1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?

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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook