taylor (x^2+1)*e^{x-1}

Lösung

taylor

(x^{2} + 1) \cdot e^{x - 1}

\frac{1}{e} + \frac{1}{e} x + \frac{3}{2 e} x^{2} + \frac{7}{6 e} x^{3} + \frac{13}{24 e} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{e} + \frac{\frac{1}{e}}{1 !} x + \frac{\frac{3}{e}}{2 !} x^{2} + \frac{\frac{7}{e}}{3 !} x^{3} + \frac{\frac{13}{e}}{4 !} x^{4} + \dots

Fasse zusammen

= \frac{1}{e} + \frac{1}{e} x + \frac{3}{2 e} x^{2} + \frac{7}{6 e} x^{3} + \frac{13}{24 e} x^{4} + \dots

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