Extended (3unit) Curve Sketching (1 Viewer)

[HekToZ]

Is there a simpler way of doing harder curve sketching? I understand how to find the vertical asymptotes but not quite sure how to find the horizontal/oblique asymptotes. These questions take so long to do and I usually get lost by the time I have to find points of inflexion.

 

[HekToZ]

And how do you distinguish between horizontal and oblique asymptotes?

 

[Trev]

wats an oblique asymptote?
do u's kno how to find slanted asymptotes?

 

[blackfriday]

oblique asymptote is an asymptote that behaves that a linear equation usually. i think you take the denominator and divide into the numerator, and the dividend is what the asymptote behaves like. correct me if im wrong here.

horizontal asymptote is taken when you consider when x approaches infinity, you see what y behaves like. oblique asymptotes usually occur when the highest power in the numerator is higher than the highest power in the denominator.

 

[Slidey]

x+1/x=y

Say, 'hello' to oblique asymptote.

Specifically, at y=x

y != x
check:
x+1/x != x
1/x != 0

And stuff.

 

[redslert]

!=

mean not equal to

 

[Slidey]

Somebody delete a post?

 

[Xayma]

mean not equal to

I hate that for it:

You should use <> which is mathematically correct and doesn't look like factorial.

Or &ne;

 

[Slidey]

!= is computationally correct. ! signifies logical negation.

I've never seen <>. Is it really not equal?

 

[Xayma]

Well <> would mean less than or greater than ie all but equal to.

&ne; is the best though. Things like 2!=3 looks way to much like factorial. 3!=6 it doesn't really matter

 

[HekToZ]

I think I understand now....

 

[Archman]

<> works in vb too

 

[Slidey]

Visual Basic is a pseudo-language.

 

[redslert]

Somebody delete a post?

no body deleted any posts
i just thought you should give people the meaning because not everyone will know what that means

/= is more common
<> well that's just vb

 

[Xayma]

&ne; is the best though and it doesn't take long to type out only a fraction longer then /= quicker if you aren't familiar with the placement of the / and = keys.

 

[Slidey]

How, pray tell, do you type it without copying and pasting it?

alt+xxxx?

 

[Li0n]

=!
the reason ! is there is to block out the equallness
ok so imagine water flowing inbetween the =, if you put a ; there for example the water comes out! so it is partially equal
so :. let =; = partially equal

now if you do !, the water is clogged up! so it goes back the other way
so let =! = not equal to
now if you put a $ in there, then water goes all over the place depending upon the speed that the water is travelling throught the =, so if you have NFI what the answer is then write =$ and that means "could be equal to, couldn't be, random"
then you will get marks for it

 

[withoutaface]

How, pray tell, do you type it without copying and pasting it?

alt+xxxx?

you type (and sign)ne(semicolon), like so &ne;

 

[Xayma]

Also works for the greek letters, therefore, etc (&delta;, &theta;, &pi;, &fnof;(x), &ge;, &le;, &equiv; and &there4; etc) as detailed in the notation thread in maths ext 2. You just have to be careful not to have one of the symbols next to a ) as the semicolon will form a with it.

Edit: NB: Some characters such as &there4; (therefore) will not show up on all computers, but most will.

 

[mojako]

And how do you distinguish between horizontal and oblique asymptotes?

oblique asymptote is a slanted line

to find out if its oblique or horiz:
u find the limiting value of y as x approaches infinity
if the limiting value is a constant (number) then the asymptote is horizontal
if the limiting value is infinity or negative infinity then it's not horizontal

to find the oblique asymptote:
If y=some fraction, divide.
For example:
y = (x³+x²+7) / x²
y = x³/x² + x²/x² + 7/x²
y = x + 1 + 7/x²

One you have this form, take the limit of the leftover fraction as x approaches infinity. As x approaches infinity, 7/x² approaches zero.
So, asymptote is y=x+1 (and the curve approaches this asymptote from above since 7/x² is positive)

Another example (from Slide Rule):
y = x + 1/x
here we can take the limit without dividing anything
as x-> infinity, the 1/x part approaches zero
so as x-> infinity, y=x
then asymptote is y=x
In this one, the curve approaches the asymptote from above on the right and from below on the left of the y-axis.


quote=blackfriday : "oblique asymptotes usually occur when the highest power in the numerator is higher than the highest power in the denominator."
higher by 1