#help-0
alpine sable
No but this isn't mentioned in the actual question
mental python
......
alpine sable
we figured this out
olive sentinel
then it's 👍
alpine sable
seems like they put an olympiad level question in our uni entry exam..
olive sentinel
can abc be 1 and 4?
alpine sable
yes
olive sentinel
nvm i still don't get it lol
mental python
im still curious why its not just 900?
pulsar kernel
So what I get: first place has 9 possibilities, second would still have 9 (remove one from 10), then 8, ignore the last 2 since they're fixed, what do we get ? 9x9x8 = 648 ? Which seems wrong, there's some trick to it
olive sentinel
So what I get: first place has 9 possibilities, second would still have 9 (remov...
thats what i got too
or maybe the options are wrong :p
alpine sable
So what I get: first place has 9 possibilities, second would still have 9 (remov...
That's what we got as well, we're stuck here
mental python
!original
lone heartBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
high imp
So what I get: first place has 9 possibilities, second would still have 9 (remov...
Dont forget 0 cant be for a
alpine sable
pulsar kernel
Dont forget 0 cant be for a
Yes, that's why there are 9 possibilites in a
high imp
i mean. For b and c
mental python
but b and c still have 10 possibilities
olive sentinel
b and c can be 0
high imp
Yes!
olive sentinel
but b and c still have 10 possibilities
no because u use up a digit for a
so b has 9 and c has 8
mental python
no because u use up a digit for a
where in the question does it say they need to be unique?
high imp
So: (b,c =0)\neq a
And b=0 \neq c
olive sentinel
where in the question does it say they need to be unique?
thats what he told us that a b c are different idk
mental python
thats what he told us that a b c are different idk
but thats not in the question
olive sentinel
.
alpine sable
.
alpine sable
So: (b,c =0)\neq a
And b=0 \neq c
That's correct
mental python
it doesnt say that anywhere in the question
pulsar kernel
What if it can't be 1 and 4 either 😆
mental python
10014 is still a 5 digit number
alpine sable
it doesnt say that anywhere in the question
We have to make assumptions until we get one of the answers
olive sentinel
900 if abc can be same numbers
648 if abc unique
392 if not even 1 and 4 are unique
pulsar kernel
Hmmm, 648, and 448, what if the options are a typo ?
alpine sable
it doesn't state that abc14 are different numbers, like if it was abcde
olive sentinel
right so assuming only abc are unique the answer is 648
pulsar kernel
Just choose the closest answer when not sure, that's the last resort in exams xD, jk
high imp
What if a could be 0
mental python
answer is 900
olive sentinel
maybe there's a typo so id def say choose C if there's no other way
alpine sable
Did you use the following equation: 9 x (choices-for-a) x 8 (chocies-for-b) x 8 (choices-for-c)
high imp
08314 is like abc14
olive sentinel
9 chouces for b
high imp
Think about it as a passcode
mental python
08314 is like abc14
08314 is not a 5 digit number
pulsar kernel
So at this point we're trying to find how many 3 digit numbers can be formed? What's the point of 14 , is it just there to confuse ?
olive sentinel
probably
high imp
08314 is not a 5 digit number
In passwords, it is 5 digits.
alpine sable
So at this point we're trying to find how many 3 digit numbers can be formed? Wh...
So that they can say "5 digit num"
olive sentinel
atp either answer is 900 or 648 tbh
mental python
In passwords, it is 5 digits.
in mathematics, its 4 digits
high imp
Try for a could be 0, and abc cant be 1 or 4
high imp
in mathematics, its 4 digits
Idk so, maybe he had computers sciences exam
olive sentinel
8 x 9 x 9 is still 648
alpine sable
this is math related, not cs
olive sentinel
Try for a could be 0, and abc cant be 1 or 4
for this ^
mental python
Try for a could be 0, and abc cant be 1 or 4
thats just 8^3
olive sentinel
sorry yeah 8x8x8
mental python
answer is 900
nothing more to it
possible answers are wrong or the question is not what they meant
pulsar kernel
At this point just try everything. In the end email the person who wrote this book.
