this is related
#help-26
ivory sorrel
lapis ibex
topaz sinewBOT
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sharp dew
topaz sinewBOT
sharp dew
I’m trying to solve it
keen raptor
pending postgraduate
keen raptor
Do you know the Lambert W function
sharp dew
Do you know the Lambert W function
I actually have searched it, and it looks like I got a Lambert W function here.
keen raptor
Test random values or solve using a graphing calculator
sharp dew
Test random values or solve using a graphing calculator
what about applying the Lambert W function on this one?
sharp dew
Test random values or solve using a graphing calculator
I got r=0 as one of its solutions.
thorny flameBOT
sharp dew
Ah right that one
Can Lambert W function be used to find the solution?
keen raptor
Probably not
sharp dew
then what is it used for? it is just a name for such kind of function?
keen raptor
This looks harder than a problem that would be solved with Lambert W, so I asked about it to make sure you weren't secretly actually at the postgraduate level
sharp dew
then what is it used for? it is just a name for such kind of function?
fix my grammar, lord Mickey.
gleaming thunder
WA doesn't have a closed form solutionù
sharp dew
WA doesn't have a closed form solutionù
"WA"
have all of you guys learned about Lambert W function
is it a common thing.
gleaming thunder
depends on who you ask
I'd say it's rarely in a math curriculum
You might see it in physics ?
sharp dew
depends on who you ask
I'd say it's rarely in a math curriculum
You might see i...
curriculum of some high school?
gleaming thunder
no
sharp dew
college
gleaming thunder
probably
sharp dew
I see
keen raptor
I know x + a^x = k is doable with Lambert W
I don't see a way to solve if the first x is replaced with x^2
gleaming thunder
in 2nd year for instance we had an exam on esoteric functions
it was W and elliptic integrals iirc
gleaming thunder
I don't see a way to solve if the first x is replaced with x^2
WA can't, so ofc you can't
sharp dew
in 2nd year for instance we had an exam on esoteric functions
it was W and ellip...
May I know your major? it seems like you were learning some cool shit
thorny flameBOT
gleaming thunder
May I know your major? it seems like you were learning some cool shit
that's when I was a math/physics double major, kinda
Doing 12h math and 8 or 10 h of physics a week
keen raptor
Yeah this one is doable with Lambert and Wolfram misses it
gleaming thunder
this year I was a math/CS double major, and next year I'll start my CS master's
sharp dew
I see
keen raptor
Just exp both sides
gleaming thunder
Yeah this one is doable with Lambert and Wolfram misses it
yeah it occasionally has a blind eye, but those are rare
keen raptor
It's enough for me not to accept proof by WA can't do it
,w largest odd composite number
thorny flameBOT
keen raptor
there we go
thorny flameBOT
gleaming thunder
that one is juicy
pseudo jetty
,w 628 + floor(log(49)/log(7)) + floor(log(343)/log(7))
thorny flameBOT
keen raptor
https://math.stackexchange.com/questions/57466/properties-of-inverse-lambert-w-function/57469#57469 someone on math SE asking about properties of the "inverse lambert function" lmao
keen raptor
me when the floor isn't an integer
pseudo jetty
its meant to be 633 
keen raptor
this'll never beat the day it just started returning wrong answers for things like 1/1.1
keen raptor
its meant to be 633 <:kekw:1037875930166743080>
:kekehands:
there's also my favorite wolfram answer
,w melting point of kittens
thorny flameBOT
topaz sinewBOT
@sharp dew Has your question been resolved?
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ancient beacon
please help me transforming this equaxion there must be an easy trick in it wich makes it easy but i dont get it
cinder sequoia
each of those terms can be separately integrated using known techniques
all you need here is possibly a u-substitution and then knowing the basic integral formulas (recognizing derivatives)
ancient beacon
oh okay seperating i check wich integral formulas not the basic ones right
or do i oversee somthing
cinder sequoia
by integral formulas i meant stuff like knowing that the derivative of e^x is e^x, so the integral of e^x is e^x
that's not really a "trick" or "technique", it's just basic integrals you should recognize
topaz sinewBOT
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neon iron
Rlly?
Since it’s 10% of the total 50 pieces it’s 5 meaning that 29-5 and the rest of them are the small purple pieces
Right?
Aight thanks!!
May I add u?
Nope,I just wanna make some friends if u don’t mind
odd mason
Hi
slate pebble
log is the natural log?
odd mason
yeah the most basic one
slate pebble
yes its just that
slate pebble
whats the derivative of x+3
odd mason
idk?
slate pebble
the derivative of (x+3) with respect to x
i'd go back over your notes , and make sure you know how to do stuff like that before moving on
odd mason
d3/dx ?
