#help-27
jolly bluff
restive river
yup
jolly bluff
and a and t are both 3?
jolly bluff
sheeeesh
devout snowBOT
@jolly bluff Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
covert anchor
I was working on proof for the prompt
Prove that a set of n (different) elements has exactly 2^n (different) subsets.
I was looking for feedback on my proof.
I did a proof by weak induction
devout snowBOT
I was working on proof for the prompt
Prove that a set of n (different) elements...
restive river
The proof seems alright
grizzled snow
Help
restive river
Having trouble analyzing a probably a statically indeterminate continuously supported beam. Below is the diagram and the data. I am stuck with even trying to resolve for and finding the reaction forces. Can someone walk me through on how to tackle this question?
A continuous beam of length 10 m is supported by three supports. The distances between the
supports are as follows:
• The left support is located at the left end of the beam.
• The distance between the left support and the middle support is 4 m.
• The distance between the middle support and the right support is 6 m.
The beam is subjected to the following loads:
• A point load of 15 kN at a distance of 2 m from the left support.
• A uniformly distributed load of 6 kN/m between the left support and the middle support.
• A triangular load that starts from the middle support and increases uniformly to 10 kN at the
right support.
The left support is a roller support, the middle support is also a roller support and the right support is a fixed support.
Help
grizzled snow
Help
devout snowBOT
Having trouble analyzing a probably a statically indeterminate continuously supp...
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
pale bolt
Help
this is incredibly illegible and the full problem isn't there
also need to translate because we can't read (Thai??) foreign language
devout snowBOT
@grizzled snow Has your question been resolved?
grizzled snow
also need to translate because we can't read (Thai??) foreign language
Oh my baddd
Its Georgian
@pale bolt Let's say A is the set of odd natural numbers, B is the set of even natural numbers, which entries are correct?
devout snowBOT
@grizzled snow Has your question been resolved?
idle tinsel
Rewrite cosh 6x + sinh 6x in terms of exponentials
devout snowBOT
Rewrite cosh 6x + sinh 6x in terms of exponentials
plush knot
I'd try with the exponential definitions in this case
idle tinsel
How would I do that?
plush knot
sinh(x) = (e^x - e^(-x)) / 2
cosh(x) = (e^x + e^(-x) / 2
Do they look familiar?
woven radishBOT
Price
idle tinsel
mm I got
$\frac{2e^{6x}}{2}$ after simplifying
woven radishBOT
Price
idle tinsel
but wasn't right
plush knot
I think that's right, you still can simplify the 2s though
brisk raft
If you have the integral sin^n(x)cos^m(x)dx and n and m are both odd, do you use the pythagorean identity or the half-angle formula?
devout snowBOT
If you have the integral sin^n(x)cos^m(x)dx and n and m are both odd, do you use...
astral niche
how can you formalize that a matrix is strictly better than another one?
stone stump
well what do you mean with "better"
astral niche
it have greater numbers in it
I have to model it in terms of utility
so the higher the value the higher the utility
so the better
stone stump
well then you can say that $A\geq B$ if and only if $a_{i,j}\geq b_{i,j}$ for all $i,j$
woven radishBOT
Denascite
viral basin
is there a way to re-write this?
supple knot
!onechannel
devout snowBOT
Please stick to your channel.
supple knot
.close
devout snowBOT
viral basin
.reopen
devout snowBOT
✅
velvet onyx
lol
devout snowBOT
@viral basin Has your question been resolved?
devout snowBOT
@viral basin Has your question been resolved?
jaunty needle
What percent pf men are between 64 and 66.5 inches tall
devout snowBOT
What percent pf men are between 64 and 66.5 inches tall
jaunty needle
This is a density curve question where i have to use 68, 95, and 99.7 to figure out the answer
Mean is 69 and std.dev. Is 2.5
Nvm i got it
Lol
.close
untold notch
devout snowBOT
pine rock
!15min
devout snowBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
untold notch
Can u help me about that
pine rock
,rccw
woven radishBOT
restive river
I’m stuck on this question
I don’t know what formula to use, I have the formulas but I never know when to use which one, and I keep getting the wrong answers according to the textbook
restive river
so you have the sum of two compounding accounts adding up to 10,000
how far have you gotten? if you need formula help I assume you know the logic of what to do?
