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Math Help - limits problem

  1. #1
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    limits problem

    Hello

    I need to give an example of a function f(x) such that limf(x), as x goes to infinity, exists but limf'(x) does not. Any help?

    Thx
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by AlexHall View Post
    Hello

    I need to give an example of a function f(x) such that limf(x), as x goes to infinity, exists but limf'(x) does not. Any help?

    Thx
    f(x)=\frac{\cos\left(x^{n\geqslant{2}}\right)}{x}
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  3. #3
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    Quote Originally Posted by AlexHall View Post
    an example of a function f(x) such that limf(x), as x goes to infinity, exists but limf'(x) does not.
    Try f(x) = (x)\left( {\arctan (x)} \right).
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Plato View Post
    Try f(x) = (x)\left( {\arctan (x)} \right).
    Isn't that the converse of this question? The limit of the function is nonexistant but its derivative is finite.
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