olive sentinel
yeah the question is incorrect and incomplete overall
alpine sable
answer is 900
we already concluded that abc can't be the same numbers
mental python
we already concluded that abc can't be the same numbers
youre wrong
it doenst say that in the question
olive sentinel
lmao
mental python
unless there is some more text above the question that you didnt show
alpine sable
unless there is some more text above the question that you didnt show
I didn't withold any info
that's all we got
mental python
yeah and there isnt, so the question is just wrong and its 900
(with the given info)
kind trellis
there are 9 options for a, 10 options for b, 10 options for c, so 9 * 10 * 10 = 900
pulsar kernel
I'm willing to put money on 648
mental python
thats a 3 digit number
kind trellis
what digit number is that
mental python
you dont include the leading 0s
alpine sable
how about 00000000123
bro is trolling rn
olive sentinel
thats 4 digit
pulsar kernel
This question is moving towards philosophy at this point.
olive sentinel
look just by the question and not assuming anything is 900, assuming abc are unique it's 648 not really much to it
just skip
olive sentinel
It is not abc × 14
damn
pulsar kernel
It is not abc × 14
Oh, what if all the numbers are multiplied ? Just an idea.
abc14 = 5 digit number. Unlikely but whatever
olive sentinel
thats fun
high imp
a and b and c cant be 0
mental python
a*b*c*1*4?
olive sentinel
yes
olive sentinel
too many assumptions
mental python
9*9*9*1*4=2916<10000
olive sentinel
then the answer is 0
if you assume a b c can be single digit numbers then only
nowhere it says a b c cant be bigger numbers
mental python
if you assume a b c can be single digit numbers then only
then the answer is much larger than the given answers
olive sentinel
IFF we are multiplying everything
pulsar kernel
What if it wants us to calculate all the 5-digit numbers below abc14
olive sentinel
then the answer is much larger than the given answers
is it
pulsar kernel
x >= 10000 and x <= abc14
kind trellis
this is so fun
mental python
multiply this by 3 for combinations
and then split it into factors
probably gives like 10^6-10^7 answers
olive sentinel
no
mental python
even if thats what they were asking, its a really poor phrasing
alpine sable
900 if abc can be same numbers
648 if abc unique
392 if not even 1 and 4 are uni...
You got it right, we got 648 after coding for a while
mental python
well somewhere between 22k so still wrong
i can brute force it if you dont believe me
olive sentinel
doesnt need coding honestly though def a wrong question
mental python
its easily more than 100k
olive sentinel
do it
pulsar kernel
648 is the answer. Don't waste more time on it.
alpine sable
648, thank you all for your patience and time, you were amazing, thank you for working SO HARD
You are all awesome, keep at it!
olive sentinel
good discussion
pulsar kernel
Had fun
olive sentinel
dont close this yet im waiting for bonk to somehow prove that if its a 5 digit number formed by a x b x c x 1 x 4 then the answer s in 100k smth
mental python
dont close this yet im waiting for bonk to somehow prove that if its a 5 digit n...
my shitty python code is rly slow
alpine sable
dont close this yet im waiting for bonk to somehow prove that if its a 5 digit n...
If you are able to close as well, I will leave you with the honors, I have to go now
olive sentinel
my shitty python code is rly slow
you know whats not slow? arithmetic progression
if its a 5 digit number that has 4 as a factor
it has to be divisible by 4
that means all 5 digit numbers divisible by 4
mental python
but you have multiplicity
also, if you have a=10000, b=1, c=1, then a=5000, b=2, c=1 is also a solution
and also a=5000, b=1, c=2
etc, etc
olive sentinel
sure is
ocean sealBOT
SELVATOR
mental python
so if you already have 24000 smth solutions for b=c=1
then its going to be many times more if you let b and c not equal to 1
olive sentinel
so if you already have 24000 smth solutions for b=c=1
how
kind trellis
???
mental python
with b=c=1
kind trellis
ah
mental python
a=2500,2501,2502,....,249999
olive sentinel
im not sure what you are getting at though because its just nothing more than all 5 digit numbers divisible by 4
olive sentinel
a=2500,2501,2502,....,249999
where did you get that extra 9 in the end from
mental python
im not sure what you are getting at though because its just nothing more than al...
there are 90000 5-digit numbers divisible by 4
kind trellis
r u ok bonk
kind trellis
true
olive sentinel
lol
you should try using A.P
10000, 10004, ..., 99996
99996 = 10000 + (n-1)x 4
do the algebra
mental python
there are 22500 5-digit numbers that are divisible by 4
olive sentinel
thats what i said
pulsar kernel
9x9x8x25 , i get 16200 🤔
mental python
yes, take b=c=1, then a can have like 20000 possibilities
.
