What is taylor (1-x)e^{x+(x^2)/2+(x^3)/3} ?

The answer to taylor (1-x)e^{x+(x^2)/2+(x^3)/3} is 1+\ldots

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

taylor

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

1 + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 1 + \dots

\int sin (ln (u)) d u

y^{^{''}} - y = 5 sin (2 t) (0) 1

\frac{1}{2 + 3 x}

y^{^{'}} = y + x, y (0) = - 1

\frac{r}{r ^{2} + 1}

What is taylor (1-x)e^{x+(x^2)/2+(x^3)/3} ?
The answer to taylor (1-x)e^{x+(x^2)/2+(x^3)/3} is 1+\ldots