aymptotes (1 Viewer)

[tacogym27101990]

hey i was just wondering if anyone knows if oblique asymptotes is part of the syllabus for ext 1?

 

[YannY]

Wow people and their laziness these days... Do you not have access to the syllabus?

 

[tacogym27101990]

meh
my teacher reckons its not but they were in the text book
i just wanted to see if anyone already knew before i went looking for the syllabus.

 

[tommykins]

Should be, but obtaining them is quite simple.

 

[tacogym27101990]

yeah i no how to obtain them
i was just wondering if i should expect them in 3 unit and not only 4 unit

 

[tommykins]

If you're doing 4unit, why worry about if assmyptotes are in 3unit if you're already doing 4unit which automatically have assmyptotes? :S

 

[tacogym27101990]

yeah i no
i was just curious

 

[DJel]

According to my teacher they are not in the 3U syllabus. The textbook we use (maths in focus) also has a question involving an oblique asymptote though. Also searching 'oblique' in the syllabus returns 0 results.

 

[Trebla]

I learnt about 'oblique' asymptotes at school and they even examined it in assessments. It hasn't been explicitly stated in the syllabus because it just says "asymptotes" in general. However, one of the examples recommended in the syllabus has an oblique asymptote of y = x:

From section 10.5 of the 2 Unit part of 'Geometrical Applications of Differentiation":

"The sketching of curves such as quadratics, cubics and higher polynomials and simple rational functions. After computing some values (which may include points where x = 0 and where y = 0), the determination of the stationary points is frequently very useful. Other considerations are symmetry about the axes, behaviour for very large positive and negative values of x, and the points at which functions such as: y= 1/(x - 1), y = x + 1/x, y = 1/x, are defined"

The curve y = x + 1/x has an asymptote of y = x, and this curve has been stated as an example in the 2 unit part of the syllabus. So from that I guess you can say that oblique asymptotes are actually in syllabus, and more surprisingly the 2 unit syllabus....

 

[tacogym27101990]

Re: asymptotes

surely it cant be part of the 2 unit course?? they dont no how to long divide polynomials.
unless there given the actual equation already divided??
would be pretty mean tho

 

[Slidey]

Re: asymptotes

You don't need to know how to divide polynomials. You just re-arrange in little groups. Unless you mean for higher degree ones like this:

y=x^3/(x-1) = (x^3-1)/(x-1) + 1/(x-1) = x^2+x+1+1/(x-1) but that won't give you an oblique asymptote so much as curve guidelines (both g(x)=x^2+x+1 and f(x)=1/(x-1) trace g(x)+f(x) for extremities)

Or do you mean these:

y=(x^2+x+1)/(x+1) ?
y=(x^2+x)/(x+1) +1/(x-1)
y=x+1/(x-1)

Or maybe:
y=(2x^2-3x+5)/(x-3)
y=(2x^2-6x +3x+5)/(x-3)
y=2x + (3x-9 +14)/(x-3)
y=2x+3+14/(x-3)

Hmm. I suppose I just did long division without realising it. It's really quite simple for quadratic or less on top... which is all oblique asymptotes are, unless the bottom is quadratic or more.

So yeah, there are certainly basic cases of oblique asymptotes that are well within the grasp and syllabus of 2u students.

I believe I remember learning what they were (and how to graph them) in 2unit and learning how to find them when not given in 3unit.

 

[mantiswhoprays]

hey i was just wondering if anyone knows if oblique asymptotes is part of the syllabus for ext 1?

yeah, they're part of curve sketching for the hsc. we just finished them, we only spent about 1 period on them, not a significant chunk.