- #1

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Hi there,

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

Thanks.

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

Thanks.

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- 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.

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

Thanks.

- #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!

At x = 0, obviously, it's 0/0, which is

of course, F(x) does tend to a

- #4

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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!

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

of course, F(x) does tend to alimitat as x -> 0

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?

wot's an oblique asymptote?

- #7

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In the graph of X/Sin(X), there appears to be an asymptote at y=x

- #8

chroot

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- #9

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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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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

- #12

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

uhh?

wot's an oblique asymptote?

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?

- #14

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and also negative infinity if the domain goes there too.

- #15

HallsofIvy

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