taylor (x+3)^{1/2}

Lösung

taylor

(x + 3)^{\frac{1}{2}}

3^{\frac{1}{2}} + \frac{1}{2 \cdot 3 ^{\frac{1}{2}}} x - \frac{1}{24 \cdot 3 ^{\frac{1}{2}}} x^{2} + \frac{1}{144 \cdot 3 ^{\frac{1}{2}}} x^{3} - \frac{5}{3456 \cdot 3 ^{\frac{1}{2}}} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 3^{\frac{1}{2}} + \frac{\frac{d}{d x} ( ( x + 3 ) ^{\frac{1}{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( x + 3 ) ^{\frac{1}{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( x + 3 ) ^{\frac{1}{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 3^{\frac{1}{2}} + \frac{\frac{1}{2 \cdot 3 ^{\frac{1}{2}}}}{1 !} x + \frac{- \frac{1}{12 \cdot 3 ^{\frac{1}{2}}}}{2 !} x^{2} + \frac{\frac{1}{24 \cdot 3 ^{\frac{1}{2}}}}{3 !} x^{3} + \frac{- \frac{5}{144 \cdot 3 ^{\frac{1}{2}}}}{4 !} x^{4} + \dots

Fasse zusammen

= 3^{\frac{1}{2}} + \frac{1}{2 \cdot 3 ^{\frac{1}{2}}} x - \frac{1}{24 \cdot 3 ^{\frac{1}{2}}} x^{2} + \frac{1}{144 \cdot 3 ^{\frac{1}{2}}} x^{3} - \frac{5}{3456 \cdot 3 ^{\frac{1}{2}}} x^{4} + \dots

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