4} + \dots

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