#help-33
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<@&286206848099549185>
How many students do rock climbing?
@still temple Has your question been resolved?
Out of which how many are doing bush walkjng
@still temple Has your question been resolved?
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i needed to find f(x) and that s what i have so far but i dont know how to find C2
LoL
Is that exp?
yes
So
f'(ln x) = 1 exp 0, when 0< x ≤ 1
?

LoL
What is the Russian?
Here
"while"
and "and" in the side
Ahhhhh
Okkkkk
AH
I GOT IT
IM STUPID
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Closed by @slender moat
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Are odd square roots of negative numbers defined?
$\sqrt[2n+1]{-k} = -\sqrt[2n+1]{k}$
kheerii
Closed by @cloud kettle
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I'm trynna convert the Cartesian equation to the equation of a line but X=1 stuck what am I supposed to do with x=1 ?
Closed by @echo jolt
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!status
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Closed by @lusty scroll
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what am i doing wrong
expanded (y-2)^2
using special products (a-b)^2=a^2-2ab+b^2
idk how they ended up with y^2-4y+4
why is it not -2
Şêro
Oh OOPS
I JUST BROUGHT THE WHOLE "-2" WIT ME
its 2
Ur right
ty for clarification
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Closed by @forest orchid
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Is it true that all lines in space of the form x = ay = z lie in the same plane?
I believe it is true but I dont know how to prove it
Not rigorous proof, just an example proof
Well, x = z defines a plane
Yes
So, since all lines imagined lie in planes with the same normal vector and both pass through the same point, they must lie in the same plane. Therefore, any two lines of the form x = ay = z will lie in the same plane.
Is that a valid reason?
Well, it is simpler. Any point on the line satisfies x = z, and that always lies on the plane x = z
True
Thanks, thats an easier explanation
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Hiw do u do this
,rccw
do you know how to solve equations like this in general
This is going to be a long-ass solution 🔥
@slim quartz Has your question been resolved?
@slim quartz Has your question been resolved?
@slim quartz Has your question been resolved?
@slim quartz
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does anyone know how to move an ellipse? like the equation, how do you shift it left and right?
im tryna make a line that goes through (-20,0), (-15, 7.5), (-7.5, 9.8)
@eager moat Has your question been resolved?
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shouldn’t the original function of x/2 be x^2/2 where did the 4 come from?
Fyi x/2 = (1/2)x, where 1/2 is a constant that you can pull out, maybe doing it like that will help you see it
Because you just integrate x
sorry m quite dum at math lol could u perhaps show me the steps on a paper/ drawing on paint or smthng
Maybe instead, try taking the derivative of x²/2, and show that you don't get x/2
umm i saw the correction of this from a vid but the guy just couldn’t explain it properly since its easy for him ig
wait ill write what m talking about im a paper
No need, he is probably doing the same thing I am
What is the derivative of x²/2, btw?
okey i kept sketching and couldn’t see it
should be x if m not wrong
Right! The derivative is x. The derivative is not x/2
If the derivative of x²/2 is not x/2,
Then the integral of x/2 is not x²/2
.
But we can fix it.
If the derivative of x²/2 is x,
Then we can divide both by 2, and get that the derivative of x²/4 is x/2
Which is what we want, and gives us our integral
We have the integral power rule for this, though. That is, whenever you're integrating x^n, add 1 to the exponent, then divide by the new exponent.
jesus m so dum
i get it now
the 2 at first get canceled therefore its just x
my mistake was still writing x/2 even tho the 2 is gone
so x becomes x^2/2
yes that makes total sense
@modest lotus Has your question been resolved?
yes thanks guys btw
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Hey I have a question regarding circle geometry
Yes
I want to know how to solve this problem I don’t want the answer I just want to know how to start solving it bc I couldn’t grasp the information on how to do it in class today
Here is the problem
@rugged coral Has your question been resolved?
You can first calculate arc VY
and then calculate arc YX, and the. The rest should be done
Ping me if you need more help
@rugged coral Has your question been resolved?
Don't click on that link
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how can i simplify arctan(3)-arctan(1)?
so that it becomes arctan(p(x))
p(x)?
some function
eh?
sounds kind of strange even if formally valid
3x^2
it says express your answer in the form arctan(p)
show exact problem statement
Find the value of arctan(3)-arctan(1), expressing your answer in the form arctan q, where $q \in Q$
yeah, sorry
q is an integer
did you mean $q \in \bQ$
yeah
Q is not the set of integers, Q is the set of rational numbers
oh
anyway
ok
consider $\tan(\arctan(3) - \arctan(1))$
Ann
do you think you need special permission, signed and notarized in triplicate, to consider the tan of an expression as opposed to an expression itself?
if this were an equation, wouldn't u have to wrap tan on both sides
we will come back to arctan(3)-arctan(1) itself soon enough.
i already know the following steps
you might say we are letting theta := arctan(3) - arctan(1) and considering tan(theta), if that makes things easier for you.
