#help-36
final saddleBOT
south dirge
wait for 20 what did you get from differentiating
south dirge
Okay, well lets differentiate step by step then
unreal robin
i literally have no idea
Do you remember any differentiation rules
south dirge
Thats an issue then
south dirge
Okay, uh do you have your notes by your side?
south dirge
Do you remember any differentiation rules
With these
tall dagger
uhhh
south dirge
Its fine if you dont
unreal robin
I suggest having a brief look at some differentiation rules for starters
Power rule, chain rule, etc
lilac bison
true
tall dagger
we didnt get deep into differentiation, i just remmeber teacher teaching the most basic rules
if u guys recall some rules, i think ill remember
tall dagger
Its fine if you dont
can u help me remember
unreal robin
if u guys recall some rules, i think ill remember
For starters, what's the derivative of x⁴
lilac bison
what r u doing here
?
unreal robin
dy over dx = 4
Incorrect
tall dagger
ok
unreal robin
Start from right to left to avoid confusion
unreal robin
i think i got it
Give it a try then!
unreal robin
but i still dont know how to find u and k with another variable
The idea is
You're given an expression of dy/dx AND an expression of y
tall dagger
yes
unreal robin
Which means, if you derive that y, you'll get an expression that's either the same as the one given
Or, and more importantly, an expression that's equal to it
tall dagger
how do we derive y
unreal robin
how do we derive y
Evaluate dy/dx
tall dagger
ok so then
unreal robin
its so hard to simplify dy over dx
Have you tried differentiating the y ?
unreal robin
If you have: y = 2x^k + ux⁷
What's dy/dx ?
unreal robin
but i did understand the formulaes
Try applying them
tall dagger
ok
unreal robin
You want to do each of them at a time
tall dagger
i see
tall dagger
so we add d(2x^k)/dx and d(2ux⁷)/dy ?
unreal robin
Yes
tall dagger
but how are we finding k and u out of this
unreal robin
We know that d(u+v)/dy = du/dx + dv/dx
tall dagger
yes
unreal robin
but how are we finding k and u out of this
Remember that we already have an expression of dy/dx
tall dagger
yes
unreal robin
The interesting thing is, that expression has not u and k values
But when we differentiate y ourselves, we'll get an expression that has k and u
tall dagger
hmm
unreal robin
Just try differentiating
tall dagger
got it
tall dagger
ok thanks
vapid hound
-# for future reference, it’s best to memorize this! it will help a lot with calculus
shell condor
lim x tends to 0 $\frac{\left(\tan\left(\tan x\right)-\sin\left(\sin x\right)\right)}{\tan x-\sin x}$
final saddleBOT
lim x tends to 0 $\frac{\left(\tan\left(\tan x\right)-\sin\left(\sin x\right)\ri...
soft zealotBOT
doctorstrangejr
shell condor
why is this not just 1, like I tried to multiply and divide tan(tanx) and sin(sinx) with tanx and sinx respectively to get $\frac{\left(\tan x\ -\ \sin x\right)}{\left(\tan x\ -\ \sin x\right)}$, which should give 1, but the answer is 2
soft zealotBOT
doctorstrangejr
shell condor
Please ping me if you're responding to this
coral prawn
what do you mean "respectively"
south dirge
he means denomitr and numeratr
coral prawn
I mean presumably you just have to use l'hopital and not screw up
shell condor
I'm here
south dirge
I mean presumably you just have to use l'hopital and not screw up
this
south dirge
**doctorstrangejr**
also this step was wrong!
shell condor
I mean yes but why does what I did not work
south dirge
Howd you cancel tanx - sinx
coral prawn
only black magic would turn a tan(tan(x)) into a tan(x)
south dirge
and the numerator
shell condor
okay okay guys listen
give me a minute
let's say you have tan(tanx) as x tends to 0 yes
you multiply divide with tanx
take tanx as t for now
so t*tan(t)/t
or just t, which was tanx
coral prawn
tan(x) and sin(x) don't approach zero at the same rate
south dirge
or just t, which was tanx
you cant say thi
shell condor
tan(x) and sin(x) don't approach zero at the same rate
I'm doing them independently of each other
south dirge
tan(x) and sin(x) don't approach zero at the same rate
tanx > sinx > x when x tends to 0
atleast thats what i remember
shell condor
guys I did them separately, if it helps I broke them into two limits
south dirge
guys I did them separately, if it helps I broke them into two limits
thats fine, but the step of writing tan(tanx)) as tan(x) is wrong
coral prawn
tanx > sinx > x when x tends to 0
at least when x>0, presumably it flips going the other way around
shell condor
and then recombined them after simplification
shell condor
thats fine, but the step of writing tan(tanx)) as tan(x) is wrong
Yes but how, that's what I'm having a problem with
coral prawn
guys I did them separately, if it helps I broke them into two limits
then your limits are
tan(tan(x)) / (tan(x) - sin(x))
and
-sin(sin(x)) / (tan(x) - sin(x))
assuming those limits exist which is not obvious
shell condor
then your limits are
tan(tan(x)) / (tan(x) - sin(x))
and
-sin(sin(x)) / (tan(...
yes, and now for the first one multiply divide with tanx, and for the second one do the same but with sinx
coral prawn
if the limits exist and you're able to compute them then you're golden
good luck with that
In the end I think you have to do the same amount of work as with l'hopital
soft zealotBOT
doctorstrangejr
shell condor
$\frac{\frac{\tan\left(\tan x\right)}{\tan x}\cdot\tan x}{\left(\tan x\ -\ \sin x\right)}$
soft zealotBOT
doctorstrangejr
coral prawn
valid
shell condor
Now, tan(tanx)/tanx should simplify to tanx (we can take tanx as y if it helps to understand why, as y tends to 0)
$\frac{\tan x}{\left(\tan x\ -\ \sin x\right)}$
soft zealotBOT
doctorstrangejr
coral prawn
tan(tan(x)) / tan(x) is not tan(x)
south dirge
tan(tan(x)) / tan(x) is not tan(x)
?
he applied it correct
thats 1, he just multiplied both numertor and denomintr
shell condor
tan(tan(x)) / tan(x) is not tan(x)
I mean if it isn't then that's my conundrum, why is it not that
coral prawn
,w plot tan(tan(x)) / tan(x) - tan(x)
soft zealotBOT
coral prawn
that should be the zero function if they were equal
shell condor
if it helps I computed this on desmos and got 1 for odd values of pi and 2 for even values
south dirge
that should be the zero function if they were equal
they both are tending tozero, its applicable acc to limits for his grade
south dirge
its a rule dude
you can try applying l hopital
same answer
tan(qwerty) / qwerty =1
when qwerty tends to 0
loud sundial
(they're doing a small angle approximation, albeit with some rigor missing)
south dirge
Right, but for his grade its fine hopefully
shell condor
I'm not saying what I did could not be wrong, what I'm saying is if it is wrong then why is it wrong
shell condor
Right, but for his grade its fine hopefully
Grade?
south dirge
arey bhai tauba tauba
south dirge
No no this is for JEE
which year?
shell condor
which year?
drop, it's tomorrow, evening shift, I'm tensed because I can't understand why this is wrong
south dirge
drop, it's tomorrow, evening shift, I'm tensed because I can't understand why th...
holy shit
coral prawn
Now, tan(tanx)/tanx should simplify to tanx (we can take tanx as y if it helps t...
