the negation of $\exists x(P(x))$ is $\forall x(\neg P(x))$. $\$
the negation of $\forall x(P(x))$ is $\exists x(\neg P(x))$.
#help-38
nova spire
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rafilou is not not born in 2003
quick knoll
but my idea was right?
nova spire
but my idea was right?
well I'm not sure
nova spire
**rafilou is not not born in 2003**
if that's what you meant then ok
otherwise some clarification was needed
nova spire
so for example the negation of $\forall x\in \bR, \exists y\in \bN, x < y$ is $\exists x\in \bR, \forall y\in \bN, x \geq y$
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rafilou is not not born in 2003
quick knoll
**rafilou is not not born in 2003**
ahh the thing with < and >= do sense jup > and <=
thx π I got it
quick knoll
I copy paste ur fragment to learn it
quick knoll
forget my mit u write it write thx
and another question about roots
why there is just 1 result
My old math teamcher say that qroot(9)= 3 and -3
but now I learned that only the positive result is right
cause a function only have 1 result
and now I get trouble und my brainππ΅βπ«
but its not important ty for help
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viscid flower
dark summit
Binomial probability formula.
N 7, k 3, p 0.5
The f you on about
You want him to count manually?
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icy hedge
Can someone help me with question 10b?
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Can someone help me with question 10b?
icy hedge
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fresh pendant
How is this yielded by Taylor?
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How is this yielded by Taylor?
zinc ginkgo
How is this yielded by Taylor?
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somber oxide
Hey i have a question,
How many route exist if the right steps are maximum two next to each other( you can go up ad many as you want) in a 6x6 grid? You start from the bottom left and the finnish is on the top right.
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Hey i have a question,
How many route exist if the right steps are maximum two n...
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errant vault
Can anyone help me with a physics problem
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Can anyone help me with a physics problem
cosmic vault
depends
spiral ocean
angular momentum is the same throughout the axis, no?
hidden dew
Oh god
solid kilnBOT
k
spiral ocean
i think u can use that to figure the rest?
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sand gull
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wraith dragon
Shift + cos?
Yes
sand gull
Why does it say cos^-1?
wraith dragon
Why does it say cos^-1?
Both are the same
sand gull
What?
wraith dragon
Arccos =cos^-1
wraith dragon
Its correct I'm getting the same answer
sand gull
Ok so effectively
Arccos of 0.965 is 15.203?
wraith dragon
Ok so effectively
Arccos of 0.965 is 15.203?
Yeah
sand gull
Ok thx
gusty plank
prove that three points a, b and c in a plane are collinear if and only if this determinant is zero
hallow wolf
prove that three points a, b and c in a plane are collinear if and only if this ...
area
gusty plank
i managed to do if a, b and c are collinear then the determinant is zero, having trouble doing if the determinant is zero then the points are collinear
hallow wolf
what is the area of the triangle formed by 3 points using determinants in 2d plane?
wait whats a bar
conjugate?
hallow wolf
prove that three points a, b and c in a plane are collinear if and only if this ...
ok yeah
so like
just try using $a= r_a e^{i \theta_a}$
solid kilnBOT
benadryl
gusty plank
i think we can't use that yet lol
gusty plank
professor hasn't introduced it yet
gusty plank
he did introduce the polar form with sine and cosine but not with euler's number
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subtle beacon
Had to rationalize the numerator and idrk how to do that. Anyone able to give me some tips?
limpid dawn
conjugate
digital musk
multiply the numerator and denominator with the conjugate
That is change the negative sign in between the two roots to +
a + b -> a - b
a - b -> a + b
subtle beacon
And then I just simplify the bottom if needed and Iβm done?
digital musk
yep, the bottom βhβ should cancel out the h term in the numerator along with the 2x - 2x and 1 - 1 terms
your answer should be 2
wait let me double check that
yep
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fair solar
Hello is this right?
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Hello is this right?
fair solar
umbral dragon
First 4 columns seem good, I donβt think the 5ths is correct
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mellow fox
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mellow fox
Hello, please could someone check my method for this question?