$\tan(\arctan(3) - \arctan(1))=\tan(x)$
shouldn't it become something like this?
oh is it?
idk about "should" -- are you basing this on some feedback you received from your prof where they rejected a similarly phrased solution?
no, i looked at the answer key
but expressions are weirder than equations tbf
i prefer having something on the other side
.close
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<@&268886789983436800>
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oh
bot moment
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capital lambda
what topic is this btw, rarely seen capital lambda being used, especially for angles
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my answer is coming 1/2 while the correct answer is given 1
Show your work, and if possible, explain where you are stuck.
show the answer as well
which problem number
is this
that's a mistake. 1/2 is correct
i mean yes if you're allowed to use taylor series
Closed by @gaunt ferry
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are you allowed to use LH?
meaning of LH ?
lhopital
if its also called series expansion / taylor series then yes
lhopital is when you take the derivative of the top and bottom
oh then no
alright
sir said he will teach us in few days so i think this question wont use that method
yes i have tried to use the sin and cos but how what to put on log(1-x)
no
could you please tell ?
heavy
for the taylor series at x = 0
ok could you wait till i put this value and check my answer ?
yeah sure
thanks
here in denominator there won't be factorial ?
surprisingly no
(x/3)/x = 1/3
your expression simplifies
to -1/3! - x/4! - 1/3
and you can compute the limit of that
nice
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is this right?
(not a test btw)
circ. is 18
18/2 = 9 = r
H = 8
9^2 * 8 * 3.14 / 3 gave me a decimal
rounded to the tenths.
you round to the whole number
The numbers you plugged in look fine
I did.
,calc 9^2 * 8 * 3.14 / 3
Result:
678.24
Oh right the /3
doesn't look like it
I missed that too (I haven't slept today)
so 678? @odd turret
,calc 9^2 * 8 * 3.141592653589 / 3
Result:
678.58401317522
679?
you'd have to input pi into a calc. i'm guessing..
Most calculators have a specific button for pi
Just type pi
!show
Show your work, and if possible, explain where you are stuck.
96 * 7 / 3 = 32?
Looks like you forgot to *7
,calc 96 * 7 / 3
Result:
224

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Any help is appreciated
what do you have for the definition of probability?
Im gonna be honest here I have no idea what im doing with this question thats why i am asking for help lmao, so I couldn't tell you
@winged tree Has your question been resolved?
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I dont know which one is the proportional relationship and ping me if you know this.
@wary wolf Has your question been resolved?
<@&286206848099549185>
What do you know about proportional relationships?
if it multiples or add
Okay, so
If we go back to the definition, a proportional relationship is one where y=kx for some constant, k
alr
Basically, if they’re ‘off’ by a factor
So going back to your problem, which of those fit that definition?
y=10/3x+1/3
So, what is your line of reasoning of selecting that one?
it says 10/3x + 1/3 and if you add them up its 3 2/3
Okay
Let me try and rephrase
Y is proportional to x if y=kx, right?
So for y=10/3x+1/3, that +1/3 doesn’t match with the definition
Yeah, I understand
What I mean is that by adding that, we no longer have a proportional relationship
Does that make sense?
All we can say is that y=10/3x+1/3 is not a proportional relationship
oh so y=10/3x+1/3 is not a proptional relationship
is there still more non proportional relationship
Well, what do you think?
I think thats the only one
Let’s just go through them left to right:
Is the first one a proportional relationship?
yes
Great! What about the second one?
Well, we did that one already, how about the third?
proportional
Nice! And the last one?
non
So how many non-proportional relationships are there?
2
Looks like you got your answer then! Everything make sense?
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is 30b Dne, or des it jump down to the bottom graph
no
30b, since it's coming from the right, does it jump from the graph on the right to the graph on the left?
cause if it does that then the answer is 2
but if it cant jump to the other graph the answer would just be DNE
well yes, i was just a little confused by the term "jump"
u know wht im tryna say
since this is one function
lol im sorry
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Does the operation max(A) is linear?
I mean, if I define C = [x+y | x ϵ A ^ y ϵ B}, then max(C) = max(A) + max(B)?