You can't say that something simplifies to something else just because their limits are the same
south dirge
<@&268886789983436800>
shell condor
You can't say that something *simplifies* to something else just because their l...
are you familiar with the x tends to 0 tanx/x = 1 rule?
south dirge
are you familiar with the x tends to 0 tanx/x = 1 rule?
acha sun na
shell condor
acha sun na
Haan bhai
coral prawn
I do agree that the limit of tan(tan(x)) / tan(x) is 1
but we still haven't solved the problem where the denominator is zero
shell condor
but we still haven't solved the problem where the denominator is zero
yes, but remember we multiplied a tanx too, and did the same process for sinx so should have a similar sinx left there, so tanx-sinx/(tanx - sinx), it should cancel out and be 1
coral prawn
yes, but remember we multiplied a tanx too, and did the same process for sinx so...
I don't understand what you mean
shell condor
I don't understand what you mean
I'll just solve the question with the way I did and send a pic
coral prawn
sure
south dirge
I'll just solve the question with the way I did and send a pic
Wait sun
Jab tu ye lagayega ki tan(tanx)/tanx =1
And same cheez for the sin wala
tum ye mislead kar rhe ho ki dono ka actual rate ignore karke literally same man rhe ho dono ko
ek tarah se aise socho jo tum kar rhe ho usse ye aayega ki tan(tanx) is same as sin(sinx)
south dirge
taylors ki expansions ki tayaari ki hogi na
south dirge
ek tarah se aise socho jo tum kar rhe ho usse ye aayega ki tan(tanx) is same as ...
ye padh
south dirge
taylors ki expansions ki tayaari ki hogi na
yahan taylors se kar
Dekh, tan ka expansion aur sin ka expansion different hai
shell condor
yahan taylors se kar
Bhai Taylor's se kar to loon lekin exam mein kaise samajh aayega ki ye galat hai, udhar to yaheen lagega na ki simply answer aa gaya
south dirge
Bhai Taylor's se kar to loon lekin exam mein kaise samajh aayega ki ye galat hai...
Haan isilye bol rha hun ki yahan par tumne literally ye bol diya ki tan(tanx) is = sin(sinx)
shell condor
Dekh, tan ka expansion aur sin ka expansion different hai
Haan vo to hai, lekin x tends to 0 pe to donon same hain na
south dirge
Haan vo to hai, lekin x tends to 0 pe to donon same hain na
true but tan aur jaldi increases as compared to sin
shell condor
true but tan aur jaldi increases as compared to sin
Haan lekin tends to 0 pe to infinitely small dekhte hain na, udhar to rate matter nahi karega, in general karega lekin idhar thode na karega
shell condor
hain, lekin donon mein to 1 aana chahie, bhai ye kya hai
south dirge
hain, lekin donon mein to 1 aana chahie, bhai ye kya hai
nu
shell condor
bhai traahi, hamse na hoga, is sawaal ke chakkar mein baaki sab chhuta aur ja raha hai
south dirge
bhai traahi, hamse na hoga, is sawaal ke chakkar mein baaki sab chhuta aur ja ra...
lmao
sun
simple tip
shell condor
BC itna sundar sa method dikha tha, uski bhi maar li in logon ne🥲
shell condor
then taylor hi lagega
Haan idhar l hopital shayad kaam aaye bhi na, Taylor hi lagaane padenge
south dirge
Haan idhar l hopital shayad kaam aaye bhi na, Taylor hi lagaane padenge
yes
mains mein yahi hoga
but sach bolun toh lcd zyada aise type ka nahi pich rha hai iss saal jee
mein paper analysis dekh rha tha
shell condor
Chhodo bhai phir, channel khula rehne deta hoon in case koi Euler aake kuch bata de ki kya galati hai
shell condor
but sach bolun toh lcd zyada aise type ka nahi pich rha hai iss saal jee
Bhai hopefully scam na ho bas
south dirge
wo zyada waisa nahi hota f(x) = abcd for -1<=x<=1 efgh 1<=x=<3 aisa type ka
aisa type puchta hai
shell condor
wo zyada waisa nahi hota f(x) = abcd for -1<=x<=1 efgh 1<=x=<3 aisa type ka
Abeeee
board waale sawaal pooch rahe hain
bhai scam na kar dein bas
south dirge
Haan pata hai but iska thoda higher level
south dirge
bhai scam na kar dein bas
india hai bhai kya lagta hai tujhe
shell condor
india hai bhai kya lagta hai tujhe
aakhri shift mein bomb phod ke jaayein
shell condor
Chhodo bhai phir, channel khula rehne deta hoon in case koi Euler aake kuch bata...
Chalo bhai phir, baakiyon ke liye angrezi mein ye likh doon
south dirge
lmao
shell condor
okay so I'm not stressing much on this as there are more topics I need to cover, as of now I don't really understand what went wrong, I'm leaving the channel open, if anybody is able to figure it out then please mention it here
south dirge
Chalo bhai phir, baakiyon ke liye angrezi mein ye likh doon
-# mein chalta sone (hagne)
-# atb gng
shell condor
-# mein chalta sone (hagne)
all the best bhai, machhar bahut hain aaj kal
final saddleBOT
@shell condor Has your question been resolved?
shell condor
<@&268886789983436800>
gusty ravine
Glt h
Limits hmesha ek saath dlti h u can't just put partial limits ki ek jgh kuuch daal diya u let the other part stay as a variable
gusty ravine
<@&268886789983436800>
Also why this
shell condor
bhai partial limits thode na daal raha hoon, agar koi function hai f(x) = g(x)*sinx/x, to udhar sinx/x ko to 1 karoge na bina baakiyon ko consider kare, waheen kara hai maine basically
shell condor
Also why this
scammer tha
gusty ravine
bhai partial limits thode na daal raha hoon, agar koi function hai f(x) = g(x)*s...
