Asamatopes -> 3U graphes.... (1 Viewer)

Lazarus

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I believe I went through it on the previous page of this thread. :)
 

Lazarus

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Oblique asymptotes are essentially any asymptotes that aren't a straight line - for example, y=x.
 

bilal

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hahha. oops. sorry laz...

edit: i just looked at the example.. to find out a limit.. dont u divide the x(es) by the highest power of x. and not divide the x(es) by the highest power in the denominator????

waz going on????
 
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Lazarus

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I remember when I was doing the HSC that I thought you just had to divide by the highest power of x... and that seemed to work for most cases (possibly because, by chance or otherwise, they always put the larger polynomial in the denominator instead of the numerator).

If you look at the example I did, you'll get y -> 0 as x -> oo if you try to divide by x instead of just x.

Dividing by the highest power in the denominator was something I picked up at uni.

Hmm, you should observe that, by factorising, you can rewrite the fractional function as the result you get when dividing by x (which is essentially what you're doing anyway).

....lim................x..
x -> oo..........x + 4

----------->........x......
..................
x(1 + 4/x)

----------->......x......
..................
1 + 4/x
 

Weisy

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Laz's example is v. good. I never knew about dividing through by the highest value in the denominator either! :)

To find oblique asymptotes alternatively you can divide the numerator by the denominator (since the numerator has to have a greater power if the thing has an oblique asymptote) using long division.

I hate long division though.
 

kini mini

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Originally posted by Weisy
Laz's example is v. good. I never knew about dividing through by the highest value in the denominator either! :)

To find oblique asymptotes alternatively you can divide the numerator by the denominator (since the numerator has to have a greater power if the thing has an oblique asymptote) using long division.

I hate long division though.
I seem to remember Laz's technique from horiz/vert asymptotes - bit of a pain for an oblique aymptote though. The long div method is better if ur going for the eqn I think. I think that's what Pender's book recommends in that damn curve sketching menu chapter.
 

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