we do 1600/65 bc thts the lower bound
#help-41
calm pewter
inland pulsar
then maybe 69.9?
inland pulsar
wait
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inland pulsar
kk
calm pewter
is all gd
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calm pewter
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hollow salmon
What have you attempted so far?
hollow salmon
What were you trying to figure out by multiplying those numbers?
hollow salmon
Ok, let's find the volume first. There are a few ways to approach finding that out. There are three dimensions you need to know to calculate the volume. One is obvious. Do you know the value of that dimension?
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split sail
split sail
Having trouble with bubble sort algorithm from part b
I used the logic behind swaps and got this inequality
Yet it is clearly not the one in the answer
So I’m really confused
Basically because x doesn’t swap with 17 it must be less than it. Because x swaps with 24 it must be less than it
I just realised the x>8 is wrong
So inequality really is 17<x<24
Yet that’s wrong
No idea where 17 is coming from
pallid canopy
Closed your duplicate channel
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robust ferry
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robust ferry
im kinda confused
the first one only gives a ratio for the only one of the lines
but the 2nd one says it is parallel
but parallel just means both lines are 180 degrees
which means nothing
but the answer is B
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umbral shale
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full cradle
is this total or partial
amber waspBOT
is this total or partial
sinful sapphire
it's a total function
full cradle
nvm the kecture made another mistake
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abstract arch
Can someone help me with my equation for row 3? I’m not sure if it’s right
amber waspBOT
Can someone help me with my equation for row 3? I’m not sure if it’s right
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hollow sky
Hi, I’m just wondering if my teacher made a mistake or if my method is wrong
My work is in pink and my professor in blue
hollow sky
How does she get cubed root of 64 from 2 and square root of 4 ?
hollow sky
Hi, I’m just wondering if my teacher made a mistake or if my method is wrong
My...
<@&286206848099549185>
ocean widget
(Divide numerator and denominator by 2)
ocean widget
How does she get cubed root of 64 from 2 and square root of 4 ?
Yea I see it idk how she got there too
worthy solar
So the black text equation is the thing that we need simplifying. What about the blue text?
hollow sky
It’s okay, she often makes mistakes on the key so it might be that 🥲
hollow sky
So the black text equation is the thing that we need simplifying. What about the...
Owh, the blue text is her answer and her steps to solving the equation
But it doesn’t really add up so I think it’s an error
ocean widget
I’m just looking at your thing
How do you get the sqrt 9 y^2
Oooh yea that’s right
It’s cube root
Nvm
Yea I think your working is fine
amber waspBOT
regal swift
How do I get the second soln.
fathom ruin
hey can someone help me with 11c
amber waspBOT
hey can someone help me with 11c
fathom ruin
im assuming that i need to find the number of terms
so i use the formula Tn = a + (n-1)d
but when i calculated n i got logb(1/32) / logb(1/2) + 1
when i tried substituting this into the equation Sn = 1/2n ( a + l) its not simplifying down to the answer
weak zinc
but when i calculated n i got logb(1/32) / logb(1/2) + 1
How did you get this? 
fathom ruin
hang on ill get a picture!
weak zinc
hang on ill get a picture!
Actually you're alright, I agree 
(I hadn't done the work so wanted to double check 
)
weak zinc
but when i calculated n i got logb(1/32) / logb(1/2) + 1
But, are you able to write this in a simpler form?
fathom ruin
Actually you're alright, I agree <a:nyasSnuggle:733017034207658055>
oh! okok
fathom ruin
But, are you able to write this in a simpler form?
well i guess you could use the change of base rule
to make it
log1/2 (1/32) + 1 ??
ok let me see if that will simplify it down
omg that worked!!