What's A? A vector?
No, a set
Have you given any consideration to what the answer could be?
You could try to prove using induction
Uh, but I'm not working with naturals, these are real numbers sets
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I don’t understand the underlined part, how does it imply |an|r^n tends to 0 shouldn’t it just be anr^n tends to 0 without the absolute sign
an -> 0 <=> |an| -> 0
Oh wait yes this only applies to sequences with limits that are 0 right
Yes
Because then the circle is reduced to a point
(so in general an -> a is stronger than |an| -> |a|)
@ivory laurel Has your question been resolved?
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I need to find the surface area of this composite figure
didn't you ask this question yesterday
How many 2D objects can you split the composite figure into?
find the surface area of each of them
Profit
yep, I got help on the other one not this one
<@&268886789983436800> spam
ban when :/
Legend has it all mods are American and it may be they're all asleep
:// mods really be inactive in this server tho.....there was another fight 2h ago in the help channel
I don't believe it, but it has yet to be proven false since I asked 40 min ago
America 8 21 am now
At the latest, or would that be 9:21 ?
Googled
No like there 2 shapes there and the cube has 6 sides
2 solids, which makes for a lot more than 2 faces
8:21AM EST is latest, 5:21AM PST is earliest in continental US
Oh
Why P and not W for West ?
@lapis sable Has your question been resolved?
Pacific
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why isnt sqrt(a²+b²) simplified to a+b?
No
bruh
Its A^2 + B^2 + 2AB
$(a+b)^2=(a+b)(a+b)=a(a+b)+b(a+b)=a^2+ab+ab+b^2=$\fbox{$a^2+2ab+b^2$}. Therefore $(a+b)^2\neq a^2+b^2$ and hence $\sqrt{(a+b)^2}\neq\sqrt{a^2+b^2}\implies a+b\neq\sqrt{a^2+b^2}$
XxMrFancyu2xX
so sqrt((a+b)²=a+b
Yes
Yes because square root and square cancel out
am smart
You surely are
thx
.close
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Encrpyt
Yes, this is the correct answer
yes i do
Yeah but can you explain how it would be 65 ? i need some reassurance
Ok, so, now we insert the first value, that is x=0, y=5, what will be equation in that case
^
Now, we got equation as $y = ax + 5$
Encrpyt
Now, can you insert y=125 and x=2, find what is 'a'.
@snow bison Has your question been resolved?
ohh
60
omggg
125=(60)(2)+5
Great, now can you tell me value of y when x=1 in the equation y=60x +5
65 ?
Yes you got it!
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just need help rearranging an equation
T = 2π * √(I / (m * g * d^2))
so rearranging for my g = 4π^2 * (I / (m * s))
where s is slope
Where slope is Delta_T^2/Delta_d
@slender junco Has your question been resolved?
what are you asking here?
@slender junco Has your question been resolved?
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how is the answer d?
@native tapir Has your question been resolved?
.close
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Why is he ticking the equation on the left?
2 < 3 is not in the triangle.
and why is he putting a big X on sections (he said something wont be there) but idk why he crossed it.
He used the point (1, 2) in the first equation
Because he's plugging in that coordinate, and confirmed it for the first inequality that (1, 2) satisfies it but for the others, it doesn't work
The inequality
How do ik if it satisfies the inequality
If it's a true statement
If it satisfies the inequality
Yes
Alr
Plug in the coordinates (1, 2) into the first inequality
And then why is he crossing out the other regions and sides
You have 2 < 2(1) + 1 which is 2 < 3, that's true so (1, 2) satisfies the inequality
You're picking a point from each region and plugging it into each given inequality
If it fails at least 1 inequality then that region does not satisfy all three regions
If it fails at least 1 inequality
You plug it into each inequality, and the first one that fails, you can stop
Because if it fails one then that region does not satisfy all three inequality
it failed it
why shouldnt it satisfy all 3 regions
i picked one region
I picked that region
Typo
Meant to say inequality
Because if it fails one then that region does not satisfy all three inequality
Your goal is to find the region that satisfies all 3 inequalities
You did (-4, 4) first, because it failed the first inequality, that means that region will not satisfy all three inequalities
No
No
wdym encompassed
Google it
The lines are the borders
No
Then tell me where.
Yes that's 4 of the many existing regions
No
<@&286206848099549185>
You can have as many regions as you want
I need someone to better explain.
There's not a set limit
No offence your explanation is confusing as hell to understand.