Nhi hota aisa imo bhai limits to ek saath hi dalega na
That's just ki agar ek case m shi ho gya to u make a formula out of it which ain't true
shell condor
are bhai, ye kar sakte ho, ye standard limits hoti hain, problem ye nahi hai ki jo step maine kara hai vo galat hai, vo sahi hai, lekin koi exception hai jiski wajah se ye galat ho raha hai
thode aur questions dekhoge to har jagah ye allowed hai
baaki anyways bhai thank you for attempting
gusty ravine
Idk bhai i haven't studied limits that extensively but idts ki aise hota h i could be wrong tho. Im gonna ho sleep ab but can u dm me the original question and this thing u did
shell condor
haan bhai sure, ek baar tum bhi idea le lo
gusty ravine
Thanks
shell condor
okay so I'm not stressing much on this as there are more topics I need to cover,...
^ (helpers)
final saddleBOT
@shell condor Has your question been resolved?
deep condor
Limits hmesha ek saath dlti h u can't just put partial limits ki ek jgh kuuch da...
no problem in this as long as both limits exist (product rule of limits)
deep condor
okay so I'm not stressing much on this as there are more topics I need to cover,...
when you do $$\lim_{x \to 0} \frac{ \frac{\tan (\tan(x))}{\tan(x)} \tan(x)}{\tan(x) - \sin(x)} \quad = \quad \lim_{x \to 0} \frac{\tan(\tan(x)}{\tan(x)} \cdot \lim_{x \to 0} \frac{\tan(x)}{\tan(x) - \sin(x)},$$ you have to check that both limits exist. and while $\lim_{x \to 0} \frac{\tan(\tan(x)}{\tan(x)} = 1$ (checking with WA), the other limit is $\lim_{x \to 0} \frac{\tan(x)}{\tan(x) - \sin(x)} = \lim_{x \to 0} \frac{1}{1-\cos^3(x)} \to \infty$ by L'Hôpital's
soft zealotBOT
haseeb ♥
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
deep condor
yaar
shell condor
limitsexist🙏
deep condor
when you split the limit you get $\lim_{x \to 0} \frac{\tan(x)}{\tan(x) - \sin(x)}$ as one of the products which goes to infinity by l'Hopital's
soft zealotBOT
haseeb ♥
deep condor
and the same happens for $\lim_{x \to 0} \frac{\sin(x)}{\tan(x) - \sin(x)}$
soft zealotBOT
haseeb ♥
shell condor
oh wait yeah
so basically all I need to do is check with l'hopitals whether this stays indeterminate or not?
deep condor
well you check if it's indeterminate by direct substitution
tan(x) -> 0 and (tan(x) - sin(x) ) -> (0 + 0), so the limit has form 0/0
then apply l'hopital by taking derivatives
but more importantly, you have to double-check that both limits exist after you split a product or quotient
i think it's possible for addition and subtraction too
shell condor
Alright thanks man that should be it, so basically if I do anything after which even the final l'hopital results in an indeterminate form, then I probably messed up, yes?
deep condor
if you do l'hopital and you get an indeterminate form again (0/0), you can differentiate again
however if you are differentiating 4+ times on a test maybe l'hopital isn't ideal
if you do l'hopital and you get infinity, then that just means the limit DNE
shell condor
if you do l'hopital and you get an indeterminate form again (0/0), you can diffe...
I mean in cases where I can't apply l'hopitals anymore, like in $\frac{1}{1 - cos^3x}$
soft zealotBOT
doctorstrangejr
deep condor
yeah, then the limit is now determinate (a known value), but of course that known 'value' is infinity
so l'hopital stops
shell condor
wait so then the limit does not exist, and assuming this is on a test that shouldn't happen, that means I messed up somewhere earlier yeah? (like that multiply/divide with tanx)
deep condor
wait so then the limit does not exist, and assuming this is on a test that shoul...
yeah that means you didn't use the product rule of limits correctly
shell condor
yeah that means you didn't use the product rule of limits correctly
but I did here though
deep condor
no, because for the product rule, both limits have to exist
otherwise you could do $$1 = \lim_{x \to 0} \frac{ \sin x}{x} = \left(\lim_{x \to 0} \sin x\right) \left(\lim_{x \to 0} \frac 1x\right) = 0 \cdot \infty$$
soft zealotBOT
haseeb ♥
shell condor
oh yeah makes sense
Alright then, that should do it
thank you for your help🫡
.solved
final saddleBOT
final saddleBOT
Available help channel!
inner hill
How the fuck do I take the limit here? I can't take the limit here.
final saddleBOT
How the fuck do I take the limit here? I can't take the limit here.
inner hill
to what?
timber leaf
Take screenshot of your questions, this picture resolution so bad
inner hill
timber leaf
Much better
timber leaf
you would need to take a_n+1 divide by a_n
$\frac{x^{n+1}}{(n+1)^44^{n+1}} /\frac{x^n}{n^44^n}$
soft zealotBOT
Minλ
inner hill
Yup, that's what I tried to do. And with whatever rule that causes you to flip the denominator and multiply with numerator
What do I do about this?
timber leaf
now, isn't it be: $\frac{x^{n+1}}{(n+1)^44^{n+1}} \frac{n^44^n}{x^n}$
soft zealotBOT
Minλ
candid pulsar
What do I do about this?
n^4/(n+1)^4 is the part affected by the limit
timber leaf
What do I do about this?
but when n approach infinity, what does it say
inner hill
infinity over infinity? I tried putting 1 for the limit and it didn't work.
timber leaf
notice $\frac{n^4}{(n+1)^4}$
soft zealotBOT
Minλ
soft zealotBOT
Minλ
inner hill
it didn't accept zero either
timber leaf
which is: $\frac{x}{4} \frac{n^4}{(n+1)^4}$
soft zealotBOT
Minλ
inner hill
if infinitely decreasing is what you're implying
timber leaf
so, is n+1 similar to n if they both approach infinity?
the results are all infinity
inner hill
and yes, I tried seperating that out, I don't know what the limit of n^4/n+1^4
timber leaf
do you agree that if n approach infinity, then n+1 and n also approach infinity?
which means: n and n+1 are equivalent as n -> inf
inner hill
yes, so it's infinity over infinity. That leads to 1, which it did not accept
soft zealotBOT
Minλ
inner hill
what, the limit?
timber leaf
yes
inner hill
ohhhh, I tried x/4, I probably should have put in the absolute value
inner hill
yup! that's correct. and it was my last attempt too.
timber leaf
lucky!
timber leaf
no problem man
final saddleBOT
final saddleBOT
Available help channel!
