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Thread: Calculating limit of rational function

  1. #1
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    Question Calculating limit of rational function

    For the question in the image, can someone please explain to me why we should interpret $\sqrt{x^2}$ as $|x|$?

    Calculating limit of rational function-60577775_694673997658657_7403750760413921280_n.jpg
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  2. #2
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    Re: Calculating limit of rational function

    $x\geq 0 \Rightarrow \sqrt{x^2} = x\\x< 0 \Rightarrow \sqrt{x^2} = -x\\ \text{This is identical to the definition of }|x|$
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  3. #3
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    Re: Calculating limit of rational function

    graph of $y = \sqrt{x^2}$
    Attached Thumbnails Attached Thumbnails Calculating limit of rational function-sqrt-x-2-.png   Calculating limit of rational function-sqrt-x-2-_graph.png  
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  4. #4
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    Re: Calculating limit of rational function

    The definition of the symbol $\sqrt{x}$ is that it is the positive square root.
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