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Math Help - Appreciate Some Guidance, Help, Steps on this question

  1. #1
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    Appreciate Some Guidance, Help, Steps on this question

    Use Maclaurin’s series:
    8.1. to find the first 4 terms of the expansion of Sinh(2x), then
    8.2. use this expansion to evaluate Sinh(2x) when x = 0.5, to 4 decimal places
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  2. #2
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    Re: Appreciate Some Guidance, Help, Steps on this question

    Hello, jono1966!

    \text{8.1 Use Maclaurin’s series to find the first 4 terms of the expansion of }\sinh(2x)

    \text}8.2. Use this expansion to evaluate }\sinh(2x)\text{ when }x = \frac{1}{2}\text{, to 4 decimal places.}

    The Maclaurin series begins: . \sinh(2x) \;=\;(2x) + \frac{(2x)^3}{3!} + \frac{(2x)^5}{5!} + \frac{(2x)^7}{7!} + \cdots

    If x = \tfrac{1}{2}, we have: . \sinh(1) \;=\;1 + \frac{1^3}{3!} + \frac{1^5}{5!} + \frac{1^7}{7!} \;=\; 1.175198413

    Therefore: . \sinh(1) \:\approx\:1.1752

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