What is taylor e^{x-1} ?

The answer to taylor e^{x-1} 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}

taylor

e^{x - 1}

\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

\frac{d}{d x} (\frac{3 x y}{x ^{2} + y ^{2}})

y^{^{'''}} + 2 y^{^{''}} + y^{^{'}} + 2 y = 0

n \to \infty lim (n^{- 2})

2, x, x^{2}

\frac{d}{d x} ((x^{3})^{\frac{1}{2}})

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