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Popular >

taylor e^{-x/2},3

Solution

taylor

e^{- \frac{x}{2}}, 3

Solution

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

Popular Examples

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\frac{d}{d x} (2 + x)

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

Frequently Asked Questions (FAQ)

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