I have these formulas
But I never know which one to use
restive river
how far have you gotten? if you need formula help I assume you know the logic of...
Yeah I know what to do but I don’t know what formula
the compound interest one
Am I right to do A = P(1 + r/n)^nt
Okay
A = 0(1 + 0.041/52)^52(2)
I don’t know what the principal would be
I assume 0
if they started with $0 they'd compound to $0 forever 
Uhh
they started with $50
Okay
waiittt
I just saw the regular payments one
You'd need that for the first part, I believe
they're regularly depositing $50, not just once
10,000 = 50(52)/0.041 ((1 + 0.041/52)^52(2) -1)
Wait
Is it fv = or 10,000 =
FV =, you want to know how much they make themselves, so the parents can help with the rest
Okay
,w 50(52)/0.041 ((1 + 0.041/52)^52(2) -1)
woven radishBOT
restive river
wrong formatting, hmm
Put it to the power of 104
,w ((50 * 52)/0.041)( ( 1 + 0.041/52)^(52 * 2) - 1)
i think
woven radishBOT
restive river
I got the same thing
anyway 10k - that is what the parents have to contribute
,w 10,000 - (((50 * 52)/0.041)( ( 1 + 0.041/52)^(52 * 2) - 1))
woven radishBOT
restive river
Does the second part of the question not matter
it does
this remaining 4,583 is for the second part
the parents have to ultimately have raised this much, so what starting amount do they stick in their account so the interest gets it up to 4.5k after 2 years
that's p2
Oh okay
Is that A = P(1 + r/n)^nt
The answer should be $4078.92 but I got $4078.85
.close
near stone
how would you solve for 11.b? do you need to look at x-value or y-value?
livid carbon
horizontal transformation
f(x+h) means f(x) shifted +h units to the left
While f(x)+k is vertical transformation of f(x)
near stone
,tex .transformation rules
woven radishBOT
Akira 🍉
quasi wasp
Try always remember that if its in the brackets then it affects the x values and if its outside then it affects the y-values. And remember, when its inside the bracket, it will do the opposite of what you think, so +2 would move it -2 on the graph
near stone
so it's a y value?
quasi wasp
What do you mean?
olive condor
hi
near stone
What do you mean?
I mean when you seeing a x-value you look at y-value
olive condor
f(x+2) is f(x) except shifted 2
horizontally
in the left direction
so draw the function shifted left
near stone
oh i get it now
quasi wasp
Yeah, its opposite of what you would think
near stone
so that would be +2?
quasi wasp
+2 actually does -2 on the graph
olive condor
Yeah, its opposite of what you would think
depends on how u think
makes sense to me
y = x
right
want to shift it up?
y - 1 = x
shift it right
y - 1 = x - 1
ppl say its confusing cuz shifting up is y = x + 1
move the 1, and it makes sense
quasi wasp
I wish i could think like you in that, I just hard code the rule that its opposite in my brain and call it a day
olive condor
lol
olive condor
did u read the chapter
near stone
yes I did but how they get the 5 from
olive condor
where r u seeing 5..?
quasi wasp
I think probably the answer page I imagine, can’t see why it would be 5 though if its asking you to plot the transformations
near stone
where r u seeing 5..?
wait it's something else
was checking the answer for the previous question
quasi wasp
Phahaha
rigid rain
How do i do an epsilon delta proof for a one sided limit?
devout snowBOT
How do i do an epsilon delta proof for a one sided limit?
paper latch
it would be $0 < x-3 < \delta$
woven radishBOT
Frog_Man
paper latch
as opposed to for a 2 sided limit, when it is $0 < |x-3| < \delta$
woven radishBOT
Frog_Man
devout snowBOT
@rigid rain Has your question been resolved?
silver hedge
I need help calculating these bills:
devout snowBOT
I need help calculating these bills:
little bronze
1) -2^2-4x-1x15
Umm are they supposed to be $x$ or multiplication
weak cove
can you show us a picture of the question?
