What is taylor e^{1/θ} ?

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

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taylor e^{1/θ}

taylor

e^{\frac{1}{θ}}

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

n = 0 \sum \infty \frac{3}{n n}

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9 (sin (x))^{x}

\int \frac{x ^{2} - 25}{x ^{4}} d x

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