taylor sqrt(x+4)

Lösung

taylor

x + 4

2 + \frac{1}{4} x - \frac{1}{64} x^{2} + \frac{1}{512} x^{3} - \frac{5}{16384} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 2 + \frac{\frac{d}{d x} ( x + 4 ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x + 4 ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x + 4 ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 2 + \frac{\frac{1}{4}}{1 !} x + \frac{- \frac{1}{32}}{2 !} x^{2} + \frac{\frac{3}{256}}{3 !} x^{3} + \frac{- \frac{15}{2048}}{4 !} x^{4} + \dots

Fasse zusammen

= 2 + \frac{1}{4} x - \frac{1}{64} x^{2} + \frac{1}{512} x^{3} - \frac{5}{16384} x^{4} + \dots

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