First of all I changed it to (3-2x)^1/2
And then I made it so 3^1/2(1-2x)^1/2
Am I supposed to divide 2x by 3 after Iβve taken it out? I think I forgot to do that
<@&286206848099549185>
Wait
Itβs to the power of -1
Iβm an idiot
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fierce knoll
How do I continue reducing the matrix at the bottom to rref?
snow plover
the row with 0,0,-6 can be used to get rid of the 20 in the top row and the final 1 in the second row
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rustic nest
Find the exact surface area by rotating about the x-axis. $x = \frac{1}{3}(y^2+2)^\frac{3}{2}, 1 <= y <= 2$
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wakamole
rustic nest
$\int_1^2 2\pi y \sqrt(1+y(y^2+2)^\frac{1}{2}) dy$
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wakamole
rustic nest
$\int_1^2 2\pi y \sqrt(y^4+2y^2+1) dy$
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wakamole
rustic nest
is it this $\int_1^2 2\pi y \sqrt(y^2+1) dy$
or this -> $\int_1^2 2\pi \frac{1}{3}(y^2+2)^\frac{3}{2}\sqrt(y^2+1) dy$
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rustic nest
<@&286206848099549185>
modern laurel
<@&286206848099549185>
what do you need help with?
did you take the derivative of your function first?
to put into the surface area "formula"
rustic nest
did you take the derivative of your function first?
yes i di
did that
then i got the perfect square
but
i am not sure if i am supposed to use 2pi y
or 2pi f(y)
modern laurel
you're rotating around the x axis, so your radius will be y
rustic nest
**wakamole**
so this one
rustic nest
**wakamole**
not this
modern laurel
**wakamole**
yeah
empty wyvern
Can sum1 explain why dis is -1 < x < 1, and NOT 0 < x < 1. I thought there were no square roots of negative numbers??
empty wyvern
I don't understand then, if I were to solve this say x^2 = 1, I'd have to square root both sides no?
empty wyvern
So is it just the right hand of da equation is always +-, in the case of x^2?
Like is it x^2 = +- 1, n then I square root da sides n solve for each case
empty wyvern
Ohhhhhhhhhhhh
Okay THAT makes sense
Because if it were x^2 = +- 1, and da 1 was negative, then we can't square root it yeah?
livid thunder
correct
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sweet bramble
I need to determine whether some binary operation is associative, commutative, both, or neither on some set; here are some problems im having trouble with:
sweet bramble
The composition of functions on a set of injective functions: S -> S,
The composition of functions on a set of surjective functions: S -> S,
and the composition of functions on a set of injective or surjective functions: S -> S (the exercise says that this last question is a "trap" and to be careful)
Not sure how to determine this intuitively or algebraically
sweet bramble
Sorry to bother but <@&286206848099549185>
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short cave
Consider $P(z)=z^2-rz+1$ where $|r| < 2$ with roots $\alpha$ and $\beta$. \newline
Show that $|\alpha|=|\beta|=1$.
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BOHO
short cave
no clue what to do here after getting sum and product of roots results
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@short cave Has your question been resolved?
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short cave
<@&286206848099549185>
uncut raptor
@short cave
wraith hinge
@short cave come
terse fjord
does you know what abs is the distance from the origin?
uncut raptor
no clue what to do here after getting sum and product of roots results
Now from the sum of roots, we'll denote it with s
uncut raptor
Guys is that in university?
highschool
terse fjord
no, it is just precalculus
terse fjord
highschool
well, I mean technically to understand eular you'd probably need to be at least in an advanced calculus course.
wraith hinge
highschool
π
uncut raptor
well, I mean technically to understand eular you'd probably need to be at least ...
Oh yeah
wraith hinge
well, I mean technically to understand eular you'd probably need to be at least ...
I still in prep 3
terse fjord
No clue what prep 3 means
wraith hinge
π₯²
uncut raptor
no clue what to do here after getting sum and product of roots results
What do you get from using the formulas, please write them down
uncut raptor
Oh I see, I think I'll let other helpers handle this then, sorry
terse fjord
do we just use the quadratic formula?
not sure what the hell is going on π
and I do complex analysis
wraith hinge
I still didn't learn that π
terse fjord
lets just blindly just the quadratic formula
uncut raptor
Observe how $z^{-1} = \frac{\overline{z}}{|z|^2}$
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Catgod
uncut raptor
This might help I think
terse fjord
Observe how $z^{-1} = \frac{\overline{z}}{|z|^2}$
my brother in christ I don't think we are using complex conjugets
I can't spell π
uncut raptor
my brother in christ I don't think we are using complex conjugets
We can simplify 1/alpha using that ig
dusty sleet
If $|r| < 2$ it means that $|r|^2 < 4$, or equivalently $r^2 < 4$. Therefore, you can write $\sqrt{r^2 - 4}$ as $i\sqrt{4 - rΒ²}$. Now you can write the solution splitting real and imaginary part, and show that the modulus is indeed 1
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Alberto Z.
