taylor sqrt(x),25

Lösung

taylor

x, 25

5 + \frac{1}{10} (x - 25) - \frac{1}{1000} (x - 25)^{2} + \frac{1}{50000} (x - 25)^{3} - \frac{1}{2000000} (x - 25)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 5 + \frac{\frac{d}{d x} ( x ) ( 25 )}{1 !} (x - 25) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ) ( 25 )}{2 !} (x - 25)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ) ( 25 )}{3 !} (x - 25)^{3} + \dots

Evaluate Derivatives

= 5 + \frac{\frac{1}{10}}{1 !} (x - 25) + \frac{- \frac{1}{500}}{2 !} (x - 25)^{2} + \frac{\frac{3}{25000}}{3 !} (x - 25)^{3} + \frac{- \frac{3}{250000}}{4 !} (x - 25)^{4} + \dots

Fasse zusammen

= 5 + \frac{1}{10} (x - 25) - \frac{1}{1000} (x - 25)^{2} + \frac{1}{50000} (x - 25)^{3} - \frac{1}{2000000} (x - 25)^{4} + \dots

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