taylor f(t)=ln(1+2*t)

Lösung

taylor

f (t) = ln (1 + 2 \cdot t)

2 t - 2 t^{2} + \frac{8}{3} t^{3} - 4 t^{4} + \frac{32}{5} t^{5} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{2}{1 !} t + \frac{- 4}{2 !} t^{2} + \frac{16}{3 !} t^{3} + \frac{- 96}{4 !} t^{4} + \frac{768}{5 !} t^{5} + \dots

Fasse zusammen

= 2 t - 2 t^{2} + \frac{8}{3} t^{3} - 4 t^{4} + \frac{32}{5} t^{5} + \dots

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