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copper compass
are all three of these long division? im a bit confused on these
spring summit
yes
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still rose
are all three of these long division? im a bit confused on these
you use substitutution method for the first two
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cerulean quail
i understand the question and know it is true, but how can i "prove" this, what do i need to do?
willow urchin
i understand the question and know it is true, but how can i "prove" this, what ...
use this fact to simplify calculations
given sets $S$ and $T$, we have $\Span(S)=\Span(T)$ if and only if $S\ss\Span(T)$ and $T\ss\Span(S)$
solid kilnBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
cerulean quail
Would this half of the proof be correct? @willow urchin
willow urchin
did you see and understand what i posted
willow urchin
your notation is all over the place, lets start slow
first lets define $S=\brc{a,b}$ and $T=\brc{b,c}$
solid kilnBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
cerulean quail
your notation is all over the place, lets start slow
π
cerulean quail
**π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€**
yes
willow urchin
using my fact, do you agree we should show $S\ss\Span(T)$ and $T\ss\Span(S)$?
solid kilnBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
cerulean quail
yes
willow urchin
lets show $S\ss\Span(T)$
solid kilnBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
willow urchin
how do we do that?
willow urchin
you just wrote out that statement but with bad notation
cerulean quail
and span T every linear combination of (b,c)
willow urchin
**π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€**
but i want you to break down what this means
cerulean quail
that every vector in S is a subset of the linear combinations of vector T
so vector S is a subset of c1 x v1 + c2 x v2
cerulean quail
what do u mean?
willow urchin
the right phrasing is: every vector in S is a linear combination of vectors in T
cerulean quail
ohh
willow urchin
"subset" is only used to describe two sets, namely when every element of one set is an element of the other
cerulean quail
the right phrasing is: every vector in S is a linear combination of vectors in T
yeah okay this definition makes sense
willow urchin
say $X=\brc{1,2}$ and $Y=\brc{1,2,3}$, then we can say $X$ is a subset of $Y$
solid kilnBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
willow urchin
the right phrasing is: every vector in S is a linear combination of vectors in T
ok now lets break this down
you agree this means showing a and b are linear combinations of b and c?
cerulean quail
yes
willow urchin
how do we do that
focus on a first
the numbers are easy enough without paper @cerulean quail
cerulean quail
ohh
play with the scalars of b and c until you get vector a?
so 1 times b - 1 times c
that gives a
willow urchin
yes
solid kilnBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
willow urchin
thats it
willow urchin
you explicitly demonstrated the linear combinations, thats exactly what we need
cerulean quail
and then the other half of the proof but yeah basically the same thing
willow urchin
now we can conclude $S\ss\Span(T)$
solid kilnBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
willow urchin
then we need to show $T\ss\Span(S)$
solid kilnBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
willow urchin
and yeah its very similar work
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willow urchin
np!
cerulean quail
i am so sorry to bother u again but would my notation be correct this time? @willow urchin
willow urchin
i see you tried using my fact but not quite successfully
be cleaner and simpler when writing linear combinations
tender thistle
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misty aurora
Translated: Show that maximally finite prime numbers can exists, which can be seen as random numbers (Kolmogorov-Complexity). Hint: You can use the prime number theorem
Def. for random numbers 2.19: K(n) = K(Binary(n)) >= ceil(log basis 2 (n + 1)) - 1
misty aurora
I am stuck and don't find the direction for the proof, can you help me?
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sacred socket
What is the best way to bound this to solve the limit using the squeeze theorem
misty aurora
upper bound: (2n^2 - 1)/(2n^2 + 1) <= (2n^2 - 1) / (2n^2) <= (2n^2) / (2n^2) = 1
lower bound can't see it rn
sacred socket
Yeah me too
misty aurora
you can't use lhopital?
sacred socket
Yeah
Idk if we allowed to use this? I think we allowed to assume that we know 1/n converges to 0
limpid dawn
Idk if we allowed to use this? I think we allowed to assume that we know 1/n con...
good idea
lhopital overkill
sacred socket
But actually that doesn't bound it below. It is equal to that
limpid dawn
But actually that doesn't bound it below. It is **equal** to that
do you have a start value for n?
limpid dawn
e.g. n is natural
sacred socket
do you have a start value for n?
