Why does Lim as x approaches infinity of x/(x-9) = 1?

  • Thread starter LOLItsAJ
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  • #1
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Homework Statement



Limit as x approaches infinity of [itex]x/x-9[/itex]

Homework Equations



None

The Attempt at a Solution



I know the indeterminate form infinity/infinity happens. I don't know how to fix it, but I'm assuming it's quite simple...
 

Answers and Replies

  • #2
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When x is very very large, say 6 billion. The numbers 6 billion and 6 billion minus 9 are essentially the same. As x gets larger and larger, this discrepancy diminishes. The value the ratio approaches is 1.

If you wanted to be a little more rigorous, you can divide the numerator and denominator by 1/x then take the limit and see what happens. It should pop right out.
 
  • #3
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A nice trick for these types of problems would be to divide everything by x;

[tex] \lim_{x\rightarrow\infty} \frac{x/x}{(x/x)-(9/x)} [/tex]

Then simplify and you should be able to figure it out from there
 
  • #4
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Using L'Hopitals rule for evaluating indeterminate forms, just differentiate both the numerator and the denominator separately to produce 1/1. Xyius explains well intuitively why the result is what it is.
 

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