the vertical assimptote of this function..

**transgalactic** · February 15th 2009, 04:38 AM

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?

**earboth** · February 15th 2009, 04:49 AM

Originally Posted by transgalactic

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 ...... $a_2: y= -x+1,\ x < 0$

**transgalactic** · February 15th 2009, 05:01 AM

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

**earboth** · February 15th 2009, 05:12 AM

Originally Posted by transgalactic

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)

**transgalactic** · February 15th 2009, 05:15 AM

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?

**earboth** · February 15th 2009, 05:36 AM

Originally Posted by transgalactic

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:

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

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