Well it is a natural number. But all the question asked was solve using squeeze theorem
sacred socket
squeeze theorem, for the limit towards inf?
Yeah
sacred socket
Thats over kill too
Well the question asked for it. It was just an exercise to practice squeeze theorem
misty aurora
I think yours is right
limpid dawn
Well the question asked for it. It was just an exercise to practice squeeze theo...
Ah ok understandble
limpid dawn
What is the best way to bound this to solve the limit using the squeeze theorem
Theoretically you could try to make the denominator bigger like 2nΒ²+2 for example
limpid dawn
An upper bound you can remove the +1 simply from the denominator
sacred socket
Yeah but it is the lowerbound I am looking for
limpid dawn
I suggested one
misty aurora
Idk if we allowed to use this? I think we allowed to assume that we know 1/n con...
tbis one is great
sacred socket
Theoretically you could try to make the denominator bigger like 2nΒ²+2 for exampl...
I'm not sure how this become helpful
limpid dawn
,, \frac{2n^2-1}{2n^2+2} \leq \frac{2n^2-1}{2n^2+1} \leq \frac{2n^2-1}{2n^2}
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bacc the sigmaππ€
limpid dawn
If you are required to use squeeze theorem
misty aurora
we have the upper bound already
misty aurora
upper bound: (2n^2 - 1)/(2n^2 + 1) <= (2n^2 - 1) / (2n^2) <= (2n^2) / (2n^2) = 1...
.
limpid dawn
And then calculate the limit from the upper/lower bound
Since they are the same by the squeeze theorem the middle goes also to 1
Can also use 1 as upper bound
sacred socket
Sure that works, but If I could solve the limit on the left, with the same logic I could solve the limit in the middle. I think I am looking for something more simplified if possible
limpid dawn
Yea but they want you to use squeeze theorem so thats legit
glass locust
i dont know whats going on for the 3rd line
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i dont know whats going on for the 3rd line
glass locust
2nd line i get ur doing 14 mod 5 which is -1 ^ 768 and that is even so = 1
but line 3 why is the 5 turning into a -2?
glass locust
oh
how would i know when i have to do something the the exponent
like for the first like why wouldnt it be 7 mod 5 = 2?
or do we need a negative
wraith hinge
I thought about this for a while and
I am terribly lacking in modular arithmetic practice
glass locust
and how did they get -2 into 8 ?
wraith hinge
But I think it's just a question of what's most practical
glass locust
-2^4?
wraith hinge
That would be 16
I got no idea what they did
All I could answer was your first question
I really don't know what kinda modular arithmetic magic is going on here
glass locust
its 2 * (((-2)^3)^1608) but how did they get a positive 8 and not a negative
and how did they get 2 mod 7 out of that
trail ingot
8 = 1 mod 7
trail ingot
8 = 1 mod 7
oh that wasnβt the question
spiral kettle
and then break it up into (-1)^even x 8^power
i think whoever wrote this was correct on accident though
glass locust
(((-2)^3)^1608) so how do i make it look like that
oh
rip
its from the official midterm practice
spiral kettle
they might have accidentally thought that (-2)^3 was 8, but it doesnβt matter in the end
because what youβre left with is some even power of (-2)^3
spiral kettle
(((-2)^3)^1608) so how do i make it look like that
this comes from exponent rules after doing the first step on line 3
(a^b)^c = a^(bc)
spiral kettle
cuz now its -8^1608
yes i agree, and -8 is -1 mod 7
glass locust
wait did they do 2 (-8) to get 16 mod 7 which is 2?
spiral kettle
wait did they do 2 (-8) to get 16 mod 7 which is 2?