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
basically dx/dx + d(3)/dx
1 + 0?
.
ivory sorrel
$\frac{1}{u}$ into something
thorny flameBOT
ƒ(Why am. I here)=I don't know
odd mason
0
odd mason
u = x+1 yeah
ivory sorrel
so what's the differential of x
odd mason
1/x+1 + 1
odd mason
not able to think lol
odd mason
then dx/dx + d(1)/dx
here
ivory sorrel
no
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
cool
jade fulcrum
still need help???
ivory sorrel
that's right
odd mason
still need help???
yeah, every 15 mins or so
odd mason
that's right
thanks
topaz sinewBOT
topaz sinewBOT
✅
ivory sorrel
$\frac{d(x^n)}{dx} =n x^{n-1}$
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
$x^{-2}$
thorny flameBOT
ƒ(Why am. I here)=I don't know
odd mason
:0
topaz sinewBOT
@odd mason Has your question been resolved?
mystic siren
for 2≤n∈N, how do I find the canonical rank matrix version of this matrix?
unreal kite
maybe this helps $a_{i+1;;j}-a_{ij}=2n$
thorny flameBOT
Crystopher
mystic siren
maybe this helps $a_{i+1\;\;j}-a_{ij}=2n$
it doesn't, I thought of this too
unreal kite
I am thinking that you can take some row $i$ and subtract the row $i-1$ from it. Then you should invariably get a row full of ones (after dividing it by $2n$). You repeat this process from the bottom upwards in the matrix.
thorny flameBOT
Crystopher
topaz sinewBOT
@mystic siren Has your question been resolved?
mystic siren
I am thinking that you can take some row $i$ and subtract the row $i-1$ from it....
yes I thought the same, I'll try to write something down and get back to you on that
celest quest
what are these symbols?
topaz sinewBOT
what are these symbols?
celest quest
strange whale
"= with triangle" means it's a definition, they're defining the curvy arrow symbol
craggy haven
i can tell you what the symbols themselves are but idk what they mean
celest quest
oh whats that website
celest quest
"= with triangle" means it's a definition, they're defining the curvy arrow symb...
ah thanks
strange whale
To mean specifically that f is an injection
craggy haven
strange whale
And not just any function
celest quest
so curvy arrow means injections from [k] to [n]
strange whale
Well you can talk about about injections between other sets also
celest quest
i meant in this case
strange whale
But here they're just interested in [k] and [n] prolly
topaz sinewBOT
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sharp chasm
topaz sinewBOT
sharp chasm
Are the two equations correct?
neon iron
Are the two equations correct?
Yes
topaz sinewBOT
@sharp chasm Has your question been resolved?
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glass harbor
I have no idea how to start. x-x
topaz sinewBOT
I have no idea how to start. x-x
@glass harbor Has your question been resolved?
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celest quest
prove this
topaz sinewBOT
prove this
slim maple
prove this
Expand them out
celest quest
using combinatirical arguments
cinder sequoia
oh
celest quest
lol
making up a problem that can be solved both ways
like this
i just cant think of anything for this one
cinder sequoia
what i think of when i think combinatorial arguments like the following:
nCk = (n-1)Ck + (n-1)C(k-1)
because when you're trying to choose k objects from n objects, consider only n-1 of the objects. then either you've already selected one of the objects in which case you have (n-1)C(k-1) left to choose, or you haven't selected any objects and you still have k left to choose from the n-1
cinder sequoia
so in this case, it might be analogous to the LHS as choosing 2 cats from n cats AND choosing 2 dogs from n dogs
maybe there's a way to interpret the right in this context
shell shard
i think they count the number of ways to pick an ordered pair of two unordered pairs
LHS is clearly that
nC2 is if the two pairs are equal
6nC3 is if the number of distinct elements in the two unordered pairs is 3
and 6nC4 is if the number of distinct elements in the two unordered pairs is 4
shell shard
(nC2)^2 means you first pick a subset of two elements and then another subset of two elements
celest quest
yeah
shell shard
if these two subsets are equal then there are nC2 ways of doing that
celest quest
right
celest quest
6nC3 is if the number of distinct elements in the two unordered pairs is 3
and why the 6 here?
and what if there are 2 distinct elements?
shell shard
2 distinct elements is nC2
celest quest
but those aren't necessarily distinct
shell shard
yeah they are
nC2 doesn't count {a,a}
you have elements a,b,c picked
(a,b) and (c,?)
(a,c) and (b,?)
(b,c) and (a,?)
for each of these 3 you have to pick one of the ones in the filled pair to go in the remaining open slot, so 3*2 for each choice of a,b,c
celest quest
which elements are we talking about?
celest quest
you have elements a,b,c picked
(a,b) and (c,?)