i didnt bother with the exact amount
olive sentinel
probably gives like 10^6-10^7 answers
yes you definitely did
mental python
just an order
mental python
ah wait i realise my mistake now, by guess shouldve been 10^5-10^6
kind trellis
Bonk you're right
mental python
but its definitely much more than 10^5
probably more than 10^6
but unsure if its more than 10^7
olive sentinel
HOW
mental python
its 22500 if you take b=c=1
olive sentinel
i need a proof
mental python
okay lol
olive sentinel
do you agree that a x b x c x 1 x 4 has to be a 5 digit number
mental python
yes
mental python
a=2500+n, for n in {0,1,...,22499}
b=c=1
olive sentinel
i have been ignoring a b c
mental python
which has 25000 possibilities
now i take
a=c=1
b=2500+n, for n in {0,1,...22499}
which has 25000 possibilities
so up to 50000 already
now i take a=b=1
c=2500+n, for n in {0,1,...,22499}
olive sentinel
right you are right my bad
mental python
which has 25000 possibilities
olive sentinel
i was thinking of something else
mental python
up to 75000 now
olive sentinel
thank you lol i feel stupid asf
yes you are right i only got the combinations not the permutations
mental python
now i take
b=2, c=1
a=1250+n, for n in {0,1,...,11249}
olive sentinel
order matters
mental python
which has 12500 possibilities
olive sentinel
i get it yeah
mental python
so up to 87500 now
now i take b=1, c=2
a=1250+n, for n in {0,1,...,11249}
which has 12500 possibilties
so up to 100000 now
already 10^5
i can keep going like this for quite a long time
mental python
anyway
you get my point
you were wrong
and trying to gaslight me
and paint me as the moron
olive sentinel
this is going to be a fun question though ill solve this later yeah i was wrong
olive sentinel
and trying to gaslight me
it is midnight
olive sentinel
there are 90000 5-digit numbers divisible by 4
this was wrong tho 100%
mental python
!done @alpine sable channel is finished
lone heartBOT
If you are done with this channel, please mark your problem as solved by typing .close
mental python
this was wrong tho 100%
cuz you tried to gaslight me and i second guessed myself
olive sentinel
xD
mental python
.solved
lone heartBOT
alpine sable
.close
lone heartBOT
Available help channel!
alpine sable
i already closed it, its alright
thank you very much
lone heartBOT
Available help channel!
green kelp
Can someone help me understand the question
lone heartBOT
Can someone help me understand the question
green kelp
I know squared is times itself
kind trellis
ye
green kelp
but 6x?
kind trellis
6 * (2.5) * (2.5)
green kelp
another similar question involved timing the number with the x and i just didnt get why multiplication was involved
also for one how would i type this into a calculator
kind trellis
you would type it as 6*(2.5)^2
green kelp
kind trellis
see the x^2?
green kelp
yeah
kind trellis
I think that works
green kelp
6 times 2.5 and then x^2
green kelp
type in 2.5 then press x^2, then press x, then press 6
like so?
kind trellis
Yes.
green kelp
@kind trellis what is important to keep in mind for these questions? I used to do this around primary or secondary school but it's been so long I've forgotten or at least I don't remember it being like this
I recall x + x = x2, is that true?
kind trellis
I recall x + x = x2, is that true?
no, x * x = x^2,
but, x + x = 2*x
green kelp
no, x * x = x^2,
but, x + x = 2*x
so x adding another x actually means squared?
wait no
my b
x + x = 2 times x?
or did you mean it'd be written as 2x and not x2?
crude parrot
or did you mean it'd be written as 2x and not x2?
2x and x2 are the same. but the constant is written first, its just convention. ex: 2x, -5x, 10x
green kelp
constant being the number right?
ocean sealBOT
Krish
green kelp
I don't get the use of the $
crude parrot
its just to show it as text
green kelp
oh ok
crude parrot
you don't need to worry about that, and definitely do NOT write the dollar sign when writing math questions on paper lol
green kelp
figured it coulda meant that but i got a little confused
crude parrot
anytime you see two dollar signs like that, just look at the message with the big image (in this discord at least)
green kelp
x + x = x^2 feels like a convoluted way of saying 1 + 1 = 2 because it reaches the same result
crude parrot
x+x does not equal x^2
green kelp
no, x * x = x^2,
but, x + x = 2*x
whoops i thought this was saying that
crude parrot
thats like saying $1 + 1 = 1^2$, which is not true. $1^2 = 1 * 1 = 1$.
ocean sealBOT
Krish
crude parrot
whoops i thought this was saying that
no, that person said it correctly you just interpreted it wrong
crude parrot
$x + x = 2x$ an example of this, where $x = 2$. $2 + 2 = 2(2) = 4$, which is correct
ocean sealBOT
Krish
crude parrot
$x = 2$ is actually a special case where $2 + 2 = 2 * 2 = 4$, but you wont encounter that in any other numbers.