thank so you much 🤩
weak zinc
Always a pleasure 
fathom ruin
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ionic zodiac
Not sure what to do next
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keen pawn
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valid remnant
yk what I'm bouta say right
keen pawn
$\gcd(n,n+2) = \gcd(2,n)$
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
keen pawn
if n is odd, gcd(2,n)=1
valid remnant
$\gcd(n,n+2) = \gcd(2,n)$
if a = gcd(2,b)
then a |2 and a | b
so necessarily a <= 2
👀
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
keen pawn
thanks
$\gcd(2n+1,4n^2+1)= \gcd(4n^2+1,4n^2-2n)$. One is even, one is odd, thus the $\gcd$ is 1
valid remnant
idk I would rewrite 4n^2+1 as (2n+1)^2 - 4n
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
valid remnant
$\gcd(2n+1,4n^2+1)= \gcd(4n^2+1,4n^2-2n)$. One is even, one is odd, thus the $\...
idkk this seems a lil much
idk sps a = gcd(2n+1,4n^2+1) and a > 1
then a | 2n+1 and a | -4n
keen pawn
sps?
valid remnant
suppose
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sinful sapphire
if by row you mean row and column sure
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slate gale
Hi guys, can i divide the 4tanx here?
amber waspBOT
Hi guys, can i divide the 4tanx here?
wheat rock
yes u can
because dividing by 4tan(x) on the right just leaves you with zero again
0/(anything) = 0
mint nacelle
Hi guys, can i divide the 4tanx here?
no you can't, cause tan x can be 0
valid remnant
0/(anything) = 0
0/0
mint nacelle
better to factor to get (4 tan x)(1 - cos 2x) = 0
when tan x = 0 that's just x = 0 in that domain
then consider 1 - 2 cos x = 0
slate gale
guys there is the case where dividing it will remove the function right?
wheat rock
no you can't, cause tan x can be 0
oh right, im a dumb dumb
slate gale
no you can't, cause tan x can be 0
wait what does that mean
mint nacelle
so you should factor if you don't have a constant
slate gale
ohh
mint nacelle
and 0 is in the domain
mint nacelle
so you should factor if you don't have a constant
this
always factor for a function
ancient lynx
Hi
i need help with this math
a. The shortest side of a GP triangle is 10 cm , given r>0, explain why is r to be 1.5 but not possible for 2
b. the sum of the first 4 terms is 64 and the sum of their square is 214. Find the 4 terms
slate gale
so you should factor if you don't have a constant
wait where is the constant
mint nacelle
wait where is the constant
the constant is 4 here, so tan x (1 - 2 cos x) = 0 is fine
dividing by tan x is not okay
so if you have 1 - 2 cos x = 0
you've lost solutions
slate gale
dividing by tan x is not okay
ohhh
mint nacelle
what case can i divide the trigonometric function?
never
you can't divide any function
slate gale
ohhh okokk
wait what if it can't be factorized 
im used to dividing the trigonometric functions 🤦♀️
mint nacelle
it's better to factor
then with time and practice you can see that some cases are impossible
mint nacelle
wait what if it can't be factorized <:sully:651816820122189834>
oh basically say if you have sin x = 2 cos x, you can actually divide by cos x sorry
cause you want tan x = 2 ofc
you should write $(\cos x \ne 0)$ on the side then
grizzled pagodaBOT
south's secret twin brother
mint nacelle
and like 99.9% of the time the values you get won't satisfy tan x = 2 and cos x = 0
so that's why your book or other people just divide
reef kraken
You can only divide when you are sure that value can't be 0
mint nacelle
You can only divide when you are sure that value can't be 0
yeah this is more accurate
I'm trying to simplify things but then there's limits to oversimplifications
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slate gale
You can only divide when you are sure that value can't be 0
ohhh
sorry for the late reply guys
slate gale
yeah this is more accurate
thank you sooo muchh!
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visual wren
It is known that a,b,c,d are integers and all of them are greater than 4. Find the number of solution sets of a + b + c + d = 23
a. 18
b. 20
c. 34
d. 45
visual wren
pls help 🙏
visual wren
like this?
x = a-4
y = b-4
z = c-4
w = d-4
lost star
now there's a direct formula for non negative integer solution to linear system with unit coefficients
lost star
like this?
x = a-4
y = b-4
z = c-4
w = d-4
yes
visual wren
then?
