## Dividing Functions Questions

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

Thanks.
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 What do you get when plugging 0 into F(X) ?

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 Quote by CanadianEh Hi there, Quick question. For F(X)= X/Sin(X), is there a hole at X=0? Thanks.

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

## Dividing Functions Questions

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?

 Quote by tiny-tim Hi CanadianEh! 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

Thanks so much! Can you help me explain why there is an oblique asymptote?

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 Quote by CanadianEh Thanks so much! Can you help me explain why there is an oblique asymptote?
uhh?
wot's an oblique asymptote?
 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
 Recognitions: Gold Member Science Advisor Staff Emeritus 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
 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.
 Ok, so NO oblique asymptote, correct?

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 Quote by CanadianEh 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.

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

what is limx -> 0 x/sinx ?

 Quote by CanadianEh Ok, so NO oblique asymptote, correct?
That's right.

 Quote by tiny-tim uhh? wot's an oblique asymptote?
A slant asymptote

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