ocean sealBOT
Krish
green kelp
I'm not very well versed in brackets so I'm assuming the 2(2) equalling four is via one adding onto another or multiplying
crude parrot
$2(2) = 2 * 2$
ocean sealBOT
Krish
crude parrot
also could be written as $(2)(2)$
green kelp
6x = ?
ocean sealBOT
Krish
green kelp
i guess i did i just forgot hold on a moment
x = 2.5
2.5^2 = 2.5 x 2.5 = 6.25
6.25 x 6 = 37.5
Although I got the answer I'm just trying to understand the process of these types of questions going forward
tulip lagoon
when you have and object and you have multiple of them
you dont say 6 times apple
you just say 6 apples
think of it this way
green kelp
I guess I'll have to consider it answered for now, I shouldn't keep people waiting
rugged pond
crude parrot
Although I got the answer I'm just trying to understand the process of these typ...
what are you stuck on
green kelp
what are you stuck on
Not sure at the moment, I'll have to wait until another question like that pops up which could be a while from now
crude parrot
Not sure at the moment, I'll have to wait until another question like that pops ...
$y=2x^5$ Use your calculator to work out the value of $y$ when $x=2$.
ocean sealBOT
Krish
green kelp
I'm on another question now I already got that one right
green kelp
**Krish**
20?
the ^5 confused me, it's not squared so i had it as 2 x 5
2 x 5 = 10 x 2 = 20
crude parrot
exponents mean you multiply it by itself that many times
2^3 = 2 * 2 * 2. 2^4 = 2 * 2 * 2 * 2. etc..
green kelp
exponents meaning little number?
green kelp
If you keep pressing = on the calculator you get it doubled
crude parrot
it should make you more comfortable with exponents
crude parrot
If you keep pressing = on the calculator you get it doubled
yes but dont rely on that every time. you should know how to type exponents on a calculator.
but yes 32 is 2^5
crude parrot
thats what this server is for
green kelp
green kelp
the answers i put in there are based on percentages i got from making a pie chart
yeah the video you can look at for that mentions it
but i figured it'd be percentages based on 270 (the numbers of points scored when added)
green kelp
270?
tulip lagoon
no
green kelp
I'm always overcomplicating things in my head
green kelp
using the video i looked at (https://youtu.be/L2a98g8Lx_k?si=9BLWGbHuNaVJ8u6m)
I'd have to check the fraction of 360 each of the points scored would be
green kelp
A and C seem interchangeable
green kelp
180
green kelp
180
green kelp
C and D should be 180 I see
tulip lagoon
why should they be 180?
tulip lagoon
green kelp
I was thinking of the original question
green kelp
yes
tulip lagoon
we have established that
green kelp
A = 50
B = 75
C = 100
D = 45
tulip lagoon
green kelp
Not in degrees
tulip lagoon
look here
green kelp
what happened to C
green kelp
360
tulip lagoon
yes
green kelp
It always becomes 360 I get that now
tulip lagoon
yes
green kelp
But I'm trying to figure out the fractions of the points scored
tulip lagoon
so the sum of the angles has to be 360
the total of points is 270
so if someone had 270 points
and nobody else had points
he would occupy the whole pie chart right?
green kelp
Yes
green kelp
360
tulip lagoon
yes
so for 270 points
360 degrees
you now cand make a raport of how many degrees for a point
do you understand or should i simplify it?
green kelp
do you understand or should i simplify it?
simplify it
i know it'll always add up to 360
tulip lagoon
think about this
each section is equal
i try to split A into 270 equal sections
green kelp
Each section would be worth 1 then
tulip lagoon
A=270 x B
green kelp
in terms of points not degrees
tulip lagoon
yes exactly
but A=360
so the degrees for the B section(the one worth 1 point) is equal to?
tulip lagoon
yes
lets say A is worth 4 points
that means i can divide A into 4 equal parts of 1
the equal parts of 1 we will call them B
green kelp
I think we need to address the points scored from the original chart
tulip lagoon
how much would one point be in degrees here
green kelp
1 each ik
tulip lagoon
nono in degrees
green kelp
90
tulip lagoon
but none of the points scored really are such a simple fraction
it doesnt matter
it is 45
green kelp
so it's 45 degrees
green kelp
D is 45 degrees?
