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Limits, horizontal asymptotes

  1. Sep 18, 2006 #1
    What are the horizontal asymptotes of
    I don't understand because isn't that tangent and it has asymptotes?!
  2. jcsd
  3. Sep 18, 2006 #2
    So.. why is arccotangent cot(1/x)...... I don't understand.
  4. Sep 19, 2006 #3


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    Staff Emeritus
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    It isn't. It also is not 1/cot(x) which is tan(x).

    When working with functions, the "exponent" -1 does not mean "reciprocal" (and isn't really an exponent). It means "inverse function".

    cot-1(x) is just another notation for arccot(x), the inverse function to cot(x).
    Specifically, if y= cot-1(x)= arccot(x), then x= cot(y). Notice that you have swapped x and y so the graphs will swap x and y axes. Where does cotangent have vertical asymptotes?
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