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Math Help - Limit question

  1. #1
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    Limit question

    What is the limit of (|x|)/x? I know from looking at the graph that it has to be 0, but i dont know how to do this algebraically. Thanks.
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  2. #2
    Super Member General's Avatar
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    Quote Originally Posted by Evan.Kimia View Post
    What is the limit of (|x|)/x? I know from looking at the graph that it has to be 0, but i dont know how to do this algebraically. Thanks.
    as x--> what?
    if x-->0
    You are supposed to consider the limit as x-->0 from right and from left.
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  3. #3
    Senior Member nikhil's Avatar
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    at x>0 |x|/x =1
    therefor limit at x>0 is 1
    at x<0 |x|/x=-1
    therfor limit at x<0 is -1
    1 and -1 are the right hand limit and left hand limit at x=0 respectively.
    since they are not equal therefor at x=0 limit don't exist.
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  4. #4
    Super Member General's Avatar
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    Quote Originally Posted by nikhil View Post
    at x>0 |x|/x =1
    therefor limit at x>0 is 1
    at x<0 |x|/x=-1
    therfor limit at x<0 is -1
    1 and -1 are the right hand limit and left hand limit at x=0 respectively.
    since they are not equal therefor at x=0 limit don't exist.
    Edit:
    limit when x\rightarrow 0^{+}
    limit when x\rightarrow 0^{-}
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  5. #5
    Senior Member nikhil's Avatar
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    Smile

    Quote Originally Posted by General View Post
    Edit:
    limit when x\rightarrow 0^{+}
    limit when x\rightarrow 0^{-}
    x>0 may take any value not only 0+ebsilon but also real number
    eg
    limit of |x|/x at x>0 (let us take x=5)
    =|5|/5 =1
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  6. #6
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    Thank you! Refreshed my memory.
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