tulip lagoon
so the degrees for the B section(the one worth 1 point) is equal to?
and u had from here
green kelp
what's the B in 45B for then
tulip lagoon
no i wrote poorly disregard this
you have that the total of the pie chart is 270
points
green kelp
yes ik
tulip lagoon
for those 270 points you have 360 degrees right?
lets call T total
T=A+B+C+D
and you have that degrees of T =360
because its the whole pie chart
the whole circle
is everything clear up until now
?
green kelp
well yeah i know what the total is
tulip lagoon
yeah ok we will get to the rest
green kelp
I'm asking how to find out what fraction each of the points scored is of 270
tulip lagoon
if you understand the concept you will have it much easier next time
dont just go for a formula
try to understand the concept
lets have another letter U
U=1
green kelp
if 45 is 1/6 of 270...
tulip lagoon
T=270 x U
green kelp
16.66/100
tulip lagoon
degrees of U = degrees of T : 270
so degrees of U = 1.33
A=50
U=1
A=50 x U
degrees of A= 50 x degrees of U
does this make sense
?
green kelp
what is U
tulip lagoon
U is just something we chose to simplify the problem
it is if you divided T
which is equal to 270
into 270 parts
each equal to 1 point
green kelp
45 is a sixth of the point total so it'd be 60 degrees
tulip lagoon
yes
green kelp
I think we'd get further with this by knowing what to divide
tulip lagoon
because you have D/T=degrees D/degrees T
45/270 = degrees D/360
1/6 = degrees D/360
degrees D = 360/6
so 360:6
green kelp
Yeah I know D = 60
green kelp
But what about A, B and C
tulip lagoon
you can either choose
degrees C=100 degrees U
and you have already found degrees U=1.33
green kelp
so what, 100 x 1.33?
tulip lagoon
or use C/T=degres C/degrees T
tulip lagoon
so what, 100 x 1.33?
yes
green kelp
C + D = 193
remaining = 167
75 x 1.33 = 99.75 or 100 when rounded up
@tulip lagoon Is this correct? 100 degrees?
tulip lagoon
no
dont round up
nvm
round up
sorry
you dont have 1.33 its actually 1.333333333... to infinity
tulip lagoon
and when you use 1.333333333 this
you get closer to 99.99975
and nines keep adding
green kelp
So is B 100 or not?
tulip lagoon
yes
tulip lagoon
something is wrong
oh no my bad
it s correct
yes
i added up the angles and got 330
it is getting to late for me
tulip lagoon
how old are you?
im not asking for your personal information i just want to know what grade you are in
:))
green kelp
how old are you?
27, I used to do maths like this in primary or secondary school but I'm back in college and I figured some maths revision was warranted because I'll be retaking GCSE's
tulip lagoon
yeah makes a more sense then the other theory i had
11yo with amazing vocabulary that is up at 2am seemed a bit too far
)))
green kelp
I don't think I'd be here at 11 years old
tulip lagoon
you never know
well good luck to you with your revision
hope i was of some help to you and the explanations made sense
green kelp
we got there eventually
tulip lagoon
yeah my bad i didnt really know who i was explaining this to))
lone heartBOT
@green kelp Has your question been resolved?
real glen
lone heartBOT
real glen
im pretty confused with this question
the teacher said "To be able to be differentiable at x=1, we require both f(x) and f'(x) to be continuous at x=1" but i don't understand why
why does it need to be continuous?
teal orbit
why does it need to be continuous?
because a function has to be continuous in order to be differentiable
differentiability->continuity, remember
real glen
no..
i dont remember
i will re-read my notes
is there a reason why it needs to be continuous tho
teal orbit
yes
real glen
like you said "just because" basically
teal orbit
imagine the graph has a jump
and we want to evaluate the derivative at that jump
will it exist?
answer is no, since the function doesn't have a proper limit to begin with
placid zinc
If you are proving this is differentiable, you don't necessarily also have to prove it is continuous
real glen
but is it possible to set terms on the differentiation?
placid zinc
(Maybe your teacher wants to see this anyway, though)
real glen
like if its not differentiable for a < x < b, then cant you restrict the domain for the differentiation?
teal orbit
but is it possible to set terms on the differentiation?
elaborate
teal orbit
like if its not differentiable for a < x < b, then cant you restrict the domain ...