no
they simplified 8^exponent first
like at this point theyβve already skipped steps so idk what was going on in their mind when they said this
but if youβre fine with getting to 2β’8^1608, then 8 is just 1 mod 7
so itβs the same as 2β’1^1608
glass locust
aight
i guess i just gotta show some random work on the test for partial then
similar to this
spiral kettle
itβs going through order of operations really
and simplifying it so that itβs not a pain along the way
so you make as many reductions as possible (best case scenario is that something becomes a 1 or a 0 and then life gets a lot easier)
this is really the core of modular arithmetic and why itβs so useful in math
so the question here is just one example of βcan you get something to reduce to a 1β
glass locust
for this part
its is 5k = 7L mod 35
from prevous work
how did they get 10 and 7
cuz its 1+7L since the modulo was 1 not 2
spiral kettle
a number thatβs 1 mod 5 and 2 mod 7
glass locust
yea but howd they get 10 and 7 from that
spiral kettle
solve the equation mod 7 first, 5k = 1 so k has to be 3 mod 7, and the equation mod 5 yields l = 2 mod 5
so you can try combinations of k and l where k is 3 mod 7 and l is 2 mod 5 and see what works
there arenβt very many combinations of those
spiral kettle
np good luck with the exam
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earnest nymph
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wraith hinge
ah
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wraith hinge
hey can someone check my equivalency expression
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hey can someone check my equivalency expression
wraith hinge
why minus log b z
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raw heart
hi, can someone help with this question?
The speed of a boat in calm water is 50 km/h. If it sails in the opposite direction of the current, it needs 30 min more time to complete the road than if it sails in the direction of the flow. Find the speed of the river current. (kind of a physics question, but its for extra credit in math)
lilac flame
!show
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trail ingot
hi, can someone help with this question?
The speed of a boat in calm water is 5...
your pfp is so cute
lilac flame
juicy
raw heart
i dont know if its right up to here tbh
raw heart
your pfp is so cute
aww thanks yours too
raw heart
bc i dont know how to proceed haha
lilac flame
wait are you not given l
lilac flame
bc i dont know how to proceed haha
u just need to solve for x?
raw heart
wait are you not given l
yes its not given
raw heart
u just need to solve for x?
yes
raw heart
did that but it just leads to a quadratic equation, n my teacher said it just had to do with algebraic fractions, so i jus think i have laid the equation wrong
lilac flame
well u did start with algebraic fractions
raw heart
yeah but im pretty sure its supposed to have a pretty short answer (because she gave it to us in class and gave us like 15 min, but bc no one solved it, she told us that we can solve it at home if we want) , but its just extra anyway, so ill just try a lil more n even if i dont solve it its ok
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untold shard
We know it works for specific cases and can verify those quiet easily but we're kinda stumped on what elementary matrices to pick, I guess in the sense like....if we have some mxn matrix and swap R1 and R2, then what about swapping r3 and r4 for...any general row m and n; idk we can't figure out how to generalize the idea
untold shard
spiral kettle
helo
untold shard
Hi smay
left oriole
We know it works for specific cases and can verify those quiet easily but we're ...
if you want to swap row i and j of A, let E be the m x m matrix which is the identity matrix with rows i and j swapped
untold shard
if you want to swap row i and j of A, let E be the m x m matrix which is the ide...
Ahh okay so just if we want to swap R1 and R2 in A, multiply by I_m with r1 and r2 swapped, okay, that makes sense
left oriole
yep
and for the other two types of elementary row operations there are simple E matrices you can use
untold shard
I think I got more hung up on the matrix notation than the actual problem π€¦ββοΈ
untold shard
and for the other two types of elementary row operations there are simple E matr...
Ahh okay
left oriole
then if you want to do all of the row operations, you have corresponding matrices E1, E2, E3, ... Ek
if you want to do them in order then your E becomes their product in the reverse order
E = Ek ... E2 E1
left oriole
yw
untold shard
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vestal fiber
can someone help me on how to get the derivative of $5^5x$
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Frank
vagrant prism
can someone help me on how to get the derivative of $5^5x$
$5^5 x$ or $5^{5x}$
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artemetra
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Frank
vestal fiber
chain rule
how did you know to use chain rule
because I have only used it for functions like f(g(x))
vagrant prism
because we have exponentiation and multiplying by 5
vagrant prism
because I have only used it for functions like f(g(x))
f(x) = 5^x
g(x) = 5x
f(g(x)) = 5^(5x)
vestal fiber
f(x) = 5^x
g(x) = 5x
why is f(x) not 5 and why is it 5^x?
