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Popular >

taylor e^{-x/2}e^{-1/4}

Solution

taylor

e^{- \frac{x}{2}} e^{- \frac{1}{4}}

Solution

\frac{1}{e ^{\frac{1}{4}}} - \frac{1}{2 e ^{\frac{1}{4}}} x + \frac{1}{8 e ^{\frac{1}{4}}} x^{2} - \frac{1}{48 e ^{\frac{1}{4}}} x^{3} + \frac{1}{384 e ^{\frac{1}{4}}} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{e ^{\frac{1}{4}}} + \frac{\frac{d}{d x} ( e ^{- \frac{x}{2}} e ^{- \frac{1}{4}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- \frac{x}{2}} e ^{- \frac{1}{4}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- \frac{x}{2}} e ^{- \frac{1}{4}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{e ^{\frac{1}{4}}} + \frac{- \frac{1}{2 e ^{\frac{1}{4}}}}{1 !} x + \frac{\frac{1}{4 e ^{\frac{1}{4}}}}{2 !} x^{2} + \frac{- \frac{1}{8 e ^{\frac{1}{4}}}}{3 !} x^{3} + \frac{\frac{1}{16 e ^{\frac{1}{4}}}}{4 !} x^{4} + \dots

Refine

= \frac{1}{e ^{\frac{1}{4}}} - \frac{1}{2 e ^{\frac{1}{4}}} x + \frac{1}{8 e ^{\frac{1}{4}}} x^{2} - \frac{1}{48 e ^{\frac{1}{4}}} x^{3} + \frac{1}{384 e ^{\frac{1}{4}}} x^{4} + \dots

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Frequently Asked Questions (FAQ)

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