taylor x^{3/2},4

Lösung

taylor

x^{\frac{3}{2}}, 4

8 + 3 (x - 4) + \frac{3}{16} (x - 4)^{2} - \frac{1}{128} (x - 4)^{3} + \frac{3}{4096} (x - 4)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 8 + \frac{3}{1 !} (x - 4) + \frac{\frac{3}{8}}{2 !} (x - 4)^{2} + \frac{- \frac{3}{64}}{3 !} (x - 4)^{3} + \frac{\frac{9}{512}}{4 !} (x - 4)^{4} + \dots

Fasse zusammen

= 8 + 3 (x - 4) + \frac{3}{16} (x - 4)^{2} - \frac{1}{128} (x - 4)^{3} + \frac{3}{4096} (x - 4)^{4} + \dots

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