vagrant prism
the x might be confusing but what composition of functions really means is that we replace all x's in the function's definition with what is passed to the function
so $f(g(x)) = 5^{g(x)} = 5^{5x}$
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artemetra
vagrant prism
why is f(x) not 5 and why is it 5^x?
f is your "exponentiate by 5" function
i hope this makes some sense
vestal fiber
i hope this makes some sense
I am still thinking but I don';t think I am gonna udnerstand why it is 5^x
vagrant prism
do you have any idea what it should be instead?
vestal fiber
I thought f(x) = 5
g(x) = 5x
vagrant prism
which is 25x
vagrant prism
precisely
vagrant prism
vestal fiber
f = 5^x
f`= 5^x ln(5)
g = 5x
g` = 5
wait so how do I put it like f`(g(x))? @vagrant prism
what does the g(x) stand for in f`
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artemetra
vagrant prism
replace π with g(x)
vestal fiber
$5^{5x} ln(5) 5$
vagrant prism
there you go
solid kilnBOT
Frank
vagrant prism
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latent jay
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latent jay
hi, wdym by 2,5
no itβs sqrt (2,5)
latent jay
Any doubts?
letβs see
little glen
no itβs sqrt (2,5)
sqrt(5/2) right?
latent jay
sqrt(5/2) right?
yep
little glen
okay but is it legal to write as you did
yeah whats wrong w it
latent jay
if a^b = a^c it implies b = c
where do you write by the way?
latent jay
very nice
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cursive leaf
what's a practical example of a set of points like that? Also, I understand that these continuous curves have to be drawn in the same plane only?
zinc ginkgo
define "practical"
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cursive leaf
A concrete example of a line / shape / polygon that satisfies the lemma assumptions
cursive leaf
I guess a circle would work with any point inside of it. or any polygon for that matter. I'm guessing that we do only consider arcs drawn within R^2 ONLY, otherwise I can't think of a way to staisfy those conditins
not sure about a line segment
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digital hull
Calculate an approximate value of each integral with an error less than 10^-5
digital hull
!status
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5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
What I did was find the Taylor polynomial of that (since the unit consists of that) but I barely get to the error I want when X is raised to the 3000th power, which is not very reasonable to write on paper.
Can you think of any way I could approach the problem?
little glen
Calculate an approximate value of each integral with an error less than 10^-5
Hi, still need?
digital hull
Hi, still need?
Yes please :)
digital hull
Well do you know the identity of x^3 + y^3
It doesn't sound familiar to me, but tell me and maybe it's something I've given
little glen
digital hull
Ah, yes yes, it is just a common factor of a binomial
digital hull
then do you know how you can solve an integral of that type?
Wait a minute while I try to apply it to see if I can figure out how to do it, and if I can't, I'll let you know.
digital hull
then do you know how you can solve an integral of that type?
Is it using partial fractions?
little glen
yeah
digital hull
yeah
Isn't there a way to do it where I can use the Taylor polynomial? Since using that method you tell me, I would get an exact result, however in the exercise it only asks for an approximation with a small error.
little glen
Isn't there a way to do it where I can use the Taylor polynomial? Since using th...
i dunno about that, sorry
i mean why wouldn't you want an exact result
digital hull
i dunno about that, sorry
Don't worry, I mention this because I understand what you're getting at, however, I feel like that's not the goal with this exercise, thanks anyway :)
little glen
sorry
digital hull
i mean why wouldn't you want an exact result
Mainly because if it were so, they would not have asked for the error to be less than 10^-5, in addition to the fact that in this unit, it is not important to reach an exact result, but rather to know how to approximate by using Taylor.
!15m
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digital hull
<@&286206848099549185>
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wraith hinge
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wraith hinge
i don't understand how the instantaneous value at P exists
when u only go from left
and not right
dapper swift
i don't understand how the instantaneous value at P exists
yeah, that's a weird edge case
just like how you can have a one-sided limit, you can also have a one-sided derivative (cause a derivative is a limit, by the limit definition)
wraith hinge
are they assuming the graph just keep goin up?
wraith hinge
just like how you can have a one-sided limit, you can also have a one-sided deri...
ahhh
okay
dapper swift
are they assuming the graph just keep goin up?
or that could be the other logical explanation, yes
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hollow stone
Can somebody explain what calculus is?
