What is taylor e^{1-x} ?

The answer to taylor e^{1-x} is e-ex+e/2 x^2-e/6 x^3+e/(24)x^4+\ldots

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taylor e^{1-x}

taylor

e^{1 - x}

e - e x + \frac{e}{2} x^{2} - \frac{e}{6} x^{3} + \frac{e}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= e - e x + \frac{e}{2} x^{2} - \frac{e}{6} x^{3} + \frac{e}{24} x^{4} + \dots

\int \frac{1 + t + t ^{2}}{t} d t

h \to 0 lim (\frac{h}{h})

\frac{x ^{4}}{6} - 10 x

\frac{d}{d x} (\frac{c ^{2} - x ^{2}}{c ^{2} + x ^{2}})

y = x sin (\frac{5}{x})

What is taylor e^{1-x} ?
The answer to taylor e^{1-x} is e-ex+e/2 x^2-e/6 x^3+e/(24)x^4+\ldots