woven radishBOT
ahaan
pine rock
that's not the first time he asks, he needs to calculate the value of the expression (x is multiply)
silver hedge
I don't know how to do that
pine rock
upon asking about exponents and addition demands immidiate answer
slim token
I don't know how to do that
You can use parentheses to imply if your multiplying for example (9) (1)
x is interpreted as a variable, so its better for us to understand if you use parentheses.
silver hedge
I need a prompt answer
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
sweet thorn
devout snowBOT
sweet thorn
Not sure what to do next or where I might have gone wrong..
devout snowBOT
@sweet thorn Has your question been resolved?
nova ibex
I think you messed up
cosmic pier
Do you know what the reduction formula for the integral of sec^n (x) is?
sweet thorn
I do not, although I have glanced at it.
I think I figured it out
We are supposed to set int(sec^3x) to H and add to both sides
or essentially just add to both sides
to solve for the derivative of int(sec^3x), I remember doing something similar earlier in the class so I'll go with that lol
.close
calm belfry
i know you set denominator to 0
devout snowBOT
i know you set denominator to 0
wooden wraith
nah keep one side equal to 0
It's a quadratic. You can factor it (if possible) or use the quadratic formula or complete the square
sleek cargo
yeah its possible
wooden wraith
yeah its possible
yeah I was leaving that up to op to figure out lol
sleek cargo
i prefer rooting
wooden wraith
i said if possible because in general it's not always
sleek cargo
x^2-x-12=0
solve it like this
this one is right
use formula: b^2 - 4 x a x c
b = 1
a = 1
c = -12
calm belfry
-47
calm belfry
7?
sleek cargo
yes
now x1 = b-7/2
x2 = b+7/2
you will have your asnwer)
@calm belfry what did you get?
calm belfry
-5/2 & 9/2
wooden wraith
now x1 = b-7/2
(-b-7)/2 and (-b+7)/2
calm belfry
why negative b
sleek cargo
(-b-7)/2 and (-b+7)/2
not negative
wooden wraith
yes negative, the quad formula is (-b +/- D)/2a
calm belfry
-3 & 4
wooden wraith
not always
?
wooden wraith
if b come negative
if b is negative, then -b is positive
woven radishBOT
tatpoj
wooden wraith
if b is negative, then the first term, -b is positive. you don't need to make an exception
or you can just factor it and solve and get -3 and 4 that way as well
oh what? b in this case was -1, why did you tell her it's 1?
sleek cargo
(-b-7)/2 and (-b+7)/2
if you put 1 instead of b, -8/2 = -4 and 6/2 = 3
different asnwer
wooden wraith
ask;ugbaklvanbskvnawskevanj
right
b = -1
-b = 1
(1 + 7)/2 and (1 - 7)/2
is this just a different convention in some parts of the world?
because the coefficient b is -1
I'm very confused about what you're saying
sleek cargo
wooden wraith
but
that's what I've been saying this whole time
b is -1
-b is 1
I just mistyped it in that one line
calm belfry
i did 1-7/2 and 1+7/2
wooden wraith
you have vertical asymptotes at x=-3 and x=4
wooden wraith
two vertical lines
sleek cargo
wrong dots
misty quest
Hello I need some help ik the answer is 735 but like just a bit confused on the set up
devout snowBOT
Hello I need some help ik the answer is 735 but like just a bit confused on the ...
twin flume
total students = x
students who do not eat at servo but eats at ike = (1/3-1/5)x
students who do not eat at ike but eats at servo = (2/7-1/5)x
students who do not eat at both ike and servo = (1/5)x
students who eat at both ike and servo = (427)
devout snowBOT
@misty quest Has your question been resolved?
misty quest
Am I distributing the X?
devout snowBOT
@misty quest Has your question been resolved?
misty quest
<@&286206848099549185>
timber pebble
Hello I need some help ik the answer is 735 but like just a bit confused on the ...
id probably use some kind of venn diagram here
misty quest
One be servos and the other be Ike’s?
