anonymous
  • anonymous
please help :( evaluate lim x->positive infinity 2x-1/x-1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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jdoe0001
  • jdoe0001
well, for one \(x \ne 0 because that'd make the denominator 0 and thus the fraction undefined any value > 1 onwards, will yield a value in the denominator of "x-1" and a value on the numerator of "2x-1", or x + x -1 so notice "2x-1" will yield a bigger number than "x-1" which means the numerator will always be bigger than the denominator by "x" so if the denominator says turns out to be 25, the numerator will be x +25
jdoe0001
  • jdoe0001
so, where's that number going to? what's its limit? well, you have a rational expression, and the limit will occurr at an asymptote as "x" is moving fast rightwards, "y" is moving upwards, so that means a horizontal asymptote so, in this case the numerator and denominator are of the same degree, thus the horiziontal asymptote will occurr at the leading coefficient atop/bottom
jdoe0001
  • jdoe0001
well, for one \(x \ne 0\) because that'd make the denominator 0 and thus the fraction undefined

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jdoe0001
  • jdoe0001
ack I meant \(x \ne 1\)
jdoe0001
  • jdoe0001
1 btw is the vertical asymptote
anonymous
  • anonymous
\[\lim_{x \rightarrow \infty } 2x-1/x-1\]
jdoe0001
  • jdoe0001
yes
anonymous
  • anonymous
i'm sorry, i dont understand. your explanation is a little too complicated for me
jdoe0001
  • jdoe0001
have you done asymptotes yet?
anonymous
  • anonymous
not yet
jdoe0001
  • jdoe0001
ok, well, then you can just make a few values for "x" and see where "y" is heading to keep in mind that 2x -1 ==> x + x -1, and that will always be more than x-1 by x so if x = 5 and onwards $$ \begin{matrix} x && y\\ 5 & &\cfrac{5-4}{4}\\ \hline 10 & &\cfrac{10-9}{9}\\ \hline 25 & &\cfrac{25-24}{24} \end{matrix} \\ $$
jdoe0001
  • jdoe0001
did I get that...
jdoe0001
  • jdoe0001
haemm, no :/
jdoe0001
  • jdoe0001
let's see, 2x -1 = x +( x -1) so, the numerator will be bigger by more
jdoe0001
  • jdoe0001
$$ \begin{matrix} x && y\\ \color{red}{5} & &\cfrac{\color{red}{5}+4}{4}\\ \hline \color{red}{10} & &\cfrac{\color{red}{10}+9}{9}\\ \hline \color{red}{25} & &\cfrac{\color{red}{25}+24}{24} \end{matrix} \\ $$
jdoe0001
  • jdoe0001
so, the 1st "y" up there will be 9/4 and then 19/9 and then 49/24 ... and so on notice where or how close it's moving towards
jdoe0001
  • jdoe0001
5/4 = 1.25 19/9 = 2.11 49/24 = 2.04 if say I use 1,000,000 so I'd get 1000000-1 = 999999 thus 1999999/999999 = 2.000001
anonymous
  • anonymous
thank you :)
jdoe0001
  • jdoe0001
yw

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