lime crest
$2026$ towns want to create a security network, such that $\$ $(i)$ between any two towns, there is a connection between them. $\$ $(ii)$ each connection has an encrypted number, which is a positive integer not exceeding $k$. $\$ $(iii)$ A towns security number is defined as the sum of the encrypted numbers of every connection to that town. $\$ A group of towns is called secure if all security numbers between each town are pairwise distinct. Determine the minimum $k$ such that all 2026 towns are secure
final saddleBOT
$2026$ towns want to create a security network, such that $\\$ $(i)$ between any...
soft zealotBOT
Copter
lime crest
i dont really know how to think of this
but clearly k = 1 isnt possible
now if k = 2 the possible values of the 2026 distinct numbers are {2025,2026,...,4050} but then 2025 is only possible if all connections leading to it have only the number 1 and 4050 happens if all connections are 2
which clearly cant happen at the same time
idk about k =3
final saddleBOT
@lime crest Has your question been resolved?
ionic stirrup
For $n = 2026$, let's check if the sum of the set is even: The sum of $2025$ to $4050$ (a total of 2026 terms).$\text{Total} = \frac{2026}{2} \times (2025 + 4050) = 1013 \times 6075$. The result is Odd. Since the result is odd, this set of numbers is impossible to use. We must raise the largest number by at least 1 place to make the sum even. Therefore, the maximum security value ($S_{max}$) we need is at least $2n - 1$.
soft zealotBOT
ShiroSharata
ionic stirrup
also how did you get to 2n-1?
because the result of the parity calculation is odd
then you have to increase the largest number by at least 1 level so that the total is even.
lime crest
**ShiroSharata**
what does n represent here 
ionic stirrup
2026
ionic stirrup
then you have to increase the largest number by at least 1 level so that the tot...
$$2n - 1$$
$$2(2026) - 1$$
$$4051$$
soft zealotBOT
ShiroSharata
lime crest
i dont understand what youre trying to do, sorry
ionic stirrup
$$(n-1)k \ge 2n - 1$$
This is the formula for determining the minimum value of K.
soft zealotBOT
ShiroSharata
ionic stirrup
try find the K, i will explain it more
lime crest
k should be 3 then?
ionic stirrup
k should be 3 then?
true but do you really know how it works?
lime crest
not really ;-;
ionic stirrup
**ShiroSharata**
go try find the K, n=2026
final saddleBOT
@lime crest Has your question been resolved?
loud sundial
well we need to show k=3 is possible, then?
Ignore the above because I think they’re conflating obtaining a bound with exhibiting a construction
Consider making each town’s security number a monotone function of its index
If you think of the edge labels as a symmetric $2026 \times 2026$ matrix, then the security number of town $i$ is just the sum of row $i$, meaning you want to fill the matrix so that all of the row sums are different
soft zealotBOT
Civil Service Pigeon
loud sundial
A natural way to do this is to consider making a rule based on ||i+j|| (why?) if you don’t see why, ||consider diagonal bands||.
tldr:
,texsp ||Label the towns $1, \dots, 2026$. Then try to fill in the blanks:
$$w_{ij}=\begin{cases} 1, & i+j \leq \boxed{\cdots} \ 2, & \boxed{\cdots} i+j \leq \boxed{\cdots} \ 3, & i+j \geq \boxed{\cdots} \end{cases}$$||
soft zealotBOT
Civil Service Pigeon
lime crest
wij is the entry right
final saddleBOT
Available help channel!
timber plume
why did I get this wrong?
final saddleBOT
why did I get this wrong?
blissful meadow
For $x$ you should've brought the $-2x$ to the other side first. What you shoud have is $3x - 7 = -4$.
soft zealotBOT
Azyrashacorki
blissful meadow
And similarly for $z$ : you should have gotten $z + 7 = -14 - 2z$ whence $3z + 7 = -14$.
soft zealotBOT
Azyrashacorki
blissful meadow
Yes :c
timber plume
this too
what about this
I understand this shoudve been one of my response so dont explain this
just this
blissful meadow
As you take x to infinity, cos(x)/x goes to 0, but sin(x) oscillates between -1 and 1 so it doesn't set on a particular value
drowsy epoch
the limit of sin(x) DNE
timber plume
also this
also i know why i got this wrong but "are continuous" should also be a correct answer
because they the lhs and rhs limit are equal
there should be continuous
drowsy epoch
limits being continuous is wrong terminology
Functions are continuous or not
You are messing up the math vocabulary
timber plume
fair enough
drowsy epoch
A limit can exist or it cannot and that's about it
And if limits agree on both sides then you can conclude continuity, given the function value is the limit
timber plume
.close
final saddleBOT
final saddleBOT
Available help channel!
orchid coral
Prove that zeta(3) + zeta(2) < 3
final saddleBOT
Prove that zeta(3) + zeta(2) < 3
onyx peak
a kind of silly way to do it would be computing the first few terms and then bounding the rest by doing the cauchy condensation thing
velvet ridge
onyx peak
a kind of silly way to do it would be computing the first few terms and then bou...
this kind of works btw, you dont need too many terms
but there might be more elegant sol
hmm possibly integral
yeah that might be nicer
maybe remove the 1's first and then do an integral upper bound
yeah, removing first few terms and then integral upper bound is prolly the intended way to do it
my bound comes out to be exactly 3
final saddleBOT
@orchid coral Has your question been resolved?
onyx peak
Hi, please take casual convo to #discussion or #chill
lucid zephyr
Hi, please take casual convo to <#268882317391429632> or <#342850939306246145>
oops I thought this was the general one 😅
Thank you for reminding
onyx peak
one last way i can think of would be making it telescope
@orchid coral can you explain where you're stuck at btw?
or what do you not understand about what ive said
or what else are you looking for
final saddleBOT
@orchid coral Has your question been resolved?
shadow marlin
if $u, v$ are linear maps in finite dim such that $uv - vu$ has rank $1$, show that there's a base in which both are upper triangular
In the solution, they first proved that either Im $v$ or Ker $v$ is invariant under $u$. In the latter case we find a common eigenvector and we find the other eigenvectors by induction. However in the first case I don't see how to conclude
final saddleBOT
if $u, v$ are linear maps in finite dim such that $uv - vu$ has rank $1$, show t...
soft zealotBOT
bloubbloub
shadow marlin
in the first case, we have $Im(uv - vu) \subset Im(v)$ also
soft zealotBOT
bloubbloub
final saddleBOT
@shadow marlin Has your question been resolved?
shadow marlin
Apply induction on the invariant subspace
what if Im v is the whole space
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@shadow marlin Has your question been resolved?
