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Popular >

taylor (e^{x/2}-1)/x

Solution

taylor

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

Solution

e^{\frac{1}{2}} - 1 + \frac{- e ^{\frac{1}{2}} + 2}{2} (x - 1) + \frac{5 e ^{\frac{1}{2}} - 8}{8} (x - 1)^{2} + \frac{- 29 e ^{\frac{1}{2}} + 48}{48} (x - 1)^{3} + \frac{233 e ^{\frac{1}{2}} - 384}{384} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= e^{\frac{1}{2}} - 1 + \frac{\frac{- e ^{\frac{1}{2}} + 2}{2}}{1 !} (x - 1) + \frac{\frac{5 e ^{\frac{1}{2}} - 8}{4}}{2 !} (x - 1)^{2} + \frac{\frac{- 29 e ^{\frac{1}{2}} + 48}{8}}{3 !} (x - 1)^{3} + \frac{\frac{233 e ^{\frac{1}{2}} - 384}{16}}{4 !} (x - 1)^{4} + \dots

Refine

= e^{\frac{1}{2}} - 1 + \frac{- e ^{\frac{1}{2}} + 2}{2} (x - 1) + \frac{5 e ^{\frac{1}{2}} - 8}{8} (x - 1)^{2} + \frac{- 29 e ^{\frac{1}{2}} + 48}{48} (x - 1)^{3} + \frac{233 e ^{\frac{1}{2}} - 384}{384} (x - 1)^{4} + \dots

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Frequently Asked Questions (FAQ)

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