limits

[supple island]

hello, im new in limits
can sb tell me whats the lim (x/f(x)-x) for x→-1 i found 1/0
am i wrong?

[gritty lava]

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[weak escarp]

Hey

[supple island]

hey mate

[weak escarp]

Is the answer 2

[bitter torrent]

Is the red line f(x)

[supple island]

i need this one

[supple island]

the red line is f(x) correct

[bitter torrent]

Ok

[weak escarp]

Ohh now it makes sense

[supple island]

i found it 1/0

[bitter torrent]

Alr

[supple island]

but has 0 down

undefined?

[weak escarp]

It approaches either of the infinites

[bitter torrent]

No actually, f(x)>x in a neighborhood containing -1

[supple island]

is it actually 1/0 or am i dumb?

lmao

[bitter torrent]

f(x)-x ≥ 0 basically

[bitter torrent]

+∞

[supple island]

how

its limx/limf -limx

-1/-1-(-1)

[bitter torrent]

Wait it’s -∞ my bad

[weak escarp]

Cuz minus 1 in the numerator

[bitter torrent]

Yeah

[bitter torrent]

You can’t directly substitute here

[supple island]

-(1/0)

[supple island]

i cant

oh

[bitter torrent]

Ok, how would you interpret 1/0 in a limit sense?

[supple island]

cant i apply the lim?

[bitter torrent]

Wait, how about this

Let’s define ε(x) as f(x)-x, alr?

[supple island]

sure

[bitter torrent]

Now, near x=-1, ε(x)≥0, right?

And at x=-1, ε(x)=0

[supple island]

yes

then its -1/0?

[bitter torrent]

Now, evaluate both the left hand side and right hand side limits

[supple island]

they the same right

[bitter torrent]

That’s not the correct form of the answer unfortunately

[bitter torrent]

You have to show that

But yes, the lhs and rhs limits are the same

[supple island]

oh shit

u da best

i got it

basically i could write it like

lim= x * (1/f(x)-x)

and for x→-1+

and for x→-1-

right?

[weak escarp]

Yes

[supple island]

yes so

f(x)-x

where it goes

for example if we do x→-1+

[stable sandal]

Watch where you're putting parenthesses

[supple island]

yea

true

x*[1/(fx-x)] good?

but how i know if fx-x is >0

like 0+ or 0-

[supple island]

any idea

[stable sandal]

Well, you see where f(x)>x

Clearly when x is in the neighborhood (-infinity, 1), f(x)>x

[supple island]

yea i see thay

that

then its x*(1/0+)

(-1)*(+inf)

-inf

good shi

ty

[supple island]

f(lnx) is it -inf?
x→0+

[bitter torrent]

What

[crude berry]

@stable sandal

help

[bitter torrent]

Yes

[supple island]

its true

?

[supple island]

.

[bitter torrent]

lim x->0+ lnx is -∞

[supple island]

good stuff

how do u type infinity

what alt code

[bitter torrent]

Fucked with my phone keyboard

[supple island]

lmao

thanks btw

is there a way to rate u somewhere

[bitter torrent]

It wouldn’t be -1/0 though

[supple island]

yea i got it

[crude berry]

#helper-nominations

[stable sandal]

Was studying

[supple island]

yea so

[stable sandal]

Also please refer to my bio

[supple island]

i got the answer i needed

[supple island]

i saw

thats why i didnt tag

[bitter torrent]

Thank me when you close the post

[supple island]

ok one thing

u told me

[supple island]

this

so its f(-inf)

[bitter torrent]

Yep

[bitter torrent]

Erm what

[supple island]

i need the limit of f(lnx)

lnx for x→0+ is

-inf

so its f(-inf)

[bitter torrent]

Ahhh yeah basically yes

[supple island]

so finally its

[bitter torrent]

Is f(x) still the red curve?

[supple island]

=-3

yessir

[bitter torrent]

What

[supple island]

f(-inf)

is -3

[bitter torrent]

Send a picture of the graph again please

[supple island]

there u go

[bitter torrent]

Ok there’s a horizontal asymptote, you’re correct

[stable sandal]

You should really be saying $f\qty(\lim_{x\to -\infty}x)$, but that's alright (just a little bit of notational clearup)

[lean pecan]

Kocher

[stable sandal]

Or something of the sort

[supple island]

so f(-inf)

is wrong

?

[bitter torrent]

Notationally yes

[stable sandal]

Technically infinity is not a measureable number, so we can't really say this

[supple island]

oh thanks then

ty

[supple island]

but

we dont care about that

do we?

[bitter torrent]

Not rn

Eventually it will matter

[supple island]

cuz when x→2 the red hits it

[bitter torrent]

Rn you’re good though

[supple island]

for x→-inf it does matter

[bitter torrent]

But you should get in the practice of using conventional notation

[supple island]

the y=-3 matters

[supple island]

whats that

[bitter torrent]

Instead of f(-inf)

We say $\lim_{x\to-\infty}f(x)$

[supple island]

makes sense

We say $\lim_{x\to-\infty}(x)$

[lean pecan]

Teropic

[bitter torrent]

It’s literally the same thing, but it’s more notationally correct

[supple island]

shesh

thats latex

[lean pecan]

Ravi ≥ ^• ∧ •^ ≤

[supple island]

i need to learn this stuff

its coo

l

[bitter torrent]

It’s simple enough

[supple island]

yea i know a bit of python

im not into languages

and stuff

[bitter torrent]

LaTeX isn’t python lol

[supple island]

yea ik

[crude berry]

if you use it regularly it takes a few weeks to get used to

[supple island]

lmao

[bitter torrent]

Yep

[crude berry]

but not worth the time or effort right now

[supple island]

bet

[crude berry]

just use pen and paper

[bitter torrent]

True

[supple island]

yea idh time

so many subjects

physics chemistr

y

maths

[crude berry]

gl

[supple island]

tysm

[crude berry]

do +close if you are done

[supple island]

imma close bet

+close

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[stable sandal]

@bitter torrent why skull

[bitter torrent]

1236 is crazy 😭😭😭

[empty atlas]

Hello, I can solve your problem at a budget

[stable sandal]

Against rules!!

@supple island close the post what are you waiting for

[bitter torrent]

+close

[lavish nimbus]

You are not authorised to close this help request!

[crude berry]

+close