Asymptote : re- curve sketching (1 Viewer)

[fullonoob]

How would you find the oblique asymptotes of a implicitly differentiated graph?
Sketch the graph of x^2 - 4y^2 = 4

I've got no horizontal tangents
Vertical tangents : ( -2 , 0) , (2 , 0)

The obliques are y = +- (1/2)x
How do i find them? Help please

 

[ComingUpForAir]

what on earth are you trying to ask?

 

[cyl123]

It is perfectly clear what OP is asking for.

The graph can be rearranged into a hyperbola:

x^2 - 4y^2 = 4
--> x^2/4 - y^2 = 1
noting asymptotes of a hyperbola (of the form x^2/a^2-y^2/b^2=1) is y=bx/a and y=-bx/a then the asymptotes are y=x/2 and y=-x/2.

 

[untouchablecuz]

 

[fullonoob]

Thanks untouchable. How would you know when to find obliques though? Before you re-arrange it, its hard to see, and you wouldn't have time in a test to re-arrange equations. Being able to limit an equation will probably require 30 secs, and i wouldn't want to waste that for each graph question. So whats your intuition?

Oh and i'm just wondering...who actually does their 4u exercises on time before tests and all. I know i've just done mine a few weeks before tests and holidays, but never had the time to finish during school

 

[ComingUpForAir]

but he already gave the answer in his question..

 

[untouchablecuz]

notice that the asymptotes have general form

thus, to find asymptotes of a hyperbola without taking limits etc, rearrange it into the following form

shouldn't this be in the textbook?

 

[fullonoob]

notice that the asymptotes have general form

thus, to find asymptotes of a hyperbola without taking limits etc, rearrange it into the following form

shouldn't this be in the textbook?

hmm i see. This was not in the text book that's why. Cambridge has like 1-3 examples only with little info

 

[cutemouse]

Cambridge is crap for theory. It's alright for exercises though since they give you the level of difficulty of CSSA exams.

But then again, I don't think the 4U textbooks out there are all that great. They tend to fail in the area of conciseness. Hence why you need to make your own notes.

 

[The Nomad]

Cambridge is crap for theory. It's alright for exercises though since they give you the level of difficulty of CSSA exams.

But then again, I don't think the 4U textbooks out there are all that great. They tend to fail in the area of conciseness. Hence why you need to make your own notes.

Making notes for maths? Are you serious about this?

 

[cutemouse]

Making notes for maths? Are you serious about this?

Yes I am.