taylor 4x*ln(x)

Lösung

taylor

4 x \cdot ln (x)

4 (x - 1) + 2 (x - 1)^{2} - \frac{2}{3} (x - 1)^{3} + \frac{1}{3} (x - 1)^{4} - \frac{1}{5} (x - 1)^{5} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{4}{1 !} (x - 1) + \frac{4}{2 !} (x - 1)^{2} + \frac{- 4}{3 !} (x - 1)^{3} + \frac{8}{4 !} (x - 1)^{4} + \frac{- 24}{5 !} (x - 1)^{5} + \dots

Fasse zusammen

= 4 (x - 1) + 2 (x - 1)^{2} - \frac{2}{3} (x - 1)^{3} + \frac{1}{3} (x - 1)^{4} - \frac{1}{5} (x - 1)^{5} + \dots

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