(a,c) and (b,?)
(b,c) and (a,?)
f...
right
shell shard
there is a set consisting of n elements, the pairs i'm talking about consist of elements from that set
celest quest
yeah got that
shell shard
you have elements a,b,c picked
(a,b) and (c,?)
(a,c) and (b,?)
(b,c) and (a,?)
f...
if we pick elements a,b,c,d
then we have three choices for the one in the pair with a, and we also have 2 choices for the order the pairs are picked, so again 3*2 for each choice of a,b,c,d
basically, what i'm saying is that (nC2)^2 is the number of pairs of the form
({a,b}, {c,d})
where a isn't b and c isn't d (order doesn't matter in the inner pairs)
and nC2 is the number of pairs of the form ({a,b},{a,b})
and 6nC3 is the number of pairs of the form ({a,b},{a,c}), where c is distinct from a and b
and 6nC4 is the number of pairs of the form ({a,b},{c,d}) where all of a,b,c,d are distinct
topaz sinewBOT
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opal bronze
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meager glacier
Do you have a question?
topaz sinewBOT
@opal bronze Has your question been resolved?
opal bronze
nope
I GET A DETICATED SERVER FOR ME
DETICATED JUST FOR ME
WOW
or not
it has my name tho
shrewd horizon
well this is a channel and not an entire server
but yeah it is dedicated to just you, for now
once you close it it will then get used again
upper heath
I GET A DETICATED SERVER FOR ME
NOOOOOOOO THAT IS UNFAIR
MODS PLEASE BAN HIM
@allmods
opal bronze
why
craggy haven
azure kite
L
topaz sinewBOT
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open pollen
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open pollen
I said that the vertex is at (-1.5, 12.5)
So I found f(x)
and when I graph the reciprocal function, it looks nothing like the answer
hasty verge
reciprocal function is essentially just switching x and y then solving for y again
should look like it's reflected around y=x
open pollen
Did I get f(x) right?
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ivory sorrel
What should the relation between a,b,c be for
topaz sinewBOT
What should the relation between a,b,c be for
ivory sorrel
.close
ivory sorrel
What should the relation between a,b,c be for $\frac{(x-b)(x-c)}{x-a}$ be for the range to be $\R$
topaz sinewBOT
What should the relation between a,b,c be for $\frac{(x-b)(x-c)}{x-a}$ be for th...
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
!status
topaz sinewBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
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
ƒ(Why am. I here)=I don't know
pearl patio
won't it' range be $\R \forall a,b,c?$
it wouldnt, if a=c for example then a-b will not be in the range
thorny flameBOT
ƒ(Why am. I here)=I don't know
pearl patio
so $a \neq b \neq c$
try to graph x^2/(x+1)
ivory sorrel
done
pearl patio
isn't the range never R?
x(x+2)/(x+1)
torpid sparrow
Xd
pearl patio
could i have a hint
notice that the function behaves nicely when x<a or x>a
maybe do an analysis of what the minimum and maximum is in those regions
pearl patio
notice that the function behaves nicely when x<a or x>a
by "nice" i mean there is no undefined points
have you guys done calculus yet?
ivory sorrel
yeah
ivory sorrel
so I guess I'm looking at seeing when it's monotonically increasing
pearl patio
so I guess I'm looking at seeing when it's monotonically increasing
well somewhat
its more looking for the critical points
ivory sorrel
hmm
okay
so I have
$\frac{1}{y}\left(\frac{dy}{dx}\right)=\frac{1}{x-b}+\frac{1}{x-c}-x-a$
thorny flameBOT
ƒ(Why am. I here)=I don't know
pearl patio
$\frac{1}{y}\left(\frac{dy}{dx}\right)=\frac{1}{x-b}+\frac{1}{x-c}-x-a$
umm can you show ur step i need to verify
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
$\ln\left(y\right)=\ln\left(\left(x-b\right)\right)+\ln\left(\left(x-c\right)\right)-\ln\left(\left(x-a\right)\right)$
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
so differentiating this we get
$\frac{1}{y}\left(\frac{d.y}{dx}\right)=\frac{1}{x-b}+\frac{1}{x-c}-\frac{1}{x-a}$
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
ooh
so dy/dx is
$\left(\frac{d.y}{dx}\right)=\frac{\left(x-c\right)}{x-a}+\frac{\left(x-b\right)}{x-a}-\frac{\left(x-b\right)\left(x-c\right)}{\left(x-a\right)^2}$
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
umm can you show ur step i need to verify
here
ivory sorrel
so the critical points are where dy/dx becomes 0
$0=\left(x-c\right)+\left(x-b\right)-\frac{\left(x-b\right)\left(x-c\right)}{\left(x-a\right)}$
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
$\left(x-c\right)+\left(x-b\right)=\frac{\left(x-b\right)\left(x-c\right)}{\left(x-a\right)}$
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
now what?