misty quest
Hmmm but idk what I’d put on each side
timber pebble
Hmmm but idk what I’d put on each side
work on filling in the picture first
i mean the picture as in like idea of what you can say
heres my drawing
My thought is: you have 4 regions, and everyone fits into exactly one of these categories. So, if you add up all four regions, you should have everyone, only once, right?
misty quest
Yeah
timber pebble
My thought is: you have 4 regions, and everyone fits into exactly one of these c...
try translating this into math
misty quest
Can I subtract one from the 2/7 which would give me the amount that eats at ikes?
timber pebble
,w solve 427+2/7 x + 1/3 x + 1/5 x = x
woven radishBOT
misty quest
woven radishBOT
timber pebble
@misty quest
got it
so they are talking about more general regions
doesnt eat at ikes doesnt mean only eats at Servo
it means the entire green region here
so if you add up the red, the green, and the yellow, you get the entire region
but with a problem
you've counted the purple region twice
(because both green and red cover that region)
doing it this way gets you the correct answer
misty quest
But why am I setting it equal to x + 1/5
timber pebble
you can think of it the other way
red + green + yellow gets you N right
but youre overcounting
red and green overlap
specifically, they overlap in the purple, which is being counted twice
so red + green + yellow - purple
this accounts for the double counting with red+green
so red + green + yellow - purple = N
or red + green + yellow = purple + N
misty quest
Ohh the 1/5 isn’t a new group but just part of the other group
timber pebble
well like
green is the people that eat only at Servo, plus the people who eat at neither
and red is the people that eat only at Ike's, plus the people that eat at neither
@misty quest what you think
misty quest
Oh wait I think I get it now so like the 1/5 is the group that doesn’t eat at either so I just have to subtract it?
timber pebble
Oh wait I think I get it now so like the 1/5 is the group that doesn’t eat at ei...
so, heres this red group
this is everyone who doesnt eat at Servos
do you see how its every where except for inside the S circle?
and here's the other way
this is everyone that doesn't eat at Ike's
misty quest
Yes but wouldn’t it be both colored since they don’t eat at both?
timber pebble
Yes but wouldn’t it be both colored since they don’t eat at both?
which be both colored?
the very outside?
misty quest
The red for the circles
timber pebble
The red for the circles
red is for people that dont eat at servos
So, theres 2 possibilities
they dont eat at servos, but they do eat at Ike's
or, they don't eat at either
misty quest
Oh okay I thought red was the 1/5 that doesn’t eat at both
timber pebble
Oh okay I thought red was the 1/5 that doesn’t eat at both
but the red includes this group
do you see why?
this is the crux
Its like
if you take the group of everyone who doesn't own a cat
it includes people who only own a dog
and people who dont have a cat or a dog
do you see what I mean?
"Don't eat at Servo's" is two groups
if you dont get what i mean thats fine, this is the fundamental piece of the problem
once you get this you will get the whole thing I think
misty quest
The 2 groups are the 1/5 and the 1/3 right
timber pebble
hmm i think the 1/3 and the 2/7
but the exact amounts dont matter
you dont need to know these until the very end
misty quest
Am I counting it twice since it’s included in the 1/3 and the 2/7
timber pebble
right
Because if you are a person who doesn't eat at Ike's or Servo's
You don't eat at Servo's
and You don't eat at Ike's
you answer yes to both of those questions
misty quest
Ohhh that makes sense now
Couldn’t I also subtract the 1/5 from the 1/3 and 2/7 in the beginning
And then add the 1/5?
timber pebble
hmm I guess
misty quest
Okay I get it now thank you so much
timber pebble
misty quest
frail current
hello
frail current
my professor solved this questoin in a way i dont understand can someone explain to me why he doing it like this
this is the question
hasty umbra
<@&286206848099549185>
i have also tried no ones also helping me
frail current
yea
frail current
i have also tried no ones also helping me
i feel you on this there pretty busy or
its just this question everytime i ask it no one responds maybe its just diffculte or something
cerulean crater
its just this question everytime i ask it no one responds maybe its just diffcul...
