taylor X^{9/6},8,5

Lösung

taylor

X^{\frac{9}{6}}, 8, 5

16 \cdot 2^{\frac{1}{2}} + 3 \cdot 2^{\frac{1}{2}} (X - 8) + \frac{3}{16 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{2} - \frac{1}{256 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{3} + \frac{3}{16384 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 16 \cdot 2^{\frac{1}{2}} + \frac{\frac{d}{d X} ( X ^{\frac{9}{6}} ) ( 8 )}{1 !} (X - 8) + \frac{\frac{d ^{2}}{d X ^{2}} ( X ^{\frac{9}{6}} ) ( 8 )}{2 !} (X - 8)^{2} + \frac{\frac{d ^{3}}{d X ^{3}} ( X ^{\frac{9}{6}} ) ( 8 )}{3 !} (X - 8)^{3} + \dots

Evaluate Derivatives

= 16 \cdot 2^{\frac{1}{2}} + \frac{3 \cdot 2 ^{\frac{1}{2}}}{1 !} (X - 8) + \frac{\frac{3}{8 \cdot 2 ^{\frac{1}{2}}}}{2 !} (X - 8)^{2} + \frac{- \frac{3}{128 \cdot 2 ^{\frac{1}{2}}}}{3 !} (X - 8)^{3} + \frac{\frac{9}{2048 \cdot 2 ^{\frac{1}{2}}}}{4 !} (X - 8)^{4} + \dots

Fasse zusammen

= 16 \cdot 2^{\frac{1}{2}} + 3 \cdot 2^{\frac{1}{2}} (X - 8) + \frac{3}{16 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{2} - \frac{1}{256 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{3} + \frac{3}{16384 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{4} + \dots

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