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@shadow marlin Has your question been resolved?
final saddleBOT
final saddleBOT
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worldly spruce
loud sundial
test
loud sundial
test 2
loud sundial
.close
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crystal pawn
w Civil Service Pigeon
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latent gazelle
hi
latent gazelle
what are level curves?
formal trail
the level curves of a function of two variables, say f, is the set of all points (x,y) satisfying f(x,y) = C where C is a constant
for example x^2 + y^2 = 9 and x^2 + y^2 = 25 are level curves of the function f(x,y) = x^2 + y^2 (which also happen to be circles)
latent gazelle
okay right – and sorry if this sounds rude but what is the significance of them? How can they help me understand other multivariable concepts? The way I understand it is that they are conventionally taught early in multivar courses
formal trail
well they are used in visualizing multivariable functions, for example a contour plot of a function is just plotting a bunch of level curves (usually picking the constants to use at even intervals)
you can also understand the gradient of a two variable function geometrically as being perpendicular to its level curves
latent gazelle
sorry i am thinking
is it silly of me that i have trouble understanding contour graphs
i cant tell whether a layer is higher than another
i feel like im drawing a heat map except there is no heat
how do i determine which level is above another level by looking at a contour graph
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@latent gazelle Has your question been resolved?
formal trail
i cant tell whether a layer is higher than another
you can only tell what the values are based on the labels
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gentle zephyr
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gentle zephyr
drowsy epoch
I love help channels without comtext
spring haven
Note that any prime factor of k^2q will be a factor of either k or q
Then what does the fact that k and q are coprime tell you?
gentle zephyr
I love help channels without comtext
i got stuck dont know how to continue
gentle zephyr
Then what does the fact that k and q are coprime tell you?
dont understand
gentle zephyr
Note that any prime factor of k^2q will be a factor of either k or q
the prime factor it cant be a factor of both k and q bec gcd(k,q) = 1, k and q are coprime
gentle zephyr
Then what does the fact that k and q are coprime tell you?
gcd(k,q) = 1, so?
@spring haven
viral jewel
You can note k²=l
And you get d=7⁶gcd(l×q,7²(l+q²))
viral jewel
|| I think that's right||
final saddleBOT
@gentle zephyr Has your question been resolved?
gentle zephyr
To other helpers: this has already been answered
the person who responded didnt cared to explain how he got there, and the idea of a help channel is to guide someone to the solution instead of spitting out the answer?
drowsy epoch
well u need hand holding not guidance
gentle zephyr
what?
do you understand how the other person got there?
seems to me like he kinda skipped a lot of steps and dont care to explain
gentle zephyr
well u need hand holding not guidance
he just spitted the answer without explaining how dude
gentle zephyr
nobody is helping really
nobody really understands how the guy got there, he just skipped a bunch of steps and wants me to guess until I get to what he got\
final saddleBOT
@gentle zephyr Has your question been resolved?
blissful meadow
They just looked at the expressions in the gcd and found multiples of x and y such that their sum is just in terms of k. Then did the same for q
Like say you want to just keep $q$'s in there. \
On the left you have $x=k^2q$ and on the right you have $y= 49k^2 + 49q^2$.\
Surely for terms with $k$'s to cancel, you want some term of the form $k^2q$ on the right, and if you multiply $x$ by $q$ you get $49k^2q + 49q^3$. Now the only thing missing is that in $x$ you only have $k^2q$, not $49k^2q$. This suggests you might want to take $49x = 49k^2q$. \
Then since the gcd divides any integer combination of $x$ and $y$, you get that it must divide $qy - 49x$, which is just $49q^3$.
soft zealotBOT
Azyrashacorki
blissful meadow
If you want to just keep $k$'s, then you want $q^2$ on the left, so $qx = k^2q^2$ seems like a good choice. \
Now $y$ contains only $q^2$, so we need a term in there with $k^2q^2$. Then if you take $k^2 y$ you get $49k^4 + 49k^2q^2$.\
So far you get $k^2 y = 49k^4 + 49k^2 q^2$ and $qx = k^2q^2$, so if you take $k^2y - 49qx$, you end up with $49k^4,$ which the gcd must divide.
soft zealotBOT
Azyrashacorki
blissful meadow
So now you know $d = 7^6 r$ where $r$ divides both $49k^4$ and $49q^3$
soft zealotBOT
Azyrashacorki
gentle zephyr
Like say you want to just keep $q$'s in there. \\
On the left you have $x=k^2q$ ...
ok so
x = k^2 . q
y = 49k^2 + 49q^2
so if d' = gcd(x,y) then d' | ax + by forall a,b in Z
qx = k^2 . q^2
k^2 . y = 49k^4 + 49 . k^2 . q^2
k^2 . y = 49k^2(k^2 + q^2)
49qx = 49 . k^2 . q^2
k^2 . y - 49qx = 49k^2(k^2 + q^2) - 49 . k^2 . q^2
k^2 .y - 49qx = 49k^2(k^2 + q^2 - q^2)
k^2 . y - 49qx = 49k^4
but now what?
blissful meadow
What do you mean now what?
Then you get $k^2 y - 49qx = 49k^4 + 49k^2q^2 - 49k^2q^2 = 49k^4.$
soft zealotBOT
Azyrashacorki
blissful meadow
$k^2y - 49qx$ is an integer combination of $x$ and $y$, so $r$ must divide it
soft zealotBOT
Azyrashacorki
blissful meadow
So in particular, $r$ divides $49k^4$
soft zealotBOT
Azyrashacorki
gentle zephyr
by r you mean d'?
i see
at the end we get that
d' | 49q^3
and
d' | 49k^4
@blissful meadow but after that, then what?
d' | gcd(49q^3, 49k^4) ?
blissful meadow
Well k and q are coprime, so if r divides both of those it must divide 49...
So that restricts your choice of d', and hence of d, drastically
gentle zephyr
Well k and q are coprime, so if r divides both of those it must divide 49...
you lost me in there
gentle zephyr
Well k and q are coprime, so if r divides both of those it must divide 49...
wait a second
d' | gcd(49q^3, 49k^4) ?
is this true ^
?
d | x => x = d.k
x^3 = (d.k) ^3
x^3 = d^3 . k^3
let k^3 = m
where m in Z
x^3 = d^3.m => d^3 | x^3
d^3 | x^3 => x^3 = d^3 . m
x^3 = d . d^2 . m
let u = d^2 . m
x^3 = d .u
d | x^3
gentle zephyr
So that restricts your choice of d', and hence of d, drastically
care to explain?
blissful meadow
What do you mean?