thorny flameBOT
ƒ(Why am. I here)=I don't know
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
wait
pearl patio
how abt the Left hand side
ivory sorrel
that feels off
pearl patio
(x-a)((x-b)+(x-c))-(x-b)(x-c)=0
ivory sorrel
$(x-a)(x-c)+(x-a)(x-b)$
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
which is $x^2-(a+c)x+ac+x^2-(a+b)x+ab)$
thorny flameBOT
ƒ(Why am. I here)=I don't know
pearl patio
good
ivory sorrel
now what?
pearl patio
so I have $(x-a)((x-c)+(x-b))=(x-b)(x-c)$
solve for x in that equation
ledt hand side minus right hand side is a quadratic which should be 0
pearl patio
thats very helpful as it gives the only 2 critical points
ivory sorrel
*points
pearl patio
we'll get the critical poinst
we are using the critical points to find the maximum and minimum
ivory sorrel
$x^2-2ax+ac+ab-bc=0$
thorny flameBOT
ƒ(Why am. I here)=I don't know
pearl patio
we are using the critical points to find the maximum and minimum
this, combined with the fact that the function is continuous on x<a and x>a will give us the range of the function
ivory sorrel
,w x^2-2ax+ac+ab-bc=0
thorny flameBOT
ivory sorrel
so we now want $a^2-ab-ac+bc>0$
thorny flameBOT
ƒ(Why am. I here)=I don't know
pearl patio
so we now want $a^2-ab-ac+bc>0$
not really
now we can casework though, same idea
(a-b)(a-c)=0 would imply that a=b or a=c
we already discussed that case
pearl patio
**ƒ(Why am. I here)=I don't know**
what if (a-b)(a-c)>0
not that a^2-ab-ac+bc=(a-b)(a-c)
pearl patio
or other way around
ivory sorrel
assuming (a-c) and (a-b)>0
ivory sorrel
or other way around
yeah
pearl patio
Now hint: what is the limiting behaviour when x approches a-? what is the limiting behaviour when x approches -infinity? what does this information conclude about the point a-sqrt((a-b)(a-c))?
ivory sorrel
x tends to $-\infty$
thorny flameBOT
ƒ(Why am. I here)=I don't know
pearl patio
then (x-b)(x-c)/(x-a) will tend to?
ivory sorrel
$-\infty$
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
it tends to $\infty$
thorny flameBOT
ƒ(Why am. I here)=I don't know
pearl patio
**ƒ(Why am. I here)=I don't know**
not quite
thorny flameBOT
ƒ(Why am. I here)=I don't know
pearl patio
still $-\infty$
so what does that say about the critical point $a-\sqrt{(a-b)(a-c)}$
thorny flameBOT
qwertytrewq
pearl patio
im finally on my laptop so i can type latex
ivory sorrel
**qwertytrewq**
I don't reallt know
pearl patio
I don't reallt know
well it has to be a maximum right?
pearl patio
the proof of that might be technical but you get the intuition
ivory sorrel
yeah
pearl patio
OK, since there is only one maximum on x<a region it must be the absolute maximum on $(-\infty, a)$
thorny flameBOT
qwertytrewq
pearl patio
similarly, $a+\sqrt{(a-b)(a-c)}$ is the absolute minimum on $(a,\infty)$
thorny flameBOT
qwertytrewq
pearl patio
try to show that the absolute minimum on $(a,\infty)$ is greater than the absolute maximum on $(-\infty, a)$
thorny flameBOT
qwertytrewq
pearl patio
this way you would've shown that there is a gap in the range
ivory sorrel
hmm, I see
I actually have to write. a test now, I'll come back to this later
sorry
,close
.close
topaz sinewBOT
ivory sorrel
thanks for all the help!
ivory sorrel
this way you would've shown that there is a gap in the range
thanks!
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hot plank
Someone can explain me why when the positive limite of a function is different of the negative limite of the same function, then the limit doesnt exists?
topaz sinewBOT
Someone can explain me why when the positive limite of a function is different o...
cold eagle
hot plank
wym
cinder sequoia
from the definition of a limit
you need to be able to find some delta so that you can find x values within that distance of c so that the function value is within a distance of epsilon of your limit
when your left and right hand limits don't match, then the definition for a limit at a point is not satisfied
because you could get arbitrarily close to your x value from one side and get a drastically different limit than if you approached from the other side
cinder sequoia
Someone can explain me why when the positive limite of a function is different o...
you can also see that this is true by considering the contrapositive. if the limit exists, then the right and left limits are the same.