visual wren
">"
gloomy tide
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fading fiber
hey i have a question, how am i able to tell what the graph of an equation should look like? for example
shrewd elm
this is two lines intersecting
the first one you could think of as a "degenerate" hyperbola
it's two lines intersecting because (x-y)(x+y) = 0 implies that one of the factors is zero
so either y=x or y=-x
fading fiber
ye i get that bit
soo is there anything i can look out for to recognise smt as a hyperbola?
sorry if my question doesnt rlly make sense
shrewd elm
pattern recognition i guess
if you know that xy = c is a hyperbola centered at (0,0), then (x-4)(y-3) = 2 is a hyperbola centered at (4,3)
fading fiber
ohh so kind of how it is with circles?
shrewd elm
yea
fading fiber
is there an equation for hyperbolas like there is for parabolas?
shrewd elm
well there are a few different forms depending on the slope of the asymptotes
like x^2/a^2 - y^2/b^2 = 1 is one form, that one has diagonal asymptotes
xy=c has horizontal and vertical asymptotes
fading fiber
like x^2/a^2 - y^2/b^2 = 1 is one form, that one has diagonal asymptotes
okay i think i just need to know this one
thank uu
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visual wren
It is known that a,b,c,d are integers and all of them are greater than 4. Find the number of solution sets of a + b + c + d = 23
a. 18
b. 20
c. 34
d. 45
visual wren
<@&286206848099549185>
graceful badger
It is known that a,b,c,d are integers and all of them are greater than 4. Find t...
You should try some examples
$a + b + c + d = 23$ with $a, b, c, d \geq 5$. \ $\iff$ $a + b + c = 23 - d \leq 18$.
So it's enough if you only look at a, b and c being less than 18, you will always find a d
Surely we can pick (5, 5, 5) for example
Then we can pick one of them and go one up
(5, 5, 6)
(5, 5, 7)
(5, 5, 8)
Or pick the second position, for example
(5, 6, 5)
(5, 7, 5)
(5, 8, 5)
For the first, we get
(6, 5, 5)
(7, 5, 5)
(8, 5, 5)
10 possibilities for increasing one position
We can also increase two positions, then go up with one
Like (6, 6, 5)
(7, 6, 5)
visual wren
ok
graceful badger
There are in total $\binom{3}{2} = 3$ possibilities to choose $2$ positions out of $3$ and for each of them, we get $3$ new possibilities (because for example for increasing the first two positions we get the following: (6, 6, 5), (7, 6, 5) and (6, 7, 5))
That makes 9 possibilities
Now there is one more thing we can do, we increased one, we increased two, we can also increase all three
There is only one possibility for that
6, 6, 6
So we get in total 10 + 9 + 1 = 20 possibilities
vague thorn
It is known that a,b,c,d are integers and all of them are greater than 4. Find t...
Use Stars and Bars from combinatorics
visual wren
Use Stars and Bars from combinatorics
what is stars and bars
vague thorn
so
if you have k variables summing up to n, and all the k variables are strictly positive, then the number of combinations of the variables is (n-1)C(k-1)
in this case, a, b, c, d are greater than 4, so we need to set a new equivalent equation so that we have the variables as > 0
vague thorn
let p = a-4, q = b-4, r = c-4, s = d-4
this makes the new equation as
p + q + r + s + 4*4 = 23 or p + q + r + s = 7
clearly, p, q, r, s are all greater than 0
the number of solution sets will be by stars and bars, therefore, (7-1)C(4-1) = 6C3 = 20
visual wren
let p = a-4, q = b-4, r = c-4, s = d-4
this makes the new equation as
p + q + r...
omg tysm
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split sail
how to do this in a formal way ?
amber waspBOT
how to do this in a formal way ?
jovial field
Yo
split sail
yo
cunning birch
how to do this in a formal way ?
first thing to say is that this is equivalent to limit of x^2y^2/(x^2 + 2y^2)
cunning birch
first thing to say is that this is equivalent to limit of x^2y^2/(x^2 + 2y^2)
and focus on x^2y^2/(x^2 + 2y^2) now
final step is AM GM
cunning birch
yes
cunning birch
x^2 + 2y^2 >= 2sqrt(2x^2y^2)
cunning birch
So this will be 1
wut no
cunning birch
so i can use it for every problem
so if you wanna show the limit does exist
in those situations where the denominator goes to 0, the limit SHOULD be 0 if it exists
so you're trying to prove something of a squeeze theorem
split sail
prof leonard never explained these ...