I feel like the handwriting is a bit difficult to read
,rotate
woven radishBOT
cerulean crater
So... I'm still taking Calc III so I don't understand it fully, but I'm learning this stuff rn so I might be able to help a bit
x+1 = 2-y = z-1
frail current
I feel like the handwriting is a bit difficult to read
handwriting is my weakpoint
cerulean crater
x+1 = 2-y = z-1
x + 1 = t
2 - y = t
z - 1 = t
It looks like your professor set each equal to t to get the parametric equations
cerulean crater
handwriting is my weakpoint
I feel you, same here
frail current
thats right
and he got a vector u = <1,-1,1>
just move t to the other side and you she get this vector
cerulean crater
x + 1 = t
2 - y = t
z - 1 = t
It looks like your professor set each equal to t ...
x = t-1
y = 2-t
z = t-1
vector = <1 , -1 , 1 >
yeah, like you said
and the point is (-1,2,-1)
right?
frail current
i dont know about the other point
cerulean crater
and the point is (-1,2,-1)
that's a point on the parametric equation, actually idk if we'll need it
frail current
yea
i dont think he uses it
this is my first question why is it BA othognal
not AB
cerulean crater
BA is the vector from point B to A, vector AB moves in the opposite direction (from A to B rather than B to A)
I think you can use either, but your teacher might've chosen BA bc it gives easier numbers to work with
frail current
ah ok
idk if you can read this
but i get everything except for the last
part
how did he get this
never mind talking to you right no
w
i see how he did it
so
how is that the answer though
AB = <0, 1, 1>
I feel like its still missing something
cerulean crater
Yeah, if the dot product of two vectors is zero, then it's perpendicular.
The vector we found from the parametric equations was <1,-1,1> I think
The dot product of that with the AB vector is 0, which means they're perpendicular
cerulean crater
did u know u can try plotting these points online to get a visual of how they look
np, good luck with calc III
frail current
u2
devout snowBOT
@frail current Has your question been resolved?
halcyon karma
any idea how to start this
devout snowBOT
any idea how to start this
graceful cosmos
x = 7sinh(u)
halcyon karma
sorry but what does that do
supple knot
sorry but what does that do
Do you know any hyperbolic trig identities
halcyon karma
yes
supple knot
x = 7sinh(u)
Use the identities after this substitution
halcyon karma
.close
devout snowBOT
devout snowBOT
Available help channel!
nocturne relic
devout snowBOT
nocturne relic
is this a correct way to solve this limit?
inland seal
Why did 2log(x) turn into 2 though?
lone ravine
is this a correct way to solve this limit?
No
lyric hornet
maybe try rewriting this limit: $\lim_{x\to0}\frac{x^2}{e^{-\frac{1}{x}}}$
woven radishBOT
MrFancy
lone ravine
Or argue with the lim u->infinity (exp u)/u^2 if you are defining exp over the infinite series and want to use as less fancy maths as possible (that is how we introduced it in analysis 1)
lone ravine
A lot of l'hospital enjoyers 
lyric hornet
actually this might be DNE
lyric hornet
ohhh
hybrid snow
I mean depends on your definition of DNE
lyric hornet
gotchu I'm blind 
devout snowBOT
@nocturne relic Has your question been resolved?
urban hornet
pine rock
!show
devout snowBOT
Show your work, and if possible, explain where you are stuck.
pine rock
nice question, btw
manic condor
nice question, btw
What are you getting? I think none of these should be correct as i keep getting -cot(x).
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
devout snowBOT
@urban hornet Has your question been resolved?
normal cove
Rewrite as $I =\int\left(\operatorname{cosec}^2 x-2005\right) \sec ^{2005} x d x = \int \operatorname{cosec}^2 x \sec ^{2005} x d x-\int 2005 \sec ^{2005} x d x$ then apply integral by part.
woven radishBOT
adzetto
restive river
after many tries, i tried to get right answer but i cant. so do someone have an idea how to solve that?
devout snowBOT
after many tries, i tried to get right answer but i cant. so do someone have an ...
restive river
supple knot
after many tries, i tried to get right answer but i cant. so do someone have an ...