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Can somebody explain what calculus is?
thorn heart
Can somebody explain what calculus is?
That's quite the question, how far have you gotten in mathematics?
hollow stone
That's quite the question, how far have you gotten in mathematics?
I just learned matrices
vapid lynx
it's "what if we split things into infinitely many little parts" but the actual applications tend to be things like "rate of change" and "area under curve"
hollow stone
Uh...
thorn heart
I just learned matrices
Well, the answer they gave is pretty good, but it's mostly the study of functions
summer python
Can somebody explain what calculus is?
it's just a way to calculate things that aren't definitely defined
for example, finding the area under a curve in a graph
thorn heart
it's just a way to calculate things that aren't definitely defined
That's not true
I assure you, the concepts in calculus are very well defined
hollow stone
Can you guys recommend me a book or a video?
vapid lynx
Well, the answer they gave is pretty good, but it's mostly the study of function...
ya this is probably the better answer as you get into analysis
summer python
i meant like discretely defined
summer python
Can you guys recommend me a book or a video?
organic chemistry tutor
his videos helped me so much
summer python
I want to get good enough so that I can clear jee
ah you're an indian
it's gonna take you a while
have you done differentiation yet?
hollow stone
have you done differentiation yet?
I don't think so
hollow stone
organic chemistry tutor
So... is he good?
thorn heart
I want to get good enough so that I can clear jee
Important question, do you want to get good at calculus or at analysis?
summer python
So... is he good?
he's fine but not enough for jee
summer python
Important question, do you want to get good at *calculus* or at *analysis*?
jee is insanely difficult
it's just about the calculations
and finding integrals and stuff
bright junco
3 blue 1 brown also has a "fundamentals of calculus" series on youtube, and 3b1b is a national treasure so
thorn heart
Cal
Then I'd probably tell ya to pick up a standard book and go from start to finish, kind of ignoring the proofs
summer python
we don't learn much about what calculus is, here in india prim
hollow stone
?
summer python
it's a math book
thorn heart
jee is insanely difficult
Yeah, heard that word a lot
summer python
used in grade 12 cbse
thorn heart
If it's all about calculations and numerical problems, then any standard calculus book should be able to guide you through it
summer python
If it's all about calculations and numerical problems, then any standard calculu...
jee needs a lot more work
thorn heart
If he wanted to get into the definitions and all of that he'd probably need something more specific though
summer python
ill show u a sample question maybe
thorn heart
jee needs a lot more work
Calculus books generally cover up to uni topics, I may be misremembering, but don't quite recall anything in jee that goes past a first year undergrad course
hollow stone
Does anyone know what kind of calc questions are asked in jee?
hollow stone
ill show u a sample question maybe
Ah thanks
summer python
Calculus books generally cover up to uni topics, I may be misremembering, but do...
it's still quite difficult
hollow stone
With is this
hollow stone
get the books i tell u
Ok tell me
hollow stone
math grade 12 - rd sharma
Ok noted
summer python
and it'll get you through math
hollow stone
Basically if I read these 2 books I will be good in maths
summer python
Basically if I read these 2 books I will be good in maths
kinda
you'll have to work out every problem
hollow stone
Ok thnak you very much
summer python
do you wanna do jee mains or jee advanced
hollow stone
Both
summer python
2025??
hollow stone
?
hollow stone
I am okay if it takes under 3 years
summer python
are you done with school
you could take up some course in unacademy or some coaching institutes
thorn heart
it's still quite difficult
Won't doubt it, still think a generic calculus book would do, but I'd probably best leave it to ya
hollow stone
I did 10th and then got in a really bad college
thorn heart
You definitely know more about the indian educational system than I do
summer python
I did 10th and then got in a really bad college
oof you got into a polytechnic?
ahh that sounds difficult
hollow stone
Yup
hollow stone
Is jee basically upto 12th maths?
summer python
based on 11th and 12th maths
cloud grail
Hi
cloud grail
i have question about chemical kinetics
for formula of consumption of A
(R = -c/t)
summer python
i thought this was a math server π¨
cloud grail
can i just make it c/t
and if the answer is negative just make it positive
or i cant do that
cloud grail
yes
summer python
c turns out to be negative
summer python
if you calculate it by the usual
cloud grail
but production is +c/t
summer python
so it's fine to use c/t provided you don't write c as a negative value
summer python
assume initial conc is 10g/L and the final is 5g/L
c = -5g/L here
BUT
if you're using r = c/t
just write c = 5
summer python
but if i get a negative answer from c/t just make it positive?
