What is taylor e^{1/x} ?

The answer to taylor e^{1/x} is e-e(x-1)+(3e)/2 (x-1)^2-(13e)/6 (x-1)^3+(73e)/(24)(x-1)^4+\ldots

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taylor e^{1/x}

taylor

e^{\frac{1}{x}}

e - e (x - 1) + \frac{3 e}{2} (x - 1)^{2} - \frac{13 e}{6} (x - 1)^{3} + \frac{73 e}{24} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= e + \frac{- e}{1 !} (x - 1) + \frac{3 e}{2 !} (x - 1)^{2} + \frac{- 13 e}{3 !} (x - 1)^{3} + \frac{73 e}{4 !} (x - 1)^{4} + \dots

Refine

= e - e (x - 1) + \frac{3 e}{2} (x - 1)^{2} - \frac{13 e}{6} (x - 1)^{3} + \frac{73 e}{24} (x - 1)^{4} + \dots

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\frac{d}{d x} (\frac{4}{5} x^{10})

What is taylor e^{1/x} ?
The answer to taylor e^{1/x} is e-e(x-1)+(3e)/2 (x-1)^2-(13e)/6 (x-1)^3+(73e)/(24)(x-1)^4+\ldots