show the entire question
restive river
it says to remove ()
silver fjord
is that a semicolon
restive river
<:wg:1130147597428998184> is that a semicolon
uh that is like book and has many examples
silver fjord
well () is just a fancy way of writing multiplication
supple knot
work inside out x(5+x) = ?
restive river
work inside out x(5+x) = ?
i did
restive river
but i got diffent than this:
restive river
how did you get this?
here it is
plucky wadi
why are you multiplying 4+x with 5+x?
supple knot
mistake here
plucky wadi
You're only supposed to multiply x with 5+x
restive river
oh
plucky wadi
Yeah
willow quartz
Can someone help with question 8?
devout snowBOT
Can someone help with question 8?
deep vortex
During the "well temperament", the sound frequencies between $440$ Hz and $880$ Hz are divided by $11$ nuances (sounds) in such a way that two always have the same ratio. Determine this ratio.
devout snowBOT
During the "well temperament", the sound frequencies between $440$ Hz and $880$ ...
deep vortex
We have that $\frac{a_{n+1}}{a_n} = k$, so $a_{n+1} = k \cdot a_n$. This means that [a_{11} = k \cdot a_{10} = \cdots = k^{11} \cdot a_0 = k^{11} \cdot 440 = 880,] so $k = \sqrt[11] 2$.
topaz axle
they mean like, not including either
topaz axle
in reality, there's 11 "between them", not including either
but without knowing that, I don't think it's clear
deep vortex
in reality, there's 11 "between them", not including either
So sqrt[12]{2} is actually correct, right?
deep vortex
it's not contradictory
What do you mean with not contradictory?
topaz axle
like it's phrased in a way where you can't tell if it's supposed to be 10 or 12; but 12 is one of the options (and 11 is not)
deep vortex
Ah, you mean you can't know if there is a sound at 440Hz and then at 880Hz, the ends
In that case, there would be 9 in between
so 10 frequencies
topaz axle
yes
no
let me make an example
like if it said "there's 3 sounds between 10 and 160"
then it would make sense if it means
10, 20, 40, 80, 160: ratio = 2
and
10,40,160: ratio = 4
deep vortex
like if it said "there's 3 sounds between 10 and 160"
then it would make sense i...
Hm, in this case, there are two possibilities and maybe for larger cases, there are even more?
topaz axle
what do you mean
deep vortex
like if it said "there's 3 sounds between 10 and 160"
then it would make sense i...
Will it always be two possibilities?
"there's n sounds between k and p", then will we always have possibilities with n + 2 and n elements?
topaz axle
idk, sorry
deep vortex
Well, 12 should really be the right answer.
We can imagine a big stripe (sound), and that gets divided by 11 cuts (sounds).
The individual cut pieces are now the sound frequencies, and we'll have 12 of them
deep vortex
like if it said "there's 3 sounds between 10 and 160"
then it would make sense i...
Ah, you mean you can once think of the sounds as the frequencies and once as the distances between them
topaz axle
no, in both cases i'm thinking of frequencies, not spans
there is 12 spans, 13 total frequencies, 11 "betweens"
my main point is that it's phrased badly
devout snowBOT
@deep vortex Has your question been resolved?
deep vortex
there is 12 spans, 13 total frequencies, 11 "betweens"
What do you mean with 12 spans?
The spans between the vertical lines?
There would be 12 of them, yes, there are 11 vertical lines
Why 13 total frequencies?
deep vortex
440, ... 880 is 13
440, ..., 880 denote the segments between the vertical lines in the above picture.
So I think there should be 12 of them?
(and so ... is 10)
deep vortex
440, ... 880 is 13
Oh. You mean that after putting the 11 sounds/nuances, the ends will count as additional 2, so we'll have 13 for 440, ..., 880
topaz axle
yeah, i think that makes sense
the frequencies "contain" 11 points, and don't include the ends
devout snowBOT
deep vortex
.reopen
devout snowBOT
✅
topaz axle
alternatively they include the ends, so there's 11 frequencies, and 10 spans
so you choose between 10th root and 12th root
deep vortex
there is 12 spans, 13 total frequencies, 11 "betweens"
Ok, for 11 sounds, there are 12 spans. That means there are 13 total frequencies. Do you mean "sounds" with "betweens"?
topaz axle
i don't know the word nuance
deep vortex
i don't know the word nuance
I mean "in between sounds" with them
the vertical lines
deep vortex
It says "divided by 11 nuances (sounds)"
deep vortex
there is 12 spans, 13 total frequencies, 11 "betweens"
Yes, you mean sounds with betweens.
