3psilon
  • 3psilon
Help finding ALL asymtotes
Mathematics
chestercat
  • chestercat
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3psilon
  • 3psilon
of \[y = \frac{ x^2 - 3x + 2 }{ x^{2}-1 }\]
anonymous
  • anonymous
\[((x-1)(x-2))/((x-1)(x+1))\] \[(x-2)/(x+1)\] you have vertical asymptote at x=-1 horizontal asymptotes at negative infinity and positive infinity y=1 is your horizontal asymptote for both infinities x=-1 is your only vertical one because you canceled out the (x-1) factor
3psilon
  • 3psilon
I'm not really understanding the horizontal asymtote part :(

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anonymous
  • anonymous
you take limit as x approaches infinity and negative infinity. when you do that, you get 1. limit x approaches negative infinity = limit x approaches infinity =1
3psilon
  • 3psilon
Do you always do that to find the horizontal asymtote ?
anonymous
  • anonymous
yea. horizontal retricemptotes describe the behavior of the graph as x increases
3psilon
  • 3psilon
@josiahh Doing it algebraically I'm not so good with limits So can you show me algebraically how the limit = 1 please?
anonymous
  • anonymous
when you are taking limits at infinity, you look at the degree of the polynomials in the denominator and the numerator
3psilon
  • 3psilon
Ohhhh and if they are equal its Coeffcient over coeffcient?
anonymous
  • anonymous
yea that rule...
3psilon
  • 3psilon
Thank YOU!
anonymous
  • anonymous
welcome

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