Thus limit
#This limit pls
glad vigil
untold oak
Thus limit
I assume both roots are cubic?
In that case factor x^(2/3) from the whole thing.
glad vigil
I assume both roots are cubic?
In that case factor x^(2/3) from the whole thing.
No no
One is cubic
The other is normal
Like the 2
Nothing
untold oak
The other is normal
Ah.
In that case, start by factoring x from everything here. Then both roots will be of the form (1 + const/x)^a.
glad vigil
In that case, start by factoring x from everything here. Then both roots will be...
I did
I got an indeterminate form
0x infinite
untold oak
I got an indeterminate form
Right.
But now notice how the expression inside the root is of the form 1 + (infinitesimal function).
So, remember how there's a nice series for (1 + x)^a for x -> 0?
glad vigil
So, remember how there's a nice series for (1 + x)^a for x -> 0?
I dont understand what u tryna say
untold oak
I dont understand what u tryna say
I mean that you can use the binomial series here.
Ah, although, just to clarify.
Is that x^2 or x^3 under the first root?
glad vigil
Is that x^2 or x^3 under the first root?
Two
untold oak
Two
Ah, then it's even easier.
If we factor x out from everything here, what do we get under the first root?
glad vigil
Wait do u want me to like factor by x even outside the root?
Like Xroot of 1/x+ 2/x^2?
untold oak
Like Xroot of 1/x+ 2/x^2?
Yup, nice! And now notice that you have a product of x and a difference of two roots.
But one of the roots just goes to 0.
So, there isn't actually an indeterminate form.
untold oak
But infini x0 is indeterminate form
The second root isn't approaching 0.
Ah, wait...
It's x. Sorry, didn't notice.
In that case, notice how the first term grows like x^(2/3), but the second grows as x^(1/2).
So, which grows faster?
untold oak
Since 2/3>1/2
In this case we can try factoring x^(2/3) from both, instead. The first root will approach 1, but what about the second root?
glad vigil
In this case we can try factoring x^(2/3) from both, instead. The first root wil...
Wairt we can do that?
untold oak
Wairt we can do that?
Why not?
untold oak
So wait can u write me in a paper what it will become
Like this.
glad vigil
Like this.
I think there is an easier methode cuz this hzrd thing isnt in my school lvl
untold oak
Well, I don't see any other easy methods.
fossil hound
Thus limit
since its a difference of cubic roots, maybe you can multiply and divide by the factor so in the numerator it simply becomes x^2+1 -x +2
like, how would you factorize a^3-b^3?
mhm i dont think this will work cause its still indterminate at the numerator
well i tried
fossil hound
since its a difference of cubic roots, maybe you can multiply and divide by the ...
wait after that just group the highest factor since it tends to + infinity no?
glad vigil
like, how would you factorize a^3-b^3?
By identity
fossil hound
By identity
so, write it down
glad vigil
What if i actually just add -x and +x each side since the udneterminate is + ♾️- ♾️
glad vigil
so, write it down
But the issue is we have different rootd
The method u will simplify cubic one isnt the same as root one
fossil hound
But the issue is we have different rootd
oh wait mb i thoguth they both were cubics
u wrote a 3 on both sides
fossil hound
What if i actually just add -x and +x each side since the udneterminate is + ♾️-...
what do u conclude by adding it?
fossil hound
Thus limit
well then what if you multiply and divide by the cubic root + the square root
so u can get some variables out of the square root and they will be the highest grade variable
mmmmm
glad vigil
u wrote a 3 on both sides
No no the second is normal
glad vigil
well then what if you multiply and divide by the cubic root + the square root
Like conjugate?
fossil hound
Like conjugate?
if thats what u call it
glad vigil
what do u conclude by adding it?