this has to be true because if the limit exists then you can always get within a distance delta of your point to have the function become arbitrarily close to your limit
if your point is c, and you are arbitrarily close to the right of c, then x - c > 0, and if you're arbitrarily close to the left, x - c < 0, and in both cases, the absolute value part of the definition ensures you'd be within a distance delta of c
so the left and right limits are guaranteed
i'm assuming that's probably an overkill answer but other than that you kind of just have to take people's word for it
stoic shuttle
Well if lets say you want to find the value of tan(90). If you approach it from the left that is tan(89.99999...) then it would tend to infinity but if you approach it from right that is (90.00000...1) then it would tend to negative infinity so we say that a value of a limit is defined only when the left hand limit is equal to the right hand limit. In this case since left hand and right hand limits are clearly not same we say that tan 90 isnt defined
cinder sequoia
Well if lets say you want to find the value of tan(90). If you approach it from ...
i think OP might understand that if the left and right hand limits aren't equal then the limit doesn't exist, but i think they want to know why
hot plank
Well if lets say you want to find the value of tan(90). If you approach it from ...
hm so about a negative expoentiation function with a odd expoent, theres no limits?
stoic shuttle
i think OP might understand that if the left and right hand limits aren't equal ...
your answer is too professional tho if I were to read limits for the first time I would'nt understand that
stoic shuttle
hm so about a negative expoentiation function with a odd expoent, theres no limi...
wdym-
hot plank
what epsilon and the other letter represents?
cinder sequoia
your answer is too professional tho if I were to read limits for the first time ...
i understand, but there isn't really a way to explain "why" the definition is that way without this approach
cinder sequoia
what epsilon and the other letter represents?
ignore that, it's kind of a much more rigorous explanation but i assumed you wanted to know exactly "why", and most calculus teachers don't really give you a good answer
most professors just say "we say the limit exists at a point if and only if the left and right hand limits are equal at that point"
but it's probably best to just take their word for it for now
hot plank
maybe its because if the variant dont stay constant?
stoic shuttle
when I first learned about limits my teacher had this really cool way of explaining it to me. Lets you go near a bermuda triangle and it emits alot of radiation from it. and when you go inside the triangle you can no longer detect the amount of radiation. Now limit of the radiation is just the value of radiation emited from that bermuda triangle the closer we go to its border. Kinda silly but it was the best way I could've understood that
stoic shuttle
xy=1 graph?
hot plank
so theres no limit of x aproxim 0?
hot plank
xy=1 graph?
wym
stoic shuttle
so theres no limit of x aproxim 0?
yea the limit at 0 doesnt exist
cinder sequoia
so theres no limit of x aproxim 0?
i mean intuitively, if you want to say your function "approaches" a value near a point, it probably shouldn't matter what direction you approach the point from
hot plank
u can explain me this?
cinder sequoia
u can explain me this?
actually you definitely should ignore this, it's higher level than what's taught in most calculus courses
i misunderstood what kind of explanation you were looking for
stoic shuttle
u can explain me this?
ive no idea tbh
hot plank
actually you definitely should ignore this, it's higher level than what's taught...
a ask
if x is aproxim c
so why 0 < abs(x-c)
0 < 0
?
cinder sequoia
well the whole point of a limit is that you don't care about x being exactly c
just that it's really near c
hot plank
hm
cinder sequoia
so no matter what, x != c, so abs(x-c) > 0
hot plank
ohhhhhhhhhhhhhhhhhhhhhhhhh
cinder sequoia
but like i said, this is probably not too useful of an explanation for what you originally asked
cinder sequoia
so why theres a module?
the distance between x and your point, this is what allows for you to approach from both the left and right
reef fjord
this is a different function to think about, the sgn(x) (sign function), outputs 1 for positives, 0 for 0, and -1 for negatives. Note limit as you approach 0 from the right(positive direction) is 1, and the limit as you approach 0 from the left, is -1
reef fjord
the limit of this couldnt be the medium point?
well, the idea of a limit is that you're approaching it from both directions
and you can split this into two separate ideas
approaching from left (negative direction/below) and approaching from right( positive diection/above)
hot plank
hm
reef fjord
like for sign function, 0.00000001 would still have a positive sign, and you can keep adding 0s and it'll still be positive
so it'll still be 1
likewise for -0.000000001, it'll always be negative, and so output -1, no matter how many 0s you add
does this make sense?
hot plank
yes
hot plank
likewise for -0.000000001, it'll always be negative, and so output -1, no matter...
btw u can represent this by abs(x)/x
hot plank
what sgn function return at 0 ?
reef fjord
0
sgn function can be equivalently defined as a piecewise function where its |x|/x everywhere besides 0, and at 0, its 0
hot plank
ye but where the limits came in this?
