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Thread: Equation using derivative: Use a derivative to estimate g(e+0.1) for g(x) = xln(x)

  1. #1

    Post Equation using derivative: Use a derivative to estimate g(e+0.1) for g(x) = xln(x)

    Let g(x)=xln(x). We know g(e)=e. Use a derivative to estimate g(e+0.1). You may leave an unsimplified numerical answer.

    I understand how to plug g(e+0.1) in, but not using the derivative. Please Help!!!

  2. #2
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    Quote Originally Posted by tsj1114 View Post
    Let g(x)=xln(x). We know g(e)=e. Use a derivative to estimate g(e+0.1). You may leave an unsimplified numerical answer. I understand how to plug g(e+0.1) in, but not using the derivative.
    If [TEX]h \approx 0 [/TEX] then [TEX]g'(x_0)\approx \dfrac{g(x_0+h)-g(x_0)}{h} [/TEX] then rearranging we get
    [TEX]g(x_0+h)\approx h\cdot g'(x_0)+g(x_0)[/TEX].

    [tex]g(x)=x\log(x)~ \Rightarrow~g'(x)=\log(x)+1[/tex] Thus let [tex]x_0=e~\&~h=0.1[/tex].
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

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