Dividing Functions Questions

  • Thread starter CanadianEh
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  • #1
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Hi there,
Quick question. For F(X)= X/Sin(X), is there a hole at X=0?

Thanks.
 

Answers and Replies

  • #2
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What do you get when plugging 0 into F(X) ?
 
  • #3
tiny-tim
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Hi there,
Quick question. For F(X)= X/Sin(X), is there a hole at X=0?

Thanks.
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:
 
  • #4
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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?
 
  • #5
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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:

Thanks so much! Can you help me explain why there is an oblique asymptote?
 
  • #6
tiny-tim
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Thanks so much! Can you help me explain why there is an oblique asymptote?
uhh? :blushing:

wot's an oblique asymptote? :confused:
 
  • #7
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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
 
  • #8
chroot
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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
 
  • #9
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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.
 
  • #10
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Ok, so NO oblique asymptote, correct?
 
  • #11
tiny-tim
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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
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:
 
  • #12
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Ok, so NO oblique asymptote, correct?
That's right.


uhh? :blushing:

wot's an oblique asymptote? :confused:
A slant asymptote
http://home.att.net/~srschmitt/precalc/precalc-fig12-03.gif [Broken]
 
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  • #13
tiny-tim
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A slant asymptote
So that's only at infinity? :blushing:
 
  • #14
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and also negative infinity if the domain goes there too.
 
  • #15
HallsofIvy
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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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