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calculus

Please help. I got stuck on this problem all week. And please show steps. Use Taylor Inequality to estimate approximation f(x)Tn(x) when x lies in the given interval. Round your answer to six decimal places. a=3, n=3, 2.5<=x<=3.5?

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Anonymous

  1. well, the formula is
    |Rk(x)| <= M/(n+1)! |x-a|n+1

    Now, 2.5 <= x <= 3.5 means |x-3| <= 1/2

    Using your values, that means that
    |R3(x)| <= M/4! * 1/16
    where M is a bound on the 4th derivative of f(x), which you have not specified, but maybe you can fix that

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    oobleck

  2. The function is f(x)=ln(1+2x) but the 4th derivative I don't know. So, how do I plug in now?

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    Anonymous

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