What is taylor e^{x-1},0 ?

The answer to taylor e^{x-1},0 is 1/e+1/e x+1/(2e)x^2+1/(6e)x^3+1/(24e)x^4+\ldots

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taylor e^{x-1},0

taylor

e^{x - 1}, 0

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

y + sin (x) = x^{3} y^{^{'}}

\int e^{4 y} d y

x \to 0 + lim (x^{6 x})

s

What is taylor e^{x-1},0 ?
The answer to taylor e^{x-1},0 is 1/e+1/e x+1/(2e)x^2+1/(6e)x^3+1/(24e)x^4+\ldots