This shows that d' must divide 49
What numbers can divide 49?
gentle zephyr
This shows that d' must divide 49
d' | 49k^3 => d' | 49k
d ' | 49q^3 => d' | 49q
?
blissful meadow
Well if you want $d' | \gcd(49q^3, 49k^4) = 49 \gcd(q^3,k^4) = 49$
soft zealotBOT
Azyrashacorki
blissful meadow
Since q and k are coprime
gentle zephyr
Well if you want $d' | \gcd(49q^3, 49k^4) = 49 \gcd(q^3,k^4) = 49$
how is gcd(q3, k4) = 1?\
blissful meadow
Since q and k are coprime
.
gentle zephyr
but why
blissful meadow
Why do you think?
gentle zephyr
i get that q and k are coprime
gentle zephyr
Why do you think?
there must be a gcd property to make it more clear
blissful meadow
Think about it.
gentle zephyr
Think about it.
I will try to prove it
suppose gcd(q^3, k^4) = v with v in Z \ {1}
then v | q^3 and v | k^4
blissful meadow
You just need to show that if k and q are coprime, so are k^m and q^n
It's pretty much by definition of k and q being coprime...
gentle zephyr
You just need to show that if k and q are coprime, so are k^m and q^n
i mean if m=n its straightforward
but in this case m ≠ n
blissful meadow
It's pretty much by definition of k and q being coprime...
.
gentle zephyr
It's pretty much by definition of k and q being coprime...
k and q are coprime so gcd(k,q) = gcd(k,q)^n = gcd(k^n, q^n) = 1
blissful meadow
What does it mean that k and q are coprime?
Apart from the fact that gcd(k,q) = 1
gentle zephyr
What does it mean that k and q are coprime?
the only common divisor in both are 1
blissful meadow
Ok, so if k and q don't share any divisor other than 1, what about k^m and q^n?
gentle zephyr
say for example the prime factorization of q is p1 p2 p3
then the prime factorization of q^n is p1^n p2^n p3^n
gentle zephyr
Ok, so if k and q don't share any divisor other than 1, what about k^m and q^n?
like exponentiation is not changing the primes that divide q or k
is just multiplying the exponent by n or m
if they are coprime then none of the primes that divide q are present in the prime factorization of k
blissful meadow
Yes, so if you have a divisor of k^m and q^n, it needs to be a divisor of k and q, and the only one is 1.
gentle zephyr
Yes, so if you have a divisor of k^m and q^n, it needs to be a divisor of k and ...
nice
so d = 7^6 * 7^2 = 7^8
right?
blissful meadow
No, d' must be a divisor of 49, not necessarily 49
gentle zephyr
i see
gentle zephyr
No, d' must be a divisor of 49, not necessarily 49
so d' is either 1,7,49
and d = 7^6 . d'
blissful meadow
Yes
blissful meadow
Yes, so then you need examples displaying those three values.
gentle zephyr
Yes, so then you need examples displaying those three values.
you are a lifesaver azyra
I really appreciate your help
I am rn in uni in a advanced calculus class, but I think I can continue from here
i would be busy with the lecture for like 2 hr more so I think I would close this and continue by myself when I get home
gentle zephyr
.solved thanks
final saddleBOT
gusty citrus
any math tutor?
barren sphinx
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Available help channel!
gentle zephyr
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soft zealotBOT
Renato
drowsy epoch
What have you tried
opaque ember
r is any real number satisfying condition given in each part
gentle zephyr
how to do this?
opaque ember
for (a) and (b) use epsilon definition of limit and given condition on r
opaque ember
thats only the definition for limit = 0, not the general one
gentle zephyr
which one is the general one
opaque ember
i shouldnt have to write it for u. should be in ur notes
gentle zephyr
there is a bunch of definitions
opaque ember
there is essentially only ONE epsilon definition. it should look like what u posted but for a general limit
opaque ember
thats functions not sequences
gentle zephyr
isnt a sequence a function from N to R
opaque ember
this is function on interval not sequence...
gentle zephyr
opaque ember
yes
soft zealotBOT
Renato
opaque ember
if u dont understand the definition then ur not ready at all for this type of problem
pls review ur notes. they should have many examples to help u understand the definition
opaque ember
do u have a concrete question about n0?
opaque ember
then u do not understand the purpose of n0 in the definition
gentle zephyr
what is the purpose of n0
gentle zephyr
,w threshold
soft zealotBOT
gentle zephyr
|a_n-A|<e is desired. n0 is the threshold for it to happen
i guess so, it has to start somewhere, is just tough to grasp somehow
n0 always = 1?
i dont really get it, if (an)_(n in N) then n0 = 1
gentle zephyr
forall epsilon > 0, there exists some n0 in N such that |an - L| < epsilon forall n >= n0
thats for the convergence of a sequence to L
opaque ember
"exists n0" follows "forall epsilon", so n0 generally depends on epsilon
the main part of an epsilon proof is to find the correct n0
for example 3.1.3 n0=1 works and so does n0=100
for other types of sequences the correct n0 is not as simple. see example 3.1.4
my time is up. i need to eat dinner. pls ask follow up questions and maybe other helpers can answer them
TO OTHER HELPERS: do not help with original problem until renato fully understands ALL textbook examples and prior exercises about epsilon definition of sequence limit
final saddleBOT
@gentle zephyr Has your question been resolved?
gentle zephyr
.close
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hushed imp
how do you solve in 41 for AF?
final saddleBOT
how do you solve in 41 for AF?
hushed imp
and moreso, how do you inscribe the circle?
do i just adjust the compass until something fits? or is there a more formal process?
final saddleBOT
@hushed imp Has your question been resolved?
hushed imp
<@&286206848099549185>
loud sundial
how do you solve in 41 for AF?
loud sundial
and moreso, how do you inscribe the circle?
Solve for the radius, use that to construct the centre (it's directly above the midpoint of AB), and draw the circle.
loud sundial
Thank you mann
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@hushed imp Has your question been resolved?
shut birch
im trying to self studying math, i know till high school level, from where should i and what should i study
final saddleBOT
im trying to self studying math, i know till high school level, from where shoul...
deep condor
try #study-discussion, this is for specific questions
midnight fjord
im trying to self studying math, i know till high school level, from where shoul...
