taylor sqrt(2+x),-1

Lösung

taylor

2 + x, - 1

1 + \frac{1}{2} (x + 1) - \frac{1}{8} (x + 1)^{2} + \frac{1}{16} (x + 1)^{3} - \frac{5}{128} (x + 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{1}{2}}{1 !} (x + 1) + \frac{- \frac{1}{4}}{2 !} (x + 1)^{2} + \frac{\frac{3}{8}}{3 !} (x + 1)^{3} + \frac{- \frac{15}{16}}{4 !} (x + 1)^{4} + \dots

Fasse zusammen

= 1 + \frac{1}{2} (x + 1) - \frac{1}{8} (x + 1)^{2} + \frac{1}{16} (x + 1)^{3} - \frac{5}{128} (x + 1)^{4} + \dots

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