jovial field
Yes got it
See generally
you can take limit of one variable at once
And then the limit of other variable at another time
cunning birch
And then the limit of other variable at another time
no that doesn't work
jovial field
But you should always first check by interchanging the order in which you take as the expression might be discontinuous at that point
split sail
ig we use it when questions says "prove limit doesn't exist" ?
cunning birch
it doesn't mean x goes to 0 then y goes to 0, NOR vice versa
and I said that's not what it is
jovial field
General method
jovial field
Lemme do it and check
split sail
yeah
cunning birch
then this inequality is often very useful
here's a tame example of how young inequality helps us in similar questions
jovial field
I was saying this
This might not always be the case that's why one should always check
cunning birch
which is not always the case
cunning birch
and doesn't necessarily help us towards finding what happens when (x,y)-> (0,0)
cunning birch
Maybe it is the case here?
if lim when (x,y) -> (0,0) exists then it's true
split sail
idk how to do these
ike before inputing the values directly we have to prove that the limit exists right
not just this function
others
cunning birch
for piecewise defined functions, I think the only problem here is when (x,y) -> (0,0)
jovial field
Is this not 0?
cunning birch
you can go back to epsilon delta definition
jovial field
Tell me
split sail
for piecewise defined functions, I think the only problem here is when (x,y) -> ...
not just for piecewise,idk how to do these also
cunning birch
ike before inputing the values directly we have to prove that the limit exists r...
if you remember the proof as to how in 1D a limit exists if and only if left and right limits exist and they're the same
jovial field
Cz when I checked by interchanging the order we take limits on x and y it comes 0
By both orders
cunning birch
not just for piecewise,idk how to do these also
ok we're going to this next
cunning birch
here's an example
cunning birch
$\lim_{(x,y)\to (0,0)}\frac{x^{\frac 43}y}{x^2+y^2}$
cunning birch
?
cunning birch
But always make sure to check
Just because
cunning birch
this is true
jovial field
My logic says we consider one variable at a time
cunning birch
doesn't mean the limit exists
cunning birch
My logic says we consider one variable at a time
you want a counterexample?
jovial field
And if we take first y in one case
The limits are equal
If not
Then this is not true
jovial field
you want a counterexample?
I k ik I literally said that in my complete statement
cunning birch
$\lim_{(x,y)\to (0,0)}\frac{xy}{x^4 + y^4}$
grizzled pagodaBOT
rafilou is not not born in 2003
jovial field
Bro relax
cunning birch
what happens now
jovial field
I literally said that above in my statements
One should check first
What happened chill bro?
I literally said that
Ik
cunning birch
okok but you said "check if lim(x-> 0) lim(y-> 0) (f(x,y)) = lim(y->0) (x->0)
I'm telling you in almost all cases this is unnecessary
jovial field
Yes if it's true
You can apply
Considering this
If not then you cannot consider it
cunning birch
yes but this is a consequence of lim((x,y)->(0,0)) existing
jovial field
I said this
Which is correct I feel
In this case at both the limits were equap
Equal*
I applied taking one at a time
cunning birch
I really don't understand the meaning of what you wrote under
jovial field
I said if one limit=other limit
We can consider taking limit of one variable at a time
But if limits are not equal
We cannot consider it
cunning birch
We can consider taking limit of one variable at a time
but what does this mean
jovial field
Like say x tends to 0 and y tends to 0
So first I take limit only on x
And treat say y as constant
In second case I first take limit on y only and treat x as constant
If value of limit in both the cases is equap
equal*
This means our consideration is valid
If not this means our consideration is not true and cannot be applied
cunning birch
This means our consideration is valid
What do you mean by "our consideration is valid"
jovial field
Our consideration is this
cunning birch
what?
jovial field
This
cunning birch
so you're literally saying "if A is true then A is true?"
