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Math Help - Another Limit problem :X

  1. #1
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    Another Limit problem :X

    Do x is NONE? Since 8/0 = undefined if I plug 0 into x? Agree? Just want to make sure. I am not good with math
    Please give me a helping hand! Thank you!


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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by greenbee View Post
    Do x is NONE? Since 8/0 = undefined if I plug 0 into x? Agree? Just want to make sure. I am not good with math
    Please give me a helping hand! Thank you!


    Recall that \left|x\right|=\left\{\begin{array}{rl}x & x\geq 0\\ {\color{red}-x} & {\color{red}x<0}\end{array}\right.

    So in your case,

    \lim_{x\to0^-}\left(\frac{8}{x}-\frac{8}{\left|x\right|}\right)=\lim_{x\to0^-}\left(\frac{8}{x}+\frac{8}{x}\right)=\lim_{x\to 0^-}\frac{16}{x}

    I'm sure you can take it from here.
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    Recall that \left|x\right|=\left\{\begin{array}{rl}x & x\geq 0\\ {\color{red}-x} & {\color{red}x<0}\end{array}\right.

    So in your case,

    \lim_{x\to0^-}\left(\frac{8}{x}-\frac{8}{\left|x\right|}\right)=\lim_{x\to0^-}\left(\frac{8}{x}+\frac{8}{x}\right)=\lim_{x\to 0^-}\frac{16}{x}

    I'm sure you can take it from here.
    Please tell me that it's 16?
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  4. #4
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    Quote Originally Posted by greenbee View Post
    Please tell me that it's 16?
    No, it's not 16.

    Try graphing f(x) = \frac{16}{x} and see what happens when x \to 0 from the left...
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  5. #5
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    Quote Originally Posted by Prove It View Post
    No, it's not 16.

    Try graphing f(x) = \frac{16}{x} and see what happens when x \to 0 from the left...
    It doesn't go to 0
    It goes to like -Infinity
    So the answer is -Infinity?
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by greenbee View Post
    It doesn't go to 0
    It goes to like -Infinity
    So the answer is -Infinity?
    Yes, \lim_{x\to0^-}\frac{16}{x}=-\infty.
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  7. #7
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    Quote Originally Posted by Chris L T521 View Post
    Yes, \lim_{x\to0^-}\frac{16}{x}=-\infty.
    YAY thank you so much!!! (Thanks thanks thanks button)!!!
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