yes
i don't see a problem with that
answers your question pretty well
real glen
then a function doesnt have to be continous to differentiate it
real glen
okay
but if you restrict the domain for the differentiation, the law can be broken! thats what i dont get
but i understand that for the differentiation to be continuous (and just like a basic, non restrained domain & with the same function throuhgout) then the function beforehand must be continuous too
also, does this mean that f(x) being continuous automatically means f'(x) will be continuous and so will f''(x) and so on, or are there other factors
teal orbit
but if you restrict the domain for the differentiation, the law can be broken! t...
if you restrict for differentiation, you must for continuity
else the function will just not behave like a function
teal orbit
but i understand that for the differentiation to be continuous (and just like a ...
yes
teal orbit
also, does this mean that f(x) being continuous automatically means f'(x) will b...
no
big nono
real glen
so restricting a domain makes it continuous
teal orbit
$\text{differentiability}\implies\text{continuity}$, but $\text{continuity}\cancel{\implies}\text{differentiability}$
real glen
ah i see
real glen
but it does say for it to be differentiable, both f(x) and f'(x) must be continuous
ocean sealBOT
ooaa
real glen
i do understand that
teal orbit
but it does say for it to be differentiable, both f(x) and f'(x) must be continu...
indeed
teal orbit
always
real glen
sorry i am just like brain dead at the moment
teal orbit
its fine
real glen
but the statement that they said, for it to be differentiable, it must be continuous
sorry does that notation mean that if something is differentiable it is continuous
or if it is continuous it is differentiable
because if it means if differentiable it is continuous, then f(x) isnt necessarily differentiable just because its continuous
HUH
but then
proving that its continuous does not prove that its differentiable
real glen
just because its continuous at these values does not mean its differentiable at these values bc continuity =/> differentiability
teal orbit
because if it means if differentiable it is continuous, then f(x) isnt necessari...
yes
again, going back to the statement
real glen
then whats the point of proving its continuous?
teal orbit
because we are given differentiability, not continuity
real glen
the teacher said "To be able to be differentiable at x=1, we require both f(x) and f'(x) to be continuous at x=1" but you're saying that it doesnt mean its differentiable
que
what do you mean "given differentiability"
cinder compass
ur teacher wrong bruh
cinder compass
you should change ur role to undergraduate math
cinder compass
hablas espanol?
hola
real glen
but its mathematics specialist, a bridging course
bc i only did a year of it in hs instead of 2 years
teal orbit
what do you mean "given differentiability"
like, we are given the function is differentiable, or are told that it is so
cinder compass
i mean idk if ur teacher actually said that
teal orbit
the teacher said "To be able to be differentiable at x=1, we require both f(x) a...
the f' continuous implies differentiability part is iffy, but in higher mathematics
for now, just be a sponge
real glen
wait
placid zinc
So I remember my teacher also asked to show continuity. I think they just wanted to see it done. But indeed, you don't need to show this
placid zinc
oh
real glen
but i dont understand how it being continuous means it is going to be differentiable
because you guys are saying that it doesnt mean it necessarily
placid zinc
That's questionable yes. We all make mistakes!
real glen
so shes wrong?
but then how would i know what values its differentiable for
like how would i do it correctly?
placid zinc
The way you really should solve this is with the limit definition of the derivative, applied at x = 1
real glen
ok well whats that?
thank you guys btw
im sorry if im coming off as annoying or argumentative, im just pissed that its not actually right
cinder compass
ok well whats that?
whats ur defn of being diffble
placid zinc
Okay well hold up.
They are choosing a value of a and b, such that f is differentiable.
They used the fact that f is continuous, to help get those values.
f' being continuous is weird to include, and I feel you can find examples where this gets the wrong answer
real glen
Okay well hold up.
They are choosing a value of a and b, such that f is differ...
because f'(x) is not necessarily differentiable because we arent given that it is?
cinder compass
u mean f
f depends on a and b
set a = 1, b = 2
u gotta check f is diffble in dis case
real glen
well we know that f(x) is differentiable if it is continuous because differentiability => continuous
wait no
thats what she said
we know that for it to be differentiable it must be continuous
placid zinc
because f'(x) is not necessarily differentiable because we arent given that it i...
The goal of the question is to find a,b such that f is differentiable.
