fp`1

[supple wadi]

.

part e

so i got the ans right, bcs, what else u gonna say

but, if k not 2, then u get infinity aS ANSWER

If lim x--> 0 of f(x) = infinity, does that mean it 'doesnt exist'? I thought doesnt exist means indeterminate means 0/0 or infinity/infiniftyy

[iron echo]

is this pure further maths?

[iron echo]

my understanding is

(if the question youre asking is what if we have 0/0)

that 0/0 is an indeterminate form as anything can be multiplied by 0 to get 0 so we have to do more work and cant simply say it tends to infinity

[supple wadi]

yee

[supple wadi]

sorry i was unclear i meant specifically this step here

why must k=2

we have (2-k)/x

• constant

because all other terms have an x term in them

for lim x-->0 of (2-k)/x

the question claims that, k=2

whats wrong with lim x-->0 k/x =inf?

[iron echo]

ohhhh

because thats infinity right

and we want the expression to EXIST

cuz the que says that if u read at the bottom

and the expression only exists WITH those limits if the LIMIT allows the expression to be FINITE so to converge

and IF we do wat you propose, it would DIVERGE and be infinite

is that helpful??

[supple wadi]

So a limit exists if and only if it is convergent?

L=0 exists

Abs L=inf does not exist

[iron echo]

wats abs?

[supple wadi]

Absolute

[iron echo]

yes

[supple wadi]

Modulus

[iron echo]

i dont get wat u mean by modolus of L = infinity

[supple wadi]

If the limit = +- infinity

L is just notation I saw in Wikipedia

[iron echo]

ohhhh yh positive or negative infinity doesnt matter

like we dont rlly deal with it at alevel fm

only if e is to the negative x and then lim x --> infinity

but thats not negative infinity

but getting back to the main que we were speaking abt

if the limit makes expression tend to infinity

then THAT expression does NOT exist, it diverges

like in improper integrals?

yk that topic?

so for this que we WANT the expression to exist and k is a constant cuz it says it above so if we find the value for which we get 0 on the top then when lim x --> 0 we get 0/0 which is NOT infinity it is just indeterminate form so essentially it has a value but we dont know it and as far as fm alevel we dont ever really have to find it or do anything with it

so if the numerator is 0 thats the only time we can get the full expression to be finite

do u understand?

ik im waffling a lot and repeating points but idk any other way to explain it

[subtle gull]

it can be a bit ambiguous

but converge, diverge, doesnt exist should all be different

i think you CAN say exists but diverges

however in this case it doesnt work

because lim x->0 k/x is not infinity

if you approach 0 from the right it is

but from the left its -inf

so it doesnt exist because the limits from both sides are different

[iron echo]

no

it only exists when k=2

[subtle gull]

yeah

which is what ive said

[iron echo]

oh right

mb

[supple wadi]

ye u are wafflign 😭

thansk for effort though

[supple wadi]

gotchu thanks

so overall

Existenece != convergence

L exists if and only if limit from both sides is the same

Therefore

the set of all convergent limits, is a subset of the set of all existing limits

but they are not the same set (so not vice versa)

ye?

[subtle gull]

I would say yes

But honestly I do think it’s ambiguous and some people will say convergence and existence are the same

Maybe context dependant which isn’t a very good answer

If you just stick with convergence = existence you can’t go wrong really so maybe don’t worry about this

[iron echo]

bruh thats exactly wat i said

[iron echo]

exactly

[elder granite]

that's not what you said

[iron echo]

...

bro is arguing with a shadow

[supple wadi]

you wropte a fuckine sssay

[iron echo]

bruvv

water under the bridge

not that deep