Then understand it, it's not complex
Your doing everything but answering my question
You asked
So shouldnt it be 3 invalid?
Anyways ill wait for someone else go have some tea.
I'm saying no because you can have 10 regions if you wanted
And only certain ones will work
.close
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.reopen
✅
Don't be a prick
A video revising the techniques and strategies for completing questions on graphical inequalities & shaded regions (Higher Only)
This video is part of the Inequalities module in GCSE maths, see my other videos below to continue with the series focussed on Inequalities.
Download the Worksheet: https://thegcsemathstutor.co.uk/lesson-home/
Usefu...
If you look at the video, notice this, there are 7 regions, but only one region satisfies all three inequalities, the green shaded part
if you're confused, ask a question and explain what you don't understand. saying this is not useful
I already started watching the video before u linked it m8
stop reopening this ticket its solved.
.close
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can anyone explain squaring the ceiling function? Do I just square the inner terms?
think of it as two operations in one
ceiling(3.1) = 4
ok so a composition
4^2 = 16
so in this case it'd be, take the ceiling value and square it ?
thank you!
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hey so apparently you can raise both sides of an equation to the power of 2
you're asking why x = y implies x^2 = y^2 ?
yeah
oh well
now it's obvious
hm
but does this mean you can only raise to power of 2 if x > 0 and y > 0?
x=y => x²=y²
but x²=y² does not imply x = y
madmike
so uhh wolframalpha says the real solutions are this
I am not sure how to get there
because I'd assume xy = 0 is true if either x=0 or y=0
but then why not x < 0
or y < 0
you're squaring the above equation so you're getting more solutions then you're supposed to have for the original equation
y=0 and x<0 won't satisfy above equation because the output of sqrt function is positive
same is true for y<0
ah yeah I see ...
how do you catch stuff like this?
I had no idea
thought I just need to solve for xy and then I'd get the solution
Please note that sqrt(x²)=|x| (look at my about ^_^)
And hence putting y = 0 gives |x|=x which is true only for x>0
ohhhh
I wouldn't have caught it either if I was giving some test my marks would've been deducted because of that lol
But since you asked it why it isn't true I had to obviously use my mind
ok tricky question then l0l
hm
tbh this rly confuses me
so squaring both sides is not a safe operation l0l
No, because x² is an not an injective function
you'll have to check all the solutions manually after getting to the answer
ahhhh that makes sense
not injective means one input can be mapped to multiple outputs so when we square we will get some solutions that might not work
Yes
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draw a triangle
But somehow I didn’t get the right answer
!show
Show your work, and if possible, explain where you are stuck.
So.. I got sin = 5/rad34
how did you get that
sec is 1/cos
Closed by @loud hamlet
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Hi
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
<@&286206848099549185>
Draw a diagram and send a labelled pic
nope, 3m is the length of the ladder
I know
not the height that the ladder reaches when tilted
the distance between the two extremities of an object
damn I’m not that smart I’m only year 9
my pleasure'
Your very smart
thanks.............
!nosols
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
ohk great didnt knew
Fuck off you stupid bot
Also probably a ' ChatGPT answer '
ok i still dont recommend you using less of those words you know it makes your personality less likable by people
no dont sorry
Don’t have it
oh great
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This will probably be a hard one to explain (abstract set theory)
So we have classes that are sets and classes that aren't sets right? (I'm talking about ZFC here) There are classes that aren't sets like the sets of all sets or the sets of all tiny sets that are known to create paradoxes if one consider them a set. But are all classes that are not sets create paradoxes? If we can't answer the question, to what other question in math the provlem equivalent to?
Bro I already opened it. I dont know the answer to your question but feel free to move it to another place
delete your message please
@cyan radish Has your question been resolved?
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What do I do now
there's no question
dividing what ? your handwriting is all over
what are you solving for?
it'd be a lot faster if you just showed the question with instructions
instead of going back and forth asking clarifying question
no i don't know
this question doesn't make sense on its own
It's not a question
Its just my query
@ocean marsh Has your question been resolved?
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Türk biri çözse daha iyi olur
@urban grail Has your question been resolved?
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Quite easy little thing yet I am paranoid
Did I do everything correct
Basically task is to say if these logical operations have no contradictions
It has no contradictions right?
Oh wait
What about A/B?
I am mega stupid
Yes
2 is not supposed to not exist
How stupid is that
Close
.close
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is this not 7pi/6
what makes you think that?
