taylor sqrt(x),\at 25

Lösung

taylor

x, at 25

\frac{\frac{1}{2 at 25}}{1 !} (x - at 25) + \frac{- \frac{1}{4 ( at 25 ) ^{\frac{3}{2}}}}{2 !} (x - at 25)^{2} + \frac{\frac{3}{8 ( at 25 ) ^{\frac{5}{2}}}}{3 !} (x - at 25)^{3} + \frac{- \frac{15}{16 ( at 25 ) ^{\frac{7}{2}}}}{4 !} (x - at 25)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= at 25 + \frac{\frac{1}{2 at 25}}{1 !} (x - at 25) + \frac{- \frac{1}{4 ( at 25 ) ^{\frac{3}{2}}}}{2 !} (x - at 25)^{2} + \frac{\frac{3}{8 ( at 25 ) ^{\frac{5}{2}}}}{3 !} (x - at 25)^{3} + \frac{- \frac{15}{16 ( at 25 ) ^{\frac{7}{2}}}}{4 !} (x - at 25)^{4} + \dots

Fasse zusammen

= \frac{\frac{1}{2 at 25}}{1 !} (x - at 25) + \frac{- \frac{1}{4 ( at 25 ) ^{\frac{3}{2}}}}{2 !} (x - at 25)^{2} + \frac{\frac{3}{8 ( at 25 ) ^{\frac{5}{2}}}}{3 !} (x - at 25)^{3} + \frac{- \frac{15}{16 ( at 25 ) ^{\frac{7}{2}}}}{4 !} (x - at 25)^{4} + \dots

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