What is taylor e^{x/5} ?

The answer to taylor e^{x/5} is 1+1/5 x+1/50 x^2+1/750 x^3+1/15000 x^4+\ldots

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taylor e^{x/5}

taylor

e^{\frac{x}{5}}

1 + \frac{1}{5} x + \frac{1}{50} x^{2} + \frac{1}{750} x^{3} + \frac{1}{15000} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{\frac{x}{5}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{\frac{x}{5}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{\frac{x}{5}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{\frac{1}{5}}{1 !} x + \frac{\frac{1}{25}}{2 !} x^{2} + \frac{\frac{1}{125}}{3 !} x^{3} + \frac{\frac{1}{625}}{4 !} x^{4} + \dots

Refine

= 1 + \frac{1}{5} x + \frac{1}{50} x^{2} + \frac{1}{750} x^{3} + \frac{1}{15000} x^{4} + \dots

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What is taylor e^{x/5} ?
The answer to taylor e^{x/5} is 1+1/5 x+1/50 x^2+1/750 x^3+1/15000 x^4+\ldots