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August 20, 2019, 01:20:57 pm

Author Topic: Oblique asymptotes  (Read 531 times)  Share 

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clovvy

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Oblique asymptotes
« on: April 22, 2018, 03:37:54 pm »
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If I get a curve sketching question and have an oblique asymptote in it,  how do I recognize them? In general, how do I test for oblique asymptote (I am not sure if it's 2U/3U/4U,  so I post here, feel free to move this somewhere else)
2018 HSC: 4U maths, 3U maths, Standard English, Chemistry, Physics

RuiAce

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Re: Oblique asymptotes
« Reply #1 on: April 22, 2018, 03:41:08 pm »
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Never occurs in 2U.

In 3U, if you have an oblique asymptote, you should be doing polynomial long division to identify it.

4U questions (that aren't really just harder 3U questions) will hint towards it if necessary.

clovvy

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Re: Oblique asymptotes
« Reply #2 on: April 22, 2018, 04:33:41 pm »
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Never occurs in 2U.

In 3U, if you have an oblique asymptote, you should be doing polynomial long division to identify it.

4U questions (that aren't really just harder 3U questions) will hint towards it if necessary.

I have looked it up on google, though I don't quite understand it (yes long division if the leading coefficient ended up being higher or something)...  I don't quite understand so I might need some examples for 3U and 4U perhaps
2018 HSC: 4U maths, 3U maths, Standard English, Chemistry, Physics

RuiAce

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Re: Oblique asymptotes
« Reply #3 on: April 22, 2018, 07:49:42 pm »
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I have looked it up on google, though I don't quite understand it (yes long division if the leading coefficient ended up being higher or something)...  I don't quite understand so I might need some examples for 3U and 4U perhaps
Situations beyond polynomial long division will never occur in 3U. You should provide your own examples (along with any questions that you have regarding it).

Also note that if the degree of the polynomial in the numerator is not exactly 1 higher than the degree of the denominator, then there will not be an oblique asymptote. In general, if the degree of the polynomial is the numerator is less, we can only ever have horizontal asymptotes.

The occurrence of these in 4U are really handled case-by-case. These examples are hard to single out because you never know whether or not they will be examined (i.e. they are rare). Most of the time, if they appear in 4U then they require the same methods in 3U, however they could occasionally occur from something more mysterious (e.g. sketching \( y = x\, f(x) \) given that \(y = f(x) \) has a horizontal asymptote that's not at \(y=0\)).