reef fjord
like for sign function, 0.00000001 would still have a positive sign, and you can...
this idea can be rigorized, like made more intricate, which was what neil was trying to show, but limits came into this in showing that sgn(x) has what's called a 'discontinuity' at 0
i.e. the limit approaching 0 from the left, and the limit approaching 0 from the right are not equal
reef fjord
this idea can be rigorized, like made more intricate, which was what neil was tr...
more specifically a jump discontinuity
reef fjord
?
reef fjord
hot plank
like
in a x^n function
n is a positive number and its integer
the limit of any function exists
cause
the derivate of this functions is costants
hot plank
what is the first image?
hot plank
the derivate of this functions is costants
so it grows constantly in left and right side
reef fjord
a removable discontinuity is 'removable' because the limit exists at that point, but the function value doesn't exist for some reason, (mainly due to an indeterminate form)
hot plank
what is "i.e" ?
astral blaze
for example
hot plank
a removable discontinuity is 'removable' because the limit exists at that point,...
oh so its like a remaing part
reef fjord
its like x/x
astral blaze
it is removable in the sense that you can define the value there to make function continuous
hot plank
it is removable in the sense that you can define the value there to make functio...
hmmmmmmm
so like
u cant find a value to put in there right?
cinder sequoia
for removable discontinuities, you can
reef fjord
you can
cinder sequoia
for example, if you defined the function as sinx/x for x != 0 and 1 for x = 0, then that function would be continuous everywhere
it used to be discontinuous at 0 but since the limit there exists, you can define a function value there to create a continuous function
on the other hand, if you considered 1/x, there isn't really a single value that you could choose to define there at the discontinuity to make the function continuous
so vertical asymptotes like that, as well as jump discontinuities, are different from removeable discontinuities
hot plank
in a x^n function
n is a positive number and its integer
the limit of any functi...
this is right?
hot plank
so vertical asymptotes like that, as well as jump discontinuities, are different...
like
cinder sequoia
this is right?
yes, polynomials are continuous everywhere so their limits exist everywhere
hot plank
so u can put a vallue in the "missing part" that this vallue follow the pattern of the function
k i understanded it
and abou the limits?
hot plank
and abou the limits?
i know now like if the variation of left and right sides are equal and the limit of a function of x going to a is indefined u can "approx" it
and the limit will still exists
like this
hot plank
i know now like if the variation of left and right sides are equal and the limit...
@cinder sequoia its right??
topaz sinewBOT
@hot plank Has your question been resolved?
hot plank
<@&286206848099549185>
topaz sinewBOT
@hot plank Has your question been resolved?
sleek haven
how would I make this graph linear? Ignore that stuff about trend line
sleek haven
I want to make "current is proportional to 1 divided by the resistance (y∝1/x) " to y=mx+c
long stirrup
keen raptor
Make one of the graph axes inverted
sleek haven
one of the requirments for achieved is making your graph linear
and I have no clue of how to do that in the case for a hyperbola
keen raptor
If y~1/x then you should graph y vs 1/x
That's not a parabola, it's part of a hyperbola
sleek haven
If y~1/x then you should graph y vs 1/x
I'm not sure what you mean
keen raptor
So instead of ohms use 1/ohms for the axis
sleek haven
So instead of ohms use 1/ohms for the axis
oh! so instead of doing x^2 like normal I go 1/x
so for example 1 divided by 2.78
keen raptor
Yeah
neon iron
how would I make this graph linear? Ignore that stuff about trend line
V=IR yes? V/R = I so plot I against 1/R
keen raptor
Np
sleek haven
V=IR yes? V/R = I so plot I against 1/R
ye
sleek haven
V=IR yes? V/R = I so plot I against 1/R
that's another thing I'm supposed to talk about voltage somewhere but I'm not sure how that's relevant. the aim for my investigation is looking at how the amount of resistance affects the current
I suppose you don't know that
indigo island
is there a simple way to solve this instead of taking the LCM for all of this and getting a very very very big equation
topaz sinewBOT
is there a simple way to solve this instead of taking the LCM for all of this an...
restive inlet
its make it easier to identify the lcm
as opposed to taking the product of the original denominators
indigo island
i have completed the table but how do i solve these questions, and what do they mean by you can use a spreadsheet to verify maybey its the spreadsheet on my calculator??
topaz sinewBOT
i have completed the table but how do i solve these questions, and what do they ...
rapid wyvern
do you perhaps know the formula for (b)
for the spreadsheet i also dont know its probably like to check if your formula works
rapid wyvern
ok
ill just do a geometric approach i saw on a youtube video
notice how you can arrange the numbers in a triangle
indigo island
wait i do know a formaula for b
rapid wyvern
■
■■
■■■
■■■■
■■■■■
...