We can use the fact that f is continuous to help us.
f' is not necessarily continuous, that's a mistake.
real glen
but it might not necessarily be differentiable because its continuous
but we are given that it is differentiable
so it must be continuous
cinder compass
but we are given that it is differentiable
u are just given the function
u not given that it diffble
real glen
but f'(x) is not necessarily continuous because we dont know if its differentiable
real glen
u are just given the function
but then couldnt it not be differentiable at any values?
cinder compass
of a,b?
real glen
yeah
cinder compass
correct
real glen
lke how do u find that its differentiable then
cinder compass
a priori that is a possibility
cinder compass
whats ur defn of being diffble
^
real glen
wait so if you differentiate a continuous function f(x)
does that mean f'(x) is continuous
cinder compass
absolutely not
real glen
then what she said is wrong
cinder compass
yes we established that
cinder compass
diffble just means f' EXISTS
real glen
it says for what values is it differentiable
at x = 1
how do you find that then
because we just found when its continuous
cinder compass
ie the limit of difference quotient exists
a=1, b=2
check if it's diffble in this case
using limit defn
do u know limits
cinder compass
$f'(1) = \lim_{h\to0} \frac{f(1+h) - f(1)}{h}$
real glen
do you mean this?
ocean sealBOT
martingale
cinder compass
do you mean this?
yes ofc
cinder compass
did u do epsilon delta defn
cinder compass
ok so is this like an analys course or whats up
cuz ur trying to be rigorous but not fully at the same time
cinder compass
no i mean which law
im talking abt defin
cinder compass
**martingale**
dis
cinder compass
what's f(1)
real glen
no i dont know that
oh wait
thats just differentiation
yes thats the basic form of differentiation
placid zinc
"The derivative exists" means that limit exists. So you can use that to get a,b
cinder compass
u don't neeed diff for f(1) bruh
real glen
"The derivative exists" means that limit exists. So you can use that to get a,b
but how do we know that the derivative exists
sorry guys
i feel like an idiot rn
placid zinc
That's part of the question, as far as I can tell. "Derivative exists. What's a and b?"
real glen
Okay, so i should assume a question like that means the derivative exists
because to me
its saying "the derivative may exist"
because there may be no values of a and b that work
placid zinc
I assume it's stated in the question, but I admit I haven't seen it
cinder compass
so we back to trying to understand the question now 💀
real glen
yeah basically thats the whole problem
placid zinc
Tbh the question might have been "the derivative exists and is continuous" now that I think about it, haha
cinder compass
idk the question is pretty clear to me
placid zinc
Oh wait, you posted the question way above. Nvm I take that last statement back. We don't know the derivative is continuous. But it's stated in the question that f is differentiable.
(at x = 1)
real glen
(at x = 1)
it says "for what values" it doesnt necesarrily mean there are values right?
or am i thinking too hard on it
cinder compass
i think i answered this twice
placid zinc
True, an answer could be "there are no values". But you'd just figure that out by assuming f is differentiable, and getting a contradiction
real glen
,tex $\lim\limits_{x \rightarrow 1^{-}} f'(x) = \lim\limits_{x \rightarrow 1^{+}} f'(x)$
what was this for tho
placid zinc
You are thinking a bit too hard on it, haha. They ask this with the intention of values existing
real glen
okay sorry
i will now assume that that means that its differentiable at some value for sure
cinder compass
or am i thinking too hard on it
not hard enough imo
real glen
not hard enough imo
i meant as in just what the question was trying to say, because "for what values" can include no values
cinder compass
mhm
real glen
like "what are the roots of" and then a quadratic equation with no roots
ocean sealBOT
suds
cinder compass
like "what are the roots of" and then a quadratic equation with no roots
thats a bit different
real glen
but lets move on
yeah i get that now but lets just continue lmao
so after proving continuity, why must these two be equal?
cinder compass
they mustn't.
real glen
because thats the next move of the teacher
cinder compass
yeah she's wrong
real glen
they said for it do be differentiable, we require (continuity proof) and that
oh
okay
but she got the values of a and b?
cinder compass
does ur teacher have a phd
real glen
i believe so
real glen
yes
she has a long linkedin
anyway
IT DOESNT MATTER
i need help
you cant just say my teacher is wrong, im cooked and not tell me how to do it 
real glen
True, an answer could be "there are no values". But you'd just figure that out b...
how do i do this
cinder compass
whats f(1)
cinder compass
technically we didn't prove cty.
we showed that if it's cts then a=1, b=2
but it's easy to see that's it's cts in this case
now u prove it's diffble
ocean sealBOT
martingale
cinder compass
?
real glen
oh
real glen
you first prove continuity, find out the values for that
and then sub them in to see if its differentiable?
cinder compass
u don't prove cty
real glen
then how do you get a = 1 b = 2
cinder compass
u find for what values of a,b is it cts
cinder compass
and then sub them in to see if its differentiable?
