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Math Help - linearization

  1. #1
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    linearization

    Find the linearization of at .
    =
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  2. #2
    Member Black's Avatar
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    L(x)=f(a)+f'(a)(x-a)

    f'(x)=-10\text{sin}x\, \text{sin}(5x)+50\text{cos}(5x)\text{cos}x

    f'(0)=50

    f(0)=0, so

    L(x)=50x.
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  3. #3
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    Quote Originally Posted by Black View Post
    L(x)=f(a)+f'(a)(x-a)

    f'(x)=-10\text{sin}x\, \text{sin}(5x)+50\text{cos}(5x)\text{cos}x

    f'(0)=50

    f(0)=0, so

    L(x)=50x.

    thanks
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