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Math Help - the vertical assimptote of this function..

  1. #1
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    the vertical assimptote of this function..

    x>0
    <br />
f(x)=|x-1|+\frac{1}{x}\\<br />
    for m i get:
    m=lim |x-1| +1/x=infinity
    x->infinity
    so there is no vercital assimptote here?
    Last edited by transgalactic; February 15th 2009 at 06:01 AM.
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  2. #2
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    Quote Originally Posted by transgalactic View Post
    x>0
    <br />
f(x)=|x-1|+\frac{1}{x}\\<br />
    for m i get:
    m=lim |x-1| +1/x=infinity
    x->infinity
    so there is no vercital assimptote here?
    You get vertical asymptotes at those values of x where the function isn't defined. This happens here at x = 0.

    Beside the vertical asymptote this graph has two skewed asymtotes:

    a_1: y= x-1,\ x > 0 ...... and ......  a_2: y= -x+1,\ x < 0
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  3. #3
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    i agrre that there is an vertical assimptote here on x=0

    is there any horisontal assimptote
    i cant get the "m" value for it?

    y=mx+n
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  4. #4
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    Quote Originally Posted by transgalactic View Post
    i agrre that there is an vertical assimptote here on x=0

    is there any horisontal assimptote
    i cant get the "m" value for it?

    y=mx+n
    No, there aren't any horizontal asymptotes (if by "horizontal" you mean parallel to the x-axis) but there are 2 skewed asymptotes with the slopes m = 1 or m = -1. (Compare my previous post)
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  5. #5
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    there is a horisontal assmiptote y=mx+n

    m=lim f(x)/x x->infinty
    n=lim [f(x)-mx0] x->infinty

    and my m limit is not defined so there is no horisontal assimptote
    correct?
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  6. #6
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    Quote Originally Posted by transgalactic View Post
    there is a horisontal assmiptote y=mx+n

    m=lim f(x)/x x->infinty No
    n=lim [f(x)-mx0] x->infinty

    and my m limit is not defined so there is no horisontal assimptote
    correct?
    If

    m=\lim_{|x|\to \infty}\left(\dfrac{f(x)}x\right)=1,\ x > 0 ~\vee~ m=\lim_{|x|\to \infty}\left(\dfrac{f(x)}x\right)=-1,\ x < 0

    and:

    n=\lim_{|x|\to \infty}\left(f(x)- m\cdot x\right)=-1,\ x > 0 ~\vee~ n=\lim_{|x|\to \infty}\left(f(x)-m\cdot x\right)=1,\ x < 0
    Attached Thumbnails Attached Thumbnails the vertical assimptote of this function..-absfkt_zweiasympt.png  
    Last edited by earboth; February 15th 2009 at 07:03 AM.
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