yes
cinder compass
that was for cty
real glen
yes
real glen
okay, you just said we dont prove it lol
cinder compass
real glen
no i dont want to, i thought u were just starting from the start lol
cinder compass
if we prove diff we auto prove cts
real glen
so its getting it cty, getting the valyes of a =1 b = 2
cinder compass
we only need prove diff
real glen
then sub to differentiate
cinder compass
mhm
cinder compass
then sub to differentiate
no not to differentiate
to prove it's differentiable!
to prove we CAN DIFFERENTIATE!
cinder compass
i'm not angry btw just emphasis
cinder compass
in this case**
yes i guess so
real glen
we sub in to find f'(x)
cinder compass
ok now time to sub
cinder compass
u can do it anytime u want
real glen
okay
wait a second
you said not to do what she said
i.e. the second part
but how else would you find the values of a and b?
real glen
why u want this
unless we just use the value of a -b = -1
bc that second line is trying to prove that f'(x) is continuous correct? when it is not necessarily?
real glen
yes
cinder compass
u should've told me
real glen
oh okay
cinder compass
wait a second
the second part gives u the right answer tho
u can still do that
just logically wrong
real glen
yes
then
thats not right
chat gpt says something similar
it says the left hand derivative must = the right hand
for differentiability at x = 1
does that make it more logical?
i dont understand why
cinder compass
chat gpt says something similar
correct
lim exists if and only if (iff) left and right hand limit exists
real glen
but for f'(x)
cinder compass
it says the left hand derivative must = the right hand
i mean this correct
cinder compass
but for f'(x)
f'(x) = lim
real glen
yes but isnt that what the teacher did
cinder compass
no
real glen
f'(x) = lim = 1? you mean?
worldly prawn
when you search, you find things like this
real glen
bc its 2ax and 2
worldly prawn
the final part is similar to this
cinder compass
left hand derivative is $\lim_{h\to0^-} \frac{f(1+h) - f(1)}{h}$
similar for rgith
ocean sealBOT
martingale
cinder compass
this diff to ur teacher
real glen
how is it different?
cinder compass
it's way different
u gotta understand lim defn first
will take a while
but do what she says and u get right answer
real glen
okay chat gpt is saying the exact same thing as you but they did it differently when actually working
because working through that ^ is a nightamre
they just did 2a = 2
for that reasoning
but thats not what you said exactly? its f'(x) 1- = f'(x) 1 +
cinder compass
when you search, you find things like this
the worst notation i have every seen
worldly prawn
probably, but the important part is in there
real glen
i cant really read that lol
real glen
real glen
feel free to dm
you said it was way different but its not???
real glen
chat gpt wrong bruh
isnt the writing of that just the equivalent of what u wrote earlier?
cinder compass
no
lone heartBOT
real glen
.reopen
lone heartBOT
✅
real glen
this is in my fucking formula sheet
earnest whale
What's the issue?
summer dirge
well...
the definition is a bit off because we don't know that f'(x) exists a priori
but if it does, then the definition is fine
it's kinda going the wrong way though
usually we define differentiability at a point first, and then say that f is differentiable if it's differentiable at each point
but I digress 
real glen
usually we define differentiability at a point first, and then say that f is dif...
but it says its differentiable at x = a provided:
summer dirge
but it says its differentiable at x = a provided:
but we don't know that f' even exists a priori 
if f' doesn't exist, the definition makes no sense, is all I'm saying
real glen
what is priori
summer dirge
a priori means without further knowledge
real glen
oh ok
thats what ive been sayign!
if u look at the original question
im supposed to assume that f'(x) exists BUT IT DOESNT IMPLY THAT IT DOES
summer dirge
well like
a differentiable function is always continuous
that's that lim_{x -> a+} = lim_{x -> a-} = f(a) means
f' already exists everywhere except at x = 1 in your problem
that's because we know that polynomials are differentiable
so the problem is simply asking you to find values for a and b such that f is differentiable at that point x = 1
f' exists on both sides of x = 1
just not at the point itself, until you decide what a and b should be
real glen
no offence but i might just not read that
no i read it
i mean not listen
because what if it messess up my understanding more
summer dirge
fair enough, I won't force you to read it
real glen
i did read it
summer dirge
ic
real glen
ok
so
what if theres no point where its differentiable at x = 1?
but everywhere else
summer dirge
I'm not sure I understand? 
real glen
that's because we know that polynomials are differentiable
but doesnt this formula apply for not just polynomials
like no value of a and b work
hole
summer dirge
ah, you're not sure whether there exists numbers a and b that will work?