I do not see any evidence for that in the image you've given
wdym
thats true
i just looked at the line between the points and it went through the middle of the circle
so how do i advance
if you are 100% sure of this, then ask your teacher
no teacher, khan academy
then this is not true
each part is unrelated
choose the angle in the correct eighth
wdym
split the unit circle into eighths
figure out which of the four angles lies in the eighth containing B
it is in 5/8
i mean it is in number 5 of the 8
yes
yeah you are right
nice
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If a function is defined wrongly, that is I get $$Range \nsubseteq Codomain$$, is it still a function?
Calamity
no
Alright, thankyou!
if an object doesn't satisfy the function definition, it is not a function
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so I will explain the context first, he called it the magical square and u basically need to make a square where every row column and diagonal sums up to 15 and he did it by the making the set of sets which has the numbers that sums up to 15 and the question was to fill in the magical square
he said the letter e has 4 lines through it so there must be a number in the sets of set which occurs 4 times and after that he did 1 I also understood that because that must be a nubmer that occurs 2 times
then he went to the number 8 and it needs to occur 3 times but also it has to be within a set of the number 1
and I don't understand why it had to be in the set of number 1
@barren lance Has your question been resolved?
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Need help
AM>=GM
do not use chatgpt, it cannot do math
k
You're better off asking a monkey for math help
AM - GM is for all positive numbers not just integers
Are integers not numbers
not just integers
I still fail to understand the point
the answer that AM GM gives is third root of 144
You can just take the integral part of the third root
all of them need to be integers
The AM-GM inequality will just give you a bound lol
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I'm having a brain fart, I forgot how to bound this type of integral :
$\int_a ^b x^{\alpha -1} e^{-x} \lvert \phi_n (x) - \phi(x) \rvert dx$ with $\phi_n \to \phi$ uniformely
Herels
if someone can help me remember
@distant peak Has your question been resolved?
are a and b positive ?
whatever that doesn't matter (though if [a, b] contains 0 then it's better to have alpha < 0)
yes they are
it doesnt contain 0
alright
then I guess you can say $$\int_a^b x^{\alpha -1} e^{-x} \lvert \phi_n (x) - \phi(x) \rvert dx \leq ||\phi_n - \phi||_{\infty} \int_a^b x^{\alpha-1} e^{-x} dx$$
Gio'
you mean an extra (b - a) factor?
yea
here we're still integrating something which is not 1 so it doesn't appear
Since you would need to bound gamma(alpha) there too nah ?
we're just using the fact that if f <= g then \int_a^b f <= \int_a^b g
it is gamma
yes of course but we can bound this by gamma(alpha) since x^alpha-1 e^-x is positive
ah yes true
I've reduced the bounds to a and b cuz I wanted to bound an integral from 0 to inf
so I made the supposition that we work on a compact set
hmm right
well if the integral converges then this rule also applies (the limit preserves large inequalities)
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np :)
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is there something like peano's axioms but for rationals or maybe even reals?
maybe try asking in#foundations
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the channel is closed for me
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How do I become an expert at integrals, I know I need to practice so Im wondering whether someone has a file that has a list of integrals from easy to hard and any tips are appreciated
Bluepenredpen video marathon
Where do I find that
youtube
Oh this 5 hour one
This comprehensive calculus video covers 100 challenging integrals, providing detailed solutions, tips, and tricks for each one. From integration by parts to trigonometric integrals and more, this video covers all the integration techniques you need to know. Whether you're a calculus student looking to improve your skills or a math enthusiast se...
have fun
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Let $f: \mathbb{R}\to\mathbb{R}$ be a function as $f(x) = (x-1)(x+2)(x-3)(x-6)-100$. If $g(x)$ is a polynomial of degree $\le 3$ such that $\int \frac{g(x)}{f(x)} dx$ does not contain any logarithm function and $g(-2) = 10$. Then the minimum value of $f(x)$ is
lmaowhat
All I was able to do till now was factorize it
$$t = (x-1)(x-3) = x^2-4x+3$$
Then $$(x-1)(x+2)(x-3)(x-6)-100 = t(t-15)-100 = t^2-15t-100$$
$$= (t-20)(t+5) = (x^2-4x-17)(x^2-4x+8)$$
lmaowhat
@bitter tulip Has your question been resolved?
<@&286206848099549185>
@bitter tulip Has your question been resolved?
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@marble glacier Has your question been resolved?
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I don't understand how my teacher rewrites the expressions, such as:
3 - 2 * ( 8 - 2 * 3 ) = -1 * 8 + 3 * 3
and the rest
generally just how he rewrites all the expressions
lol isn't it wrong