Since so i can simplify by conjugatin
fossil hound
you get like cubic root of (x^2+1)^2 -x+2
glad vigil
The issue here
fossil hound
mhm
glad vigil
Is that u need a number to set the conjuagate of cubic root
fossil hound
Is that u need a number to set the conjuagate of cubic root
wdym
cant u just use the cubic root
at the denominator you get an infinity + infinity so its fine
fossil hound
but you just told me they arent cubic roots
glad vigil
at the denominator you get an infinity + infinity so its fine
Infinity above and down is indeterminate no?
fossil hound
Its like a^3-b^3/a^2 +ab+b^2
btw a-b not the cube
fossil hound
Infinity above and down is indeterminate no?
yes, but you get the highest grade out
the rest isnt important
glad vigil
but you just told me they arent cubic roots
Im talking abt doing the first cubic alone then the second
fossil hound
the result will probably be 0 or infinity
fossil hound
Im talking abt doing the first cubic alone then the second
why would u do that
fossil hound
the result will probably be 0 or infinity
do u know the result?
glad vigil
why would u do that
Idk lol
fossil hound
Then u cant
cant do what?
ok lerts to bacvk a bit
how wouilòd u solve limit for x that tends to + infinity
of (2x^2+1)/(3x^2+2)
?
@glad vigil u there=
?
fossil hound
@glad vigil died 😔
glad vigil
<@921154055177404476> died 😔
I had studies
fossil hound
Its limit of 2x^2/3x^2
what is ur explanation fore why its 2/3?
glad vigil
what is ur explanation fore why its 2/3?
Cuz there is no more x
fossil hound
Cuz there is no more x
this makes no sense, why in the first place can you write it as 2x^2/3x^2?
glad vigil
this makes no sense, why in the first place can you write it as 2x^2/3x^2?
Cuz its a function?
Functions have limits
fossil hound
Functions have limits
this explanation makes no sense at all
why can you “forget” about the x but not the x^2 ?
glad vigil
Wdym wai
fossil hound
Wdym wai
uh?
do u want the answer
?
btw it’s useless to learn maths without understanding what you are doing
glad vigil
Give me the methode and ill see if i understand it
fossil hound
Give me the methode and ill see if i understand it
when u encounter something like 3x^2 -x -2, if x tends to infinity the you will have ♾️- ♾️ which is underterminate
so the trick is to group the highest grade variable:
x^2(3 -x/x^2 - 2/x^2)
note that something like 2/x^2 tends to 0 when x tends to infinity ♾️
so in the parenthesis u basically only have the 3
so u get x^2(3 -0 -0)
so the result in this case is simply infinite
when u have a fraction , you group the highest grade for the numerator and denominator
then simplify
the result is either 0, ♾️ if the variable on the top has a higher grade than the one on the bottom
or a certain value if they have the same grade
glad vigil
Can u do that in a piece of paper
fossil hound
Can u do that in a piece of paper
not now sorry
try to write what i said urself
i have troubles too understanding this stuff when it’s written like this 🥲
glad vigil
i have troubles too understanding this stuff when it’s written like this 🥲
Lool same as me
glad vigil
not now sorry
Its okay do that when available
fossil hound
Its okay do that when available
Okay
fossil hound
@glad vigil is it clear now?
fossil hound
U could just take the higher x/ higher x
what does it even mean to do what u said?
you are doing this acritically
you just following rules you dont understand
obviously when solving u can skip these passages, but this is the reason of why it works
wide heraldBOT
@glad vigil
glad vigil
what does it even mean to do what u said?
I mean its rational function
wide heraldBOT
@fossil hound @untold oak The user still needs help with this help request.
fossil hound
I mean its rational function
and?
fossil hound
There is a rule for limits going to infini in rational
yes but you do not understand the rule
you just use it acritically
glad vigil
Yea how do i understand it?
fossil hound
Yea how do i understand it?
i just showed u
the picture i sent
is the explanation
fossil hound
It didnt get to zro if i di ur methide
what
fossil hound
U got it as zero
?
glad vigil
U solved the limit and u got zero