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Math Help - taylor series problem n2

  1. #1
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    taylor series problem n2

    Hi.
    Evaluate.

    \lim_{\ x\to 0}\frac{(\arctan{\sqrt{x}})(sinx)-x{\sqrt{x}}}{xe^{\sqrt{x}}-cos{\sqrt{x}}+1}
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  2. #2
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    Quote Originally Posted by Shock View Post
    Hi.
    Evaluate.

    \lim_{\ x\to 0}\frac{(\arctan{\sqrt{x}})(sinx)-x{\sqrt{x}}}{xe^{\sqrt{x}}-cos{\sqrt{x}}+1}
    why makes you think this limit involves Taylor series?

    looks more like an application of L'Hopital's rule ... maybe more than once.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    why makes you think this limit involves Taylor series?

    looks more like an application of L'Hopital's rule ... maybe more than once.


    The prof said we have to solve it with taylor series.
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  4. #4
    MHF Contributor matheagle's Avatar
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    Either way I would substitute u=\sqrt{x} before doing anything.
    And notice that the limit really should only be from the right.
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