cunning birch
then what are you saying
jovial field
First solve both the limits
If they come equap
equal*
Then that is the value of the original limit
If not
cunning birch
Then that is the value of the original limit
I'm telling you that's FALSE
cunning birch
**rafilou is not not born in 2003**
ok try this then
what is the limit of that thing
jovial field
0?
jovial field
Ok
cunning birch
even though
jovial field
Understood
jovial field
,w lim x tends to 0,y tends to 0 xy/(x^4+y^4)
grizzled pagodaBOT
jovial field
Fair
cunning birch
because for example when x = y
you have x^2/(2x^4) = 1/(2x^2)
which goes to infinity
split sail
**rafilou is not not born in 2003**
we were here
jovial field
Ya okok I got it
cunning birch
**rafilou is not not born in 2003**
so ok in this example
cunning birch
In this case it works
?
anyways, young inequality can tell us that $x^2+y^2 \geq |xy|$
grizzled pagodaBOT
rafilou is not not born in 2003
jovial field
in x^2(siny)^2 case this works
cunning birch
in x^2(siny)^2 case this works
sure, but if your rule fails on one example, then it isn't true and applicable nowhere
jovial field
,w lim x tends to 0, y tends to 0 x^2(siny)^2/(x^2+2y^2)
grizzled pagodaBOT
jovial field
sure, but if your rule fails on one example, then it isn't true and applicable n...
Man they have showed a counter example too
x-y/(x+y)
If limit is evaluated along different paths
Even if both are equal
It may not exist
👍
cunning birch
(x-y)/(x+y) is a counterexample to your claim?
no
since first taking as x goes to 0 then y goes to 0 you would get -y/y = -1
and opposite would be x/x = 1
jovial field
Should I send a pic?
cunning birch
**rafilou is not not born in 2003**
ok I'm only going to focus on this for now
cunning birch
Because of Young inequality, $\left|\frac{x^{\frac 43}y}{x^2+y^2}\right| \leq \frac{x^{\frac 43}|y|}{|xy|}$
grizzled pagodaBOT
rafilou is not not born in 2003
cunning birch
and so $\left|\frac{x^{\frac 43}y}{x^2+y^2}\right| \leq |x|^{\frac 13}$
grizzled pagodaBOT
rafilou is not not born in 2003
cunning birch
so by squeeze theorem, $\lim_{(x,y)\to (0,0)}\frac{x^{\frac 43}y}{x^2+y^2}= 0$
grizzled pagodaBOT
rafilou is not not born in 2003
split sail
oh
cunning birch
does this make sense @split sail ?
cunning birch
yeah?
split sail
i wont be do use younds inequaity eveytime right ??
cunning birch
i wont be do use younds inequaity eveytime right ??
here the modulus is preferred
cunning birch
yes just be careful
in young inequality you require 1/p + 1/q = 1
so it worked in our case because p=q=2
(became cauchy schwarz)
cunning birch
it does if you take a = x and b = (sqrt2 y)
split sail
OH!
cunning birch
don't forget that constants can be included in our young inequality
split sail
i dont get you
cunning birch
i dont get you
like
we can take b = some constant * y
instead of taking b = y
it's just about shaping it to our denominator
more complex example, if we had x^4 + y^4 in the denominator
we could take a = x^2, b = y^2
but we could have also picked a = x^3, b = y
(p = 4/3, q = 4, 1/p + 1/q = 1)
cunning birch
depends on what your numerator is and how you wanna upper bound
e.g $\lim_{(x,y)\to (0,0)}\frac{x^3y^{\frac 43}}{x^4+y^4}$
cunning birch
but we could have also picked a = x^3, b = y
you'll find this works marvelously
there's some constant missing tho
since the denominator has to look like a^p/p + b^q/q
so a = constant*x^3, b = constant*y, i'll let you work the details
grizzled pagodaBOT
rafilou is not not born in 2003
cunning birch
sorry for the long ass conversation @split sail 😅
cunning birch
haha, was about to say "oh you were helpful indeed"
grizzled pagodaBOT
split sail
half my letters go missing after i wake up
s went missing again
for this question
@cunning birch ?
