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Homework Help: Dividing Functions Questions

  1. May 28, 2009 #1
    Hi there,
    Quick question. For F(X)= X/Sin(X), is there a hole at X=0?

  2. jcsd
  3. May 28, 2009 #2
    What do you get when plugging 0 into F(X) ?
  4. May 28, 2009 #3


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    Hi CanadianEh! :smile:

    At x = 0, obviously, it's 0/0, which is undefined (it's known as an "indeterminate form"), so yes in that sense there's a hole …

    of course, F(x) does tend to a limit at as x -> 0 :wink:
  5. May 28, 2009 #4
    0/Sin 0 = undefined.

    So basically, there's my answer. There is a hole at x=0. There is also an oblique asymptote of f(x)=x, correct?
  6. May 28, 2009 #5

    Thanks so much! Can you help me explain why there is an oblique asymptote?
  7. May 28, 2009 #6


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    uhh? :blushing:

    wot's an oblique asymptote? :confused:
  8. May 28, 2009 #7
    When a linear asymptote is not parallel to the x- or y-axis, it is called either an oblique asymptote or equivalently a slant asymptote.

    In the graph of X/Sin(X), there appears to be an asymptote at y=x
  9. May 28, 2009 #8


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    The function continues to have a defined value as you get arbitrarily close to zero, thus the limit as x->0 is defined. The function itself is undefined only exactly at zero.

    - Warren
  10. May 28, 2009 #9
    Try graphing x/sin(x) and you'll only see vertical asymptotes when the denominator, or sin(x), is 0.
    As far as I know, a rational function P(x)/Q(x) where P and Q are polynomials has an oblique asymptote only when the degree of the numerator is one larger than that of the denominator. In x/sin(x) you have a transcendental function in the denominator.
  11. May 28, 2009 #10
    Ok, so NO oblique asymptote, correct?
  12. May 28, 2009 #11


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    Still totally confused as to why this is called an asymptote instead of a tangent. :confused:

    Anyway I can't see how it's slanting ……

    what is limx -> 0 x/sinx ? :smile:
  13. May 28, 2009 #12
    That's right.

    A slant asymptote
    http://home.att.net/~srschmitt/precalc/precalc-fig12-03.gif [Broken]
    Last edited by a moderator: May 4, 2017
  14. May 28, 2009 #13


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    So that's only at infinity? :blushing:
  15. May 28, 2009 #14
    and also negative infinity if the domain goes there too.
  16. May 29, 2009 #15


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    tiny-tim, the word "asymptote" was wrong here. He intended "tangent" as you suggested. Because there is a "hole" at x= 0, there is no tangent there.
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