yeah
cloud grail
oh alr
summer python
yeah
summer python
hmmm it's just (final - initial)Γ·(time taken)
cloud grail
yes'
summer python
and can u confirm if it's 0.023
cloud grail
for part c?
summer python
yeah
cloud grail
yes
summer python
+?
summer python
'-' is only used in the relation to indicate that it's about disappearance
summer python
yrah
timber walrus
Does this look remotely correct?
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trail dagger
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zinc ginkgo
i have to find the general term
find the first few terms
zinc ginkgo
the numbers are very random
show the first 5
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frail wraith
Find the smallest positive multiple of 84 that has only 6 and 7 as digits
frail wraith
dont know how to even attempt this
grim knot
Ok this is an annoying problem
I would first start off by factoring 84 as much as you can
Usually writing it in terms of prime numbers is a good way to start
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wraith hinge
hi
wraith hinge
if 2tan(x) = tan(y)
find y in terms of x
there should be no trigonometric function
charred trail
maybe draw a triangle and use tan(x)=opp/adj
frozen plover
complex numbers 
lean otter
if 2tan(x) = tan(y)
is it a question or u want to know just for curiosity?
lean otter
if u r curios then du should not think about formula
lean otter
idont know sry
wraith hinge
ok no problem
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β
wraith hinge
how to know if a polynomial has real roots
zinc ginkgo
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little glen
Find the smallest positive multiple of 84 that has only 6 and 7 as digits
The number has to end with 6
What multiples of 4 end with 6?
4*4 = 16
4*9 = 36
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little glen
We notice that the numbers which when multiplied by 4 yield a 6 at the end are of the form 4 + 5n
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fast ridge
Guys, Im trying to create a bot that gets goal information (cumulative goals + timestamp) for a given handball game.
My goal is to predict the number of goals that the end of the match.
I guess the prediction will be dynamic, since maybe in a given period of X minutes we have lots of goals (so the prediction might rise), and maybe in other moments we have less goals.
So having said this, I was thinking about using poisson to predict the number of goals at the end of the match, but I might want to use other types of "predictors" also.
I wanna chart the goals, and the different predictions. We will have a line/curve describing the goals, another one describing the poisson prediction, etc etc.
So, first of, what do you think?
Like, is it possible to come up with something that around minutes 35-55 (a handball match lasts 60mins) gives somewhat accurate predictions?
What math models should I try to use apart from Poisson?
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west wharf
no clue, I dont understand what im supposed to do
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no clue, I dont understand what im supposed to do
west wharf
or more like what the process would be
patent crow
Note: lim x-> +-inf of sinx is DNE
west wharf
really?
why?
I put big numbers in my calculator and it looks like it approaches 1
thats dumb to say
idk
patent crow
I put big numbers in my calculator and it looks like it approaches 1
sin (big number) may be 1
Sin of (same big number + pi) will be -1
west wharf
oh
since it never reaches it, it doesnt exist
..?
right?
is that what you are saying?
yeah
I see
thanks again π₯
.close
jaunty cape
A fair coin is flipped until either three heads in a row or four tails in a row occur. What is the expected number of times the coin is flipped? Express your answer as a common fraction.
jaunty cape
@lyric vortex
Are you still on?
I think im starting to understand this now
I looked throught your explaination like 10 times and I think im finally starting to get it
O= 1/2(1+H_1) + 1/2(1+T_1)
H_1= 1/2 (1+H_2) + 1/2(1+T_1)
H_2= 1/2 (1) [win] + 1/2 (1+T_1)
T_1= 1/2(T_2+1) + 1/2(1+H_1)
T_2= 1/2(1+T_3) +1/2(1+H_1)
T_3= 1/2(1) [win] + 1/2(1+H_1)
So after that substitution
thats a little complicated
lyric vortex
These equations are correct. Doing the substitutions should get you the correct answer.
jaunty cape
ok
jaunty cape
These equations are correct. Doing the substitutions should get you the correct ...
also btw I saw what u said on general chat
this question is not something i learn in school