split sail
then this inequality is often very useful
also can this be extended to 3 variables /
?
cunning birch
also can this be extended to 3 variables /
cunning birch
for this question
and yes this is supposed to be 0
because |xy|/(x^2+y^2) <= 1/2
and |x^2-y^2| goes to 0
split sail
split sail
and yes this is supposed to be 0
okay
cunning birch
i would start off by writing ln(x)=< x
before doing that you should worry about the limit of the thing inside the ln
split sail
sorry i meant to write x
cunning birch
remember that upper bounding the absolute value doesn't amount to anything if the limit isn't 0
cunning birch
i would start off by writing ln(x)=< x
this won't help
split sail
yeah
cunning birch
just remember that ln is continuous
split sail
yyes
cunning birch
so if the thing inside goes to a > 0 for example
then ln(...) goes to ln(a)
so try to find the limit of this first
split sail
so try to find the limit of this first
im left with (3x/2y) - (xy/2) + (3y/2x)
after using the youngs inequality
cunning birch
after using the youngs inequality
remember young's inequality only amounts to anything if you're trying to prove the limit is 0
cunning birch
so try to find the limit of this first
in our case the limit exists, but it isn't 0
split sail
but how do we know its not 0 before we even find it ?
cunning birch
but how do we know its not 0 before we even find it ?
easy paths to (0,0) can help you find what the limit should be PROVIDED it exists
for example (x,0) or (0,y)
split sail
oh
split sail
so try to find the limit of this first
i can rewrite this as 3 - (xy)^2 / x^2 + y^2
split sail
x,y tends 0
cunning birch
i can rewrite this as 3 - (xy)^2 / x^2 + y^2
yep
split sail
now we can just concern ourself with (xy)^2 / x^2 + y^2
limit tends 0
youngs inequality now would give us modulus (xy)^2 / x^2 + y^2 =< 2xy
?
how do we prove limit xy is 0 ?
cunning birch
youngs inequality now would give us modulus (xy)^2 / x^2 + y^2 =< 2xy
with modulus but yes
cunning birch
how do we prove limit xy is 0 ?
I think you have a continuous function (polynomial) so...
amber waspBOT
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inland pulsar
you cant factorize that imo?
silent ether
Just gimme the answe
solar gust
Just gimme the answe
!noans
amber waspBOT
Just gimme the answe
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
silent ether
And explain
inland pulsar
💀
rancid raven
Just gimme the answe
Learn factorisation first maybe and quadratic equation
silent ether
Give me a egsample for quadratic equation
rancid raven
x²+2x+3=0
inland pulsar
here ^
night spade
ax^2 + bx + c = 0..
You need two numbers such that p*q = c and p+q = b
rancid raven
try to factor <:sotrue:826971355542192148>
solar gust
ax^2 + bx + c = 0..
You need two numbers such that p*q = c and p+q = b
anyway this is a good method for the question related
rancid raven
ax^2 + bx + c = 0..
You need two numbers such that p*q = c and p+q = b
They haven't even started quadratic equation, so I am sure they will not understand what's p and q
inland pulsar
||bro prob already left||
rancid raven
@silent ether if you want help or want to understand please tell us, else you can close the channel. None of us will give a direct answer unfortunately
silent ether
rancid raven
night spade
um..
solar gust
if you have a product equal to zero, then first part is equal to zero or second part is equal to zero
ab = 0
a = 0 or b = 0
just let a = x-7 and b = x-5
silent ether
Thanks bitc’h
amber waspBOT
@silent ether Has your question been resolved?
silent ether
Yess king 👑
keen pawn
amber waspBOT
keen pawn
This is obviously a direct proof
It sort of screems GP sum , but I think That's what It wants me to prove
solemn escarp
sorry, but cant you do "let this sum be S, then 2S = ... and S = ..." or is that not intended
keen pawn
I mean I could ,and that was my original idea, but eh, feels like cheating
graceful badger
I'd induction this
keen pawn
Can't
graceful badger
ah
keen pawn
Otherwise that would have been the obvious choice
ooh
$(2^{n+1}-1^{n+1}) = (2-1)(2^n+2^{n-1} + \dots + 2^0)$
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
amber waspBOT
@keen pawn Has your question been resolved?
keen pawn
Is this good rnough?