rapid wyvern
yes thats the formula
indigo island
yes it works
rapid wyvern
for (c) its more complicated
but lets skip c first and move to d
can you give the answers to your table
rapid wyvern
for T?
indigo island
1,9,36,100,225
indigo island
T=S^2
rapid wyvern
and S is?
indigo island
t = (n(n+1)/2)²
so this is the answer for C
indigo island
yes it seems like so
neon iron
that's another thing I'm supposed to talk about voltage somewhere but I'm not su...
voltage constant, gradient should be linear as the gradient of I against 1/R is the voltage
sleek haven
voltage constant, gradient should be linear as the gradient of I against 1/R is ...
spusho I'm moving to #help-48
topaz sinewBOT
@indigo island Has your question been resolved?
ivory sorrel
find the inverse of $x+ \frac{1}{x}$
topaz sinewBOT
find the inverse of $x+ \frac{1}{x}$
thorny flameBOT
ƒ(Why am. I here)=I don't know
reef fjord
does not pass HLT
neon iron
it doesn't exist ?
reef fjord
its not injective
ivory sorrel
where the function is defined from $[1,\infty) \rightarrow [2,\infty)$
outer portal
lol
reef fjord
there you go
ivory sorrel
so I've come until
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
$y=\frac{\left(x\pm\sqrt{x^2-4}\right)}{2}$
thorny flameBOT
ƒ(Why am. I here)=I don't know
ivory sorrel
I fell it should be the one with the "+" sign
outer portal
consider plugging in a test point to determine whether its + or -
ivory sorrel
due to the range
outer portal
thats correct but may be prone to errors if youre not careful with range calculations
topaz sinewBOT
prisma mesa
ivory sorrel
ghost ping
topaz sinewBOT
Available help channel!
neon obsidian
long lake
actually a physics concept. when taking very small angular displacements, we take sinθ≈θ. can we do that same for cosθ
topaz sinewBOT
actually a physics concept. when taking very small angular displacements, we tak...
dense crescent
strange whale
There is an equivalent yes
1 - theta^2 / 2
If you want something a bit more precise than just 1
long lake
.close
topaz sinewBOT
strange whale
But it's a bit less nicer than for sin cause of that square
topaz sinewBOT
Available help channel!
small hatch
f(x,y) = x^2-4x+y^2+6y
topaz sinewBOT
f(x,y) = x^2-4x+y^2+6y
small hatch
How to do it with calculus
I dont want to make squares
topaz sinewBOT
@small hatch Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
crimson sequoia
How do you find basis?
topaz sinewBOT
How do you find basis?
crimson sequoia
I looked it up online and kept getting confused
bright cradle
can you find 2 linearly independent vector that satisfies the system?
that is gonna be a basis of the subspace
crimson sequoia
sorry what do you mean by that?
bright cradle
do you know linear (in)dependence?
crimson sequoia
I dont know either, this whole section of vectors has been confusing and im kinda going through the motions without understanding exactly why things work
all i know is for part a plug the matrix into my calc do rref and then turn it into parameters
bright cradle
well this is kinda hard to explain if you dont knwo anything
topaz sinewBOT
topaz sinewBOT
Available help channel!
willow cliff
hello
loud oasis
any even integer can be written as 2k for some other integer k, and any odd integer can therefore be written as n = 2k + 1
burnt bridge
Escuse me what's 1+1,'*
ionic oar
2
willow cliff
ban this guy i will call moderators
ionic oar
do it
ionic oar
I thought it was 11
sure if you're concatenating strings
anyways uh, we get these 1+1 trolls a lot
moderation's kind of sick of it
usually get muted or banned or whatever
left on his own accord
topaz sinewBOT
@willow cliff Has your question been resolved?
vast fjord
i forgot how to do this
topaz sinewBOT
i forgot how to do this
civic schooner
i forgot how to do this
pseudo sonnet
vast fjord
do you multiply the square roots first?
thorny flameBOT
esca (@ with reply)
vast fjord
6.7
civic schooner
that doesnt sound right but i meant in exponent form
turbid holly
You can simplify using the exponent rules 😄
civic schooner
in general, $\sqrt[n]{x}=x^{\frac{1}{n}}$
vast fjord
ohhh yeahhh
thorny flameBOT
esca (@ with reply)
civic schooner
so you can rewrite the numerator and denominator and then apply usual exponent rules
turbid holly
yes
vast fjord
wait what does the 1 represent?
civic schooner
its a fraction
vast fjord
does it ever change
turbid holly
Question is the same as sqrt(5)^3 ?
