using-maclaurin-s-series-exapand-x-2-e-x-1-e-x-1-upto-x-4-term-

Question Number 172455 by pablo1234523 last updated on 27/Jun/22

using {maclaurin}^{'} s series exapand

\frac{x}{2} (\frac{e^{x} + 1}{e^{x} - 1}) upto x^{4} term

Answered by mr W last updated on 29/Jun/22

= \frac{x}{2} (\frac{e^{\frac{x}{2}} + e^{- \frac{x}{2}}}{e^{\frac{x}{2}} - e^{- \frac{x}{2}}})

= \frac{x}{2} \coth \frac{x}{2}

= \frac{x}{2} (\frac{2}{x} + \frac{x}{6} - \frac{x^{3}}{360} + O (x^{5}))

= 1 + \frac{x^{2}}{12} - \frac{x^{4}}{720} + O (x^{6})

Commented by mr W last updated on 29/Jun/22

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