$(2^{n+1}-1^{n+1}) = (2-1)(2^n+2^{n-1} + \dots + 2^0) = 2^{n+1}-1$ QED
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
keen topaz
Makes sense 😃
amber waspBOT
inland pulsar
It sort of screems GP sum , but I think That's what It wants me to prove
yup
alpine flower
?
split kraken
shell parrot
can anybody tell me integration concepts
amber waspBOT
can anybody tell me integration concepts
molten shale
can anybody tell me integration concepts
which
molten shale
do u know product rule
shell parrot
no
molten shale
ok
doens't matter
by parts is basically integrating the product of two functions
lets say f(x)g(x)
if i derive f(x)g(x) i will need to use product rule
shell parrot
can I msg u in direct?
amber waspBOT
@shell parrot Has your question been resolved?
astral flame
someone help me calculate the limits of this function as x goes to +infinity and -infinity
1+x / 1 -x
grizzled pagodaBOT
Edmund Cloudsley
split sail
this is the question right?
astral flame
i found + infinity but i cant find -infinity
split sail
we could divide the denominator and the numerator with
split sail
$$ = \lim_{x \to -\infty} \frac{\frac{1}{x} + 1}{\frac{1}{x} -1}$$
grizzled pagodaBOT
Edmund Cloudsley
split sail
yup
astral flame
+1/-1 = -1??
astral flame
but thats just wrong
split sail
,w limit x tends to negative infinity (1 + x)/(1-x)
grizzled pagodaBOT
astral flame
wait
split sail
,w plot y = (1 + x)/(1-x)
astral flame
1
grizzled pagodaBOT
astral flame
dude im a dumbass
split sail
u can use this graph to find out the lkmit
astral flame
thanks tho
split sail
dude im a dumbass
don't say that mate
I've missed the most obvious of things in maths
one feels stupid
astral flame
it can be very overwhelming at times
amber waspBOT
@astral flame Has your question been resolved?
fierce edge
amber waspBOT
fierce edge
i already solved it but just wanted to clarify
those two larger equilateral triangles are assumed to have equal areas?
I mean it doesn't look like they mentioned this in the question
oh nvm
"regular hexagon" and "trisects" implies both equilateral triangles have the same perimeter
i need reading lessons
.close
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crimson stratus
is there a mistake i dont see how they got to the parametric equations
crimson stratus
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paper spear
please help with solving lim x -> -inf -x^2-8x-3
amber waspBOT
please help with solving lim x -> -inf -x^2-8x-3
timid vault
That strategy works for rational functions, but won't work here
This is a parabola that opens downward. It goes downward forever in both directions
tulip tapir
just plug in inf and see what you get
it's fairly easy to see that the x^2 term dominates--it grows much faster than the others
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coarse night
sorry @rocky bluff for the ping, I realised I did not fully understand. why is the 2nd y coordinate b?
rocky bluff
sorry <@309005026096054274> for the ping, I realised I did not fully understand....
that's because we know that f(e^b) = ln(e^b) = b
rocky bluff
np
coarse night
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late falcon
can someone help me find the zeroes in number 37? i think i made an error
patent raptor
can someone help me find the zeroes in number 37? i think i made an error
did you factor an x?
patent raptor
did you then substitute u = x²?
late falcon
yes
wait wtf
why did i do that
wait no what
what did i do wrong
i checked desmos and the other zero is -sqrt(2)
late falcon
no
nova raft
(-2)^2 = what?
late falcon
nova raft
well, x^2 = a, meaning x = sqrt(a) or x = -sqrt(a).
late falcon
wait
omg ur so right
there are complex zeroes it just doesn’t show
+/-sqrt(-3) are zeroes
aaaa i can’t believe i forgot ab that
tysm man❤️
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amber waspBOT
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glad tiger
quick question for convenience purposes. When differentiating, is it easier if I convert all my quotients to products?
ex: should I differentiate 3t/sqrt(t) as is using the quotient rule or should I convert to (3t)t^(-1/2) and use the product rule?