civic schooner
does it ever change
$(\sqrt[n]{x})^m=x^{\frac{m}{n}}$
thorny flameBOT
esca (@ with reply)
unkempt surge
$(\sqrt[n]{x})^m=x^{\frac{m}{n}}$
thats interesting always thought it had to be the x to the power of something, thanks brother
civic schooner
thats interesting always thought it had to be the x to the power of something, t...
its the same thing
civic schooner
$(x^n)^m=x^{n\cdot m}=x^{m\cdot n}=(x^m)^n$
thorny flameBOT
esca (@ with reply)
unkempt surge
yup
civic schooner
**esca (@ with reply)**
so you rewrite the root as a normal exponent and these rules still apply
vast fjord
so
i should make both equations into exponential form
and then simplify from there?
unkempt surge
i should make both equations into exponential form
yeah
if you need any more help with that you can ping me brother
i got the result if you need
vast fjord
did you get 5 7/12? thats what i got
vast fjord
doesnt it become 5 1/3 and 5 1/4
unkempt surge
That is correct yes
theres a trick for whenever you are dividing numbers to the power of fractions
vast fjord
whats the trick?
unkempt surge
so there you have
5^ 1/3 divided by 5^ 1/4
btw this only works if the 5 is equal to the 5
meaning like
if (x^ a/b )/ (x^ y/z)
and the trick is
number stays
meaning that x or our 5 stays
and we simply do 1/3 - 1/4
a/b - y/z
unkempt surge
adition is only when x and x are multiplying
wait is it
let me check
i dont wanna give false info
vast fjord
no its division
vast fjord
i forgot how to do this
^
unkempt surge
vast fjord
okay so that'd be 5^1/12
unkempt surge
yup that is correct
vast fjord
ty
vast fjord
thanks
vast fjord
🙏
unkempt surge
🙏
unkempt surge
thanks
of course brother
anything else or?
if thats everything you can close this chatroom
vast fjord
did i get this one right 💀
unkempt surge
did i get this one right 💀
i would say so, cant really explain but i believe its that one, someone that can confirm please do it
but its honestly the only one that makes some sense
vast fjord
what about this one?
vast fjord
okay thats what i thought
unkempt surge
okay thats what i thought
Right? 🙏
vast fjord
whats the difference between option b and d?
unkempt surge
whats the difference between option b and d?
because whenever you input the value of x in years
lets say
4 years
you get the value of the house
and not the amount that it has increased in valued
get it?
like you get the actual price of it instead of how much it went up
now of course you can check how much it went up but thats not with that specific function
that would have to be with inputing the years and checking for yourself how much it went up
vast fjord
it's either this or 12, 3
unkempt surge
it's either this or 12, 3
why so
imma leave after this one let me just help you really quickly
vast fjord
ohh wait
unkempt surge
whenever g(x) = f(x) its the point that they both share
vast fjord
yeah that does look like 3,18
unkempt surge
you too brother 🙏
vast fjord
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
stray locust
So I got this so far I just don’t know how to simplify it
frozen echo
so right now we have $\frac{-6(r+1)}{-6} = 1* -6$ correct?
thorny flameBOT
Mar the Marey
thorny flameBOT
Mar the Marey
cosmic coral
see if you can figure that out
am I helping you or are you helping me 🤔
frozen echo
its no use for you if i just give you the answer
id rather teach you how to find the answer yourself
what part of this equation is confusing you?
cosmic coral
none of it, r=-7
cosmic coral
on god
frozen echo
long day lmao
frozen echo
or maybe just put it in spoilers
restive inlet
more or less the same assistance is already in the other channel so just gonna close this one
.close
wheat token
I'm so lost, wouldnt it make no sense because if it became e-c/d it would be different than e- (c/d)
topaz sinewBOT
I'm so lost, wouldnt it make no sense because if it became e-c/d it would be dif...
wheat token
so would the equation itself be wrong already? since it's changing to (e-c)/d
wheat token
tbh I'm just assuming, but isn't that what the orange box is?
forgot that picture for the second question
worthy storm
no, e - c is not the correct answer from that list
wheat token
Okay, imma redo the problem and come back
Okay, its de-c solution
But I did that by filling in the letters, could there be a faster way on solving the answer
Also it would be renaming a fraction right?
worthy storm
you have a term c/d with d in the demoninator
in order to combine this expression into a single fraction you need both terms to be over the same denominator
so you take e, multiply and divide by d, and you get de/d
then,
e - c/d = de/d - c/d
now they're over the same denominator so you can just add them in the usual way
result is
(de - c)/d
wheat token
nvm'
I don't understand where another d comes into play, because I thought you cant add another variable or number if its not already in the equation
worthy storm
you can multiply and divide by the same number
like for example,
2 = (2 x 3) / 3
(multiply and divide by 3)
wheat token
Oh I think I get it now, thank you