A square be square see square
honest ferry
im trying to self studying math, i know till high school level, from where shoul...
which field are you interested in?
shut birch
which field are you interested in?
computer science
timber leaf
Discrete Maths is a great start in early uni.
sturdy flax
discrete math is probably your next stop then, assuming by high school you mean calculus at least.
honest ferry
computer science
"Guide to Linear Algebra" by David Towers was an amazing read for me as a first year computer science student
timber leaf
Calculus 1 also highly recommended (at least)
shut birch
discrete math is probably your next stop then, assuming by high school you mean ...
yeah i know calculus
shut birch
"Guide to Linear Algebra" by David Towers was an amazing read for me as a first ...
how is this one "Linear-Algebra-by-Kenneth-Hoffman"
honest ferry
how is this one "Linear-Algebra-by-Kenneth-Hoffman"
i haven't read that book
rotund marlin
Help what's 2 + 2
midnight fjord
Help what's 2 + 2
6 or 7 I think
rotund marlin
6 or 7 I think
why.
shut birch
and what about Analysis? , is that imp
sturdy flax
Help what's 2 + 2
<@&268886789983436800> I don't know if I should classify this as trolling or intrusion, but.
sturdy flax
and what about Analysis? , is that imp
not much for CS.
rotund marlin
<@&268886789983436800> I don't know if I should classify this as trolling or int...
ok
sturdy flax
it's a 'nice to have' topic for computer scientists.
formal trail
Help what's 2 + 2
2 + 2 = 4 day mute, hope this helps!
sturdy flax
but you probably aren't going to be dealing with a lot of epsilons and deltas in computer science.
shut birch
not much for CS.
alright, will try discrete then
shut birch
anything else?
thanks for now
sturdy flax
!done, if you have nothing else. see you around.
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If you are done with this channel, please mark your problem as solved by typing .close
shut birch
.close
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tardy ember
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lunar garden
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lunar garden
Someone help pls where i went wrong
lofty goblet
,rccw
soft zealotBOT
odd seal
<:sully:651816820122189834> <:blobcry:971797574916907028> <:bleak:87709328090559...
uhh, whats the issue? $\frac{2}{\sqrt2} = \sqrt2$, you got the answer you were expecting didnt you?
lilac bison
nice handwriting
soft zealotBOT
Bacter14Fr0g
lunar garden
nice handwriting
lunar garden
uhh, whats the issue? $\frac{2}{\sqrt2} = \sqrt2$, you got the answer you were e...
I had to prove LHS =RHS and they dont equal
south dirge
I had to prove LHS =RHS and they dont equal
are you having prob in 2*(1/sqrt2)
lunar garden
this is equal to -(sqrt2)/3
Yes but idk how do I get that from what I have
stone wagon
these two are equal
south dirge
are you having prob in 2*(1/sqrt2)
then this?
lunar garden
then this?
No thats fine, just to simplify the whole thing is the problem 
odd seal
rewrite 2 as sqrt2 * sqrt2
south dirge
No thats fine, just to simplify the whole thing is the problem <:bleak:877093280...
huh?
you just proved no?
odd seal
$2 = (\sqrt{2})^2$
soft zealotBOT
Bacter14Fr0g
lunar garden
odd seal
what other issue is left? you just cancel one of the sqrt2s
south dirge
No thats fine, just to simplify the whole thing is the problem <:bleak:877093280...
do u mean the fact the Qsn is lil bit too much wacky to simplify
south dirge
what other issue is left? you just cancel one of the sqrt2s
nvm u carry on
odd seal
no, this is wrong
lunar garden
How so
odd seal
why did you multiply and divide there?
lunar garden
Oh wait over 1
odd seal
I suggested a substitution
south dirge
How so
how u write 2 as (sqrt2)^2 / sqrt(2)^2
the latter side is just 1
and last time i check 2 isnt equal to 1
lunar garden
lunar garden
a
lunar garden
Ohhk I understand it now
south dirge
Aight anymore
south dirge
Sure happens!
lunar garden
.close
final saddleBOT
south dirge
Thnks, im trying to self study trig <:blobcry:971797574916907028>
Your wlcm!
Have a great day!!
lunar garden
Your wlcm!
Have a great day!!
U too
final saddleBOT
Available help channel!
jagged flare
in an n×n grid, how many ways are there to fill the cells such that each row and column has exactly m filled cells?
final saddleBOT
in an n×n grid, how many ways are there to fill the cells such that each row and...
jagged flare
ive seen alot of these types of questions and i want to know if theres a general solution
desert mantle
theres probably a gf based solution
desert mantle
hmm you could also view the matrix as an adjacency matrix of a bipartite graph
jagged flare
i have 0 clue on what you said
lemme search up the terms
ok i searched it up and the solution seems incredibly messy
yeah nvm then
thank you though
.solved
final saddleBOT
spring haven
theres probably a gf based solution
It's the coefficient of $x_1^m\dots x_n^m y_1^m \dots y_n^m$ in $\prod_{i,j=1}^n (1+x_iy_j)$
soft zealotBOT
kheer257
spring haven
not that this is very useful
desert mantle
yeah
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Available help channel!
hard blaze
If i get a vector addition problem that goes like:
Calculate the resultant vector of a person walking 12m East and then 15m North.
I know that the final answer will have a magnitute ( size in metres ) and direction ( angle in degrees ), and that I'm supposed to draw a triangle and then use pythagerous to calculate the unknown values.
Now this is what I know, but where I get confused is where am I supposed to draw the unknown angle? Because it can be in two different places.
final saddleBOT
If i get a vector addition problem that goes like:
**Calculate the resultant ve...
hard blaze
I hope the question im trying to ask is clear if not lemme draw a diagram
eternal saffron
If i get a vector addition problem that goes like:
**Calculate the resultant ve...
If it's given in cardinal direction, you probrably want the angle as a true bearing. Calculate the (clockwise!) angle between your resultants and the vector pointing north, and that's the true bearing.
hard blaze
If i get a vector addition problem that goes like:
**Calculate the resultant ve...
I'm bad at drawing with a mouse, but here i think is what I mean, inside the triangle I drew two unknown angles ( x ) which of those angles am I supposed to calculate in this question?
hard blaze
If it's given in cardinal direction, you probrably want the angle as a true bear...
Im gonna be honest I have no clue what you're tryna say, whats cardinal direction? like compass direction?
steep nest
Do you know the cosine rule?
eternal saffron
Really sorry I gotta go. Hope someone else can help you
steep nest
Law of cosines
hard blaze
Do you know the cosine rule?
yes adjacent/hypotenuse, but im not sure how that is relevant here.
hard blaze
Really sorry I gotta go. Hope someone else can help you
No worries, thank you for trying to help. Have a good day!
steep nest
so you know how to calculate the slanted side using pythogoras right
hard blaze
yeah a^2+b^2=c^2
steep nest
And what is our goal exactly
to calculate the angle between the 12m and the slanted line?
hard blaze
to calculate the angle between the 12m and the slanted line?
Yes but thats my question how am I supposed to know that is the correct angle I'm supposed to calculate, because there is another angle that touches the slanted line.
steep nest
They most definitely mean the angle from the 12m line, That's usually how the angle of a vector is calculated
it's called the argument of a vector
hard blaze
They most definitely mean the angle from the 12m line, That's usually how the an...