grizzled pagodaBOT
riemann
glad tiger
Neither
i meant in general, not in this specific case
but yeah I should simplify fractions
pallid canopy
i meant in general, not in this specific case
There is no general rule
It's whatever is fastest for you
glad tiger
i see
I guess thatmakes sense
because when you use the product rule in that case youd likely also have to also use chain rule
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amber waspBOT
glad tiger
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crimson stratus
amber waspBOT
crimson stratus
Idk where to start
amber waspBOT
@crimson stratus Has your question been resolved?
crimson stratus
<@&286206848099549185>
slate roost
@crimson stratus to start, take that line equation and put it in the form y=mx+b
crimson stratus
how
slate roost
oof this is 3d, interesting. but the principle should be the same here I think
slate roost
well let there be that line D
the distance would be a perpendicular line to that one
so the segment that goes perpendicular to line D and reaches the point, is the distance
sterile siren
you sure you need parametric equation?
i think you can look at it in xy plane and then in xz plane and pythagoras results
hollow temple
Is what I did wrong?
amber waspBOT
Is what I did wrong?
quick ridge
weak zinc
(also, what's the derivative of x * ln(x)?)
hollow temple
1 * 1/x, right?
or would I approach it as a product rule
so then my answer would be (1/xlnx) times lnx + 1?
which I could simplify to lnx + 1 all over x ln x
I think
sick
similar question to the last one
oh god I'm fucked for tomorrow
weak zinc
If that's to be interpreted as $\sqrt{x} \cdot \cos(\sqrt{x})$, then no trig function itself should appear in roots
grizzled pagodaBOT
@weak zinc
hollow temple
how would I get rid of the roots then?
is that just a simple product rule? sqrt x times cossqrtx?
patent raptor
oh god I'm *fucked* for tomorrow
but not today chartbit saves the day
weak zinc
*but not today* chartbit saves the day
Awwwww 
weak zinc
is that just a simple product rule? sqrt x times cossqrtx?
And well, product (and also chain to differentiate cos(sqrt{x}) of course)
hollow temple
that's what I tried to do at first by taking out 1/2(cossqrtx)^-1/2
weak zinc
Hmmm, that's very sus 
hollow temple
i thought that's what chain rule says
differentiate the outside function, leave the inside as it is
weak zinc
The outside function is cos(u), the inside function u is sqrt{x}
weak zinc
The square root is inside the cos
And for the sqrt that's outside, that's where the product rule comes in
You wanna get the derivative of sqrt{x} (relatively easy) and the derivative of cos(sqrt{x}) (that one you need the chain rule for)
hollow temple
derivative of cos sqrt x is -sin (sqrtx) times (1/2x)^(-1/2) I think
patent raptor
brute forced it
patent raptor
noo that'S not what i said
weak zinc
The 
was for (1/2)x^{-1/2}, btw 
(you can have the happy cat thumbs up after it's fixed 
)
The x shouldn't be in the 
hollow temple
anyways once I get that, do I leave that as is and product rule with that and sqrtx?
ok nice
will probably be back for more pain after dinner
thank you for the help
amber waspBOT
@hollow temple Has your question been resolved?
regal swift
amber waspBOT
regal swift
hollow temple
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white python
need help urgent
amber waspBOT
need help urgent
heady willow
window
cedar plaza
lets count
we have the first 2
1
2
then the next two
3
<@&268886789983436800>
scenic dagger
@white python @heady willow don't misuse the help channels for this kind of thing. You're muted for the day.
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thick seal
amber waspBOT
thick seal
does anyone know what z= is?
what is represent
the amount of e-?
varaibles and number s involved so its kind fo math sry
elder harbor
main patrol
i only took chemistry last year and we didn't spend a lot of time on this stuff but I think z might be the atomic number?
thick seal
o
main patrol
which is also equal to protons and electrons
amber waspBOT
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fair pawn
So how would I be able to this problem for both the table and the four questions at the bottom. Work is needed to be shown
amber waspBOT
So how would I be able to this problem for both the table and the four questions...
@fair pawn Has your question been resolved?