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October 01, 2025, 03:24:14 am
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Author Topic: horizontal asymptotes can be crossed...  (Read 3456 times)  Share 

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TyErd

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horizontal asymptotes can be crossed...
« on: September 23, 2010, 12:53:26 pm »
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how?.... in the tsfx notes i got from the lectures, it says non-vertical asymptotes can be crossed.
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the.watchman

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Re: horizontal asymptotes can be crossed...
« Reply #1 on: September 23, 2010, 01:01:57 pm »
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Quote from: TyErd on September 23, 2010, 12:53:26 pm
how?.... in the tsfx notes i got from the lectures, it says non-vertical asymptotes can be crossed.

That is correct, take , there is a horizontal asymptote that applies to but it is crossed
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TyErd

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Re: horizontal asymptotes can be crossed...
« Reply #2 on: September 23, 2010, 01:15:50 pm »
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but this wouldn't apply for individual function like hyperbola and truncus yeah? Only when functions have been added, subtracted, multiplied or divided?
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superflya

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Re: horizontal asymptotes can be crossed...
« Reply #3 on: September 23, 2010, 01:29:41 pm »
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so too oblique asymptotes.
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TyErd

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Re: horizontal asymptotes can be crossed...
« Reply #4 on: September 23, 2010, 01:48:57 pm »
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what do you mean by oblique
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Re: horizontal asymptotes can be crossed...
« Reply #5 on: September 23, 2010, 01:54:31 pm »
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Oblique is when it's diagonal, ie. not parallel to x or y axis
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the.watchman

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Re: horizontal asymptotes can be crossed...
« Reply #6 on: September 23, 2010, 02:01:18 pm »
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Quote from: 99.95_for_sure on September 23, 2010, 01:54:31 pm
Oblique is when it's diagonal, ie. not parallel to x or y axis

Yep like , where is an oblique asymptote
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8039

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Re: horizontal asymptotes can be crossed...
« Reply #7 on: September 23, 2010, 02:14:58 pm »
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Quote from: the.watchman on September 23, 2010, 01:01:57 pm
Quote from: TyErd on September 23, 2010, 12:53:26 pm
how?.... in the tsfx notes i got from the lectures, it says non-vertical asymptotes can be crossed.

That is correct, take , there is a horizontal asymptote that applies to but it is crossed

But when x= 1,000,000 my calculator says 0 :/
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kenhung123

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Re: horizontal asymptotes can be crossed...
« Reply #8 on: September 23, 2010, 02:32:32 pm »
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coz its so small they round it to 0
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letsride

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Re: horizontal asymptotes can be crossed...
« Reply #9 on: September 23, 2010, 02:52:26 pm »
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Quote from: 8039 on September 23, 2010, 02:14:58 pm
Quote from: the.watchman on September 23, 2010, 01:01:57 pm
Quote from: TyErd on September 23, 2010, 12:53:26 pm
how?.... in the tsfx notes i got from the lectures, it says non-vertical asymptotes can be crossed.

That is correct, take , there is a horizontal asymptote that applies to but it is crossed

But when x= 1,000,000 my calculator says 0 :/

it's negligible so you can take it too 0. such as intergrating w/ infinity
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taiga

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Re: horizontal asymptotes can be crossed...
« Reply #10 on: September 23, 2010, 03:21:24 pm »
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an assymptote means it approaches that value as x approaches infinity, it is allowed to cross it.
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the.watchman

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Re: horizontal asymptotes can be crossed...
« Reply #11 on: September 23, 2010, 04:13:53 pm »
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On that same topic, I wonder whether the graph has an asymptote
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Re: horizontal asymptotes can be crossed...
« Reply #12 on: September 23, 2010, 08:01:31 pm »
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The precise definition of a horizontal asymptote is the following:

Let be defined on then means for every there exists a corresponding number such that if then . Likewise let be defined on then means for every there is a corresponding such that if then .

is the horizontal asymptote.

Thus horizontal asymptote can certainly be crossed.


Exercise for those interested: Using the same logic as above, can you formalise vertical asymptotes?
« Last Edit: September 23, 2010, 08:09:12 pm by TrueTears »
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brightsky

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Re: horizontal asymptotes can be crossed...
« Reply #13 on: September 23, 2010, 08:17:46 pm »
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Quote from: the.watchman on September 23, 2010, 04:13:53 pm
On that same topic, I wonder whether the graph has an asymptote

Yep.
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8039

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Re: horizontal asymptotes can be crossed...
« Reply #14 on: September 23, 2010, 10:51:46 pm »
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Quote from: TrueTears on September 23, 2010, 08:01:31 pm
The precise definition of a horizontal asymptote is the following:

Let be defined on then means for every there exists a corresponding number such that if then . Likewise let be defined on then means for every there is a corresponding such that if then .

is the horizontal asymptote.

Thus horizontal asymptote can certainly be crossed.


Exercise for those interested: Using the same logic as above, can you formalise vertical asymptotes?

Reading that hurt my head -_-
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