So in future questions am I just supposed to guess that the angle closest to the horizontal is the one I'm supposed to calculate? I thought there would be like a rule or something that I could follow.
steep nest
well, usually vectors are in a (x,y)-plane, not in "north south west east"
and the common convention is to go from the x-axis in a counterclockwise motion
to the vector
hard blaze
well, usually vectors are in a (x,y)-plane, not in "north south west east"
I see, and how would a question like this differ if we were using the xy plane?
steep nest
instead of east, we move 12 along the positive x-axis, and instead of north, we move 15 along the positive y axis
hard blaze
ahh and the angle im looking for is between those two lines correct?
steep nest
the angle for your vector, is the angle between the positive x-axis, and the vector, moving counterclockwise
really important ^
steep nest
Yes
hard blaze
okay I have one additonal question if you have the time
steep nest
Sure
hard blaze
Generally speaking for questions like these when I'm looking for a size and an angle as the answer, is the angle I'm looking for always opposite the side length I calculated using pythagerous?
I hope I worded that properly.
hard blaze
because if i drew a triangle here with a slanted line, the line would be direct opposite the angle im supposed to find
hard blaze
Could you give another practice question from your school?
Well I'm covering vectors and resultant forces in physics and im doing revision right now, Ill send you some of the examples from the notes im revising from give me a minute
steep nest
Thanks!
hard blaze
and also hard to simply explain
which is probably a good sign i shouldn't go too into this cause i already spent 30m on this topic 😭
steep nest
Hahahaha
steep nest
Yes alright great
hard blaze
but where do we draw/measure the angle from?
steep nest
when we say "moves 12 meters in the east direction" think of that as an arrow pointing to the right, with it's endpoint at 12
hard blaze
alright
steep nest
and then "Then moves 15 meters north" think of an arrow from the endpoint of the previous arroww 15 up
steep nest
and then the "resultant vector" is a vector from the origin 'so where you started' going straight to the endpoint of the 2nd arrow
steep nest
as shown here
hard blaze
as shown here
one sec let me draw it and u tell me if im right or not
steep nest
Sure!
eternal saffron
Really sorry I gotta go. Hope someone else can help you
eternal saffron
Im gonna be honest I have no clue what you're tryna say, whats cardinal directio...
yes compass direction
So like if you drew it on a plane, up would be north
and then you would calculate the angle between your resultant and a hypothetical north vector pointing straight up
hard blaze
@steep nest
sorry for the bad focus dunno what happened with my camera
one more question what is the direction of the hypotenuse in thsi triangle?
since i drew it from the orgin is it going up or down at an angle?
steep nest
vectors always start from the origin
Okay holdup Ill draw it for you
it's simpler to explain
hard blaze
and then you would calculate the angle between your resultant and a hypothetical...
like this?
hard blaze
it's simpler to explain
sounds good, I appreciate you taking the time to explain this to me btw.
hard blaze
vectors always start from the origin
ohhh i think i know what ur tryna say, since the vector started from the orgin i should also calculate the angle from the orgin right?
soft zealotBOT
steep nest
There we go
hard blaze
ahhh finally it all makes sense now
steep nest
Good!
hard blaze
Good!
wait one last question to cement my understanding
The direction of this vector is pointing upwards so why isn't it the angle drawn where i drew it with the black ink?
steep nest
They're trying to trick you by having the green arrow point the wrong way
hard blaze
or is it because it was drawn like this
hard blaze
They're trying to trick you by having the green arrow point the wrong way
they can do that?
I thought the arrow determinted the direction of the vector
by the way it was drawn i assumed the vector was drawn in the 2nd quadrant
steep nest
or is it because it was drawn like this
Well you drew it correctly here
Im gonna be honest I have no idea why the arrow is facing the wrong way
hard blaze
by the way it was drawn i assumed the vector was drawn in the 2nd quadrant
sorry not 2nd, 1st quadrant
hard blaze
Im gonna be honest I have no idea why the arrow is facing the wrong way
I think I need to switch resources this is the 2nd time these notes drew a wrong diagram that confused me
steep nest
Yeah I think so too
hard blaze
Thanks for your help, this has been a productive chat and my understanding of vectors is much more clear now.
I appreciate you @steep nest , have a good day!
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steep nest
That's good! you too!
final saddleBOT
Available help channel!
rain sentinel
find the first 3 nonzero terms in the series for secx
final saddleBOT
find the first 3 nonzero terms in the series for secx
drowsy epoch
what have u tried
rain sentinel
for this we would have to find the first second third ... derivative
of secx
or we could use the identity
im just wondering which method is easier
soft zealotBOT
rain sentinel
i meant like find f' and f'' and f'''
drowsy epoch
I was trying to see if u could derive the first few terms from cos(x) taylor series
rain sentinel
you can
drowsy epoch
thx
rain sentinel
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final saddleBOT
Available help channel!
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rugged merlin
<@&268886789983436800> mrbeast wants his mone :(
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tropic crest
strange pelican
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Available help channel!
rain sentinel
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rain sentinel
im not sure what to do for q2
drowsy epoch
im not sure what to do for q2
What do you get if you differentiate ln(1+x)
bro
I have had enough <@&268886789983436800>
final saddleBOT
@rain sentinel Has your question been resolved?
steady wraith
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steady wraith
so (a) was easy
(b) took me way longer than it should have because i didnt realise since it started at the origin x = 0 when t = 0 for some reason
or at least didnt feel confident thats what it implied
but this keeps being a problem where i cant do a question because they hide the details i need to do it
(c) was fine
(d) im confused with
so where does it say that x has to be > 0
because if it's the mean then i thought zm = (1/2d)*integral from d to -d of 1/v dx
but the limit is from d to 0, not from d to -d
and because of this it's 1/d not 1/2d
but i dont know why
also for (e)
i dont know what they want because it is 1 mark
but thats probably because i cant do (d) so it means i cant do (e) either
and also v it's just really weird
oh wait it's a projectile
that's why for (d)
WHY IS IT TAKING ME SO LONG TO REALISE THIS TF
if this were a real exam i would have wasted 30+ minutes on this one question
just because it's taking me 2 business days to notice details in the question
final saddleBOT
@steady wraith Has your question been resolved?
jagged comet
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sterile marsh
isn't this from ncert?
jagged comet
Yes u from cbse?
sterile marsh
Yes u from cbse?
mhm 11th
jagged comet
Damn which stream?
sterile marsh
Damn which stream?
pcm
sterile marsh
How to solve
well can you construct an equilateral triangle here?
jagged comet
Ohh yess
Yess
Yess
I gotta itt
Centroidd
2:1 ratio
Yes yes yes
Yesss
Tysm
sterile marsh
I gotta itt
yass
jagged comet
Tysmm
final saddleBOT
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jagged comet
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