Thank you
Though I think between two of these sounds, the same frequency will play so it's worded a bit badly if we say frequencies to the sounds.
The frequencies between 440Hz and 880Hz are divided by 11 sounds, and those 12 parts that come to be have the same frequency.
(or of course, if two of the 11 sounds are at the ends, then there will be 10 parts that have the same frequency)
.close
woven forge
hello, i need help with this permutation.
(1 2 3
2 3 1 )
devout snowBOT
hello, i need help with this permutation.
(1 2 3
2 3 1 )
woven forge
i wrote the following:
sigma I = ( 12 ) * sigma = (1 2 3) * ( 1 2 3 )= ( 1 2 3 )
( 2 2 1 ) ( 2 3 1 ) ( 2 1 2 )
is this correct ?
devout snowBOT
@woven forge Has your question been resolved?
pine rock
you have to close urself, use .close
shell quest
how is f(x) and g(x) factored out the limit
devout snowBOT
how is f(x) and g(x) factored out the limit
scarlet sequoia
zenith jacinth
g(x) doesnt depend of h
zenith jacinth
can you write g(x) in terms of h ?
shell quest
meaning
zenith jacinth
also the limit of a product of function is the product of each limit
since g doesnt depend of h, lim g(x) is still g(x)
native briar
im back
boreal karma
can you do the first derivative with the fraction to start?
native briar
no;-;
mystic scarab
Well, you shouldn't be scared of fractions if you're doing calculus😅
native briar
im behind
boreal karma
okay lets ignore the fraction then and pretend its not there. whats the derivative of just x^3?
native briar
3x^2?
boreal karma
yep now multiply that by the fraction
boreal karma
dont even have to do that
but you can if that makes it easier
you can just do it as 15/6
boreal karma
basically 5/6 + 5/6 + 5/6 is = 5/6 * 3
boreal karma
no so x^2 can be done the same way that the 3 was done
just put it into the numerator
boreal karma
15x^2/6
native briar
is this for the second derivative?
boreal karma
this is just first
native briar
??
boreal karma
now you still have to do the x^2 * the 15/6 we found earlier
boreal karma
the first derivative you found of just x^3 was 3x^2
all of that has to be multiplied by the 5/6
we only did the 3 so far and not the x^2
native briar
????
native briar
the first derivative you found of just x^3 was 3x^2
yea
boreal karma
i was breaking it into steps for you, basically you can do each part one at a time but i think i confused you
native briar
oh
boreal karma
so you dealt with the fraction and the 3 that you found
you just need to multiply that 15/6 that we got by the remaining x^2
boreal karma
the 3 comes from that yes
native briar
so is it 15/6x^2?
boreal karma
is x^2 outside of the fraction?
native briar
is it?
native briar
(15/6) x^2 or 15/(6x^2)
First ?
quaint cove
You can simplify it though
native briar
Wait
boreal karma
yes we can simplify by a factor of 3 here if you want
quaint cove
Would be easier to find the second derivative if you simplify it
boreal karma
yes
native briar
Okie
native briar
Ok
boreal karma
but as another mentioned we can simplify 15/6 to a simpler fraction then we can derivate again
boreal karma
15 and 6 are both divisible by 3
native briar
5/2?
boreal karma
yep! perfect
native briar
aye
native briar
(2)(5/2)?
boreal karma
yep
native briar
5x?
boreal karma
yes
quaint cove
Good job
boreal karma
all you great work
boreal karma
okay
this one is a bit more tricky but thats fine
I might find it helpful to rerwite the problem
native briar
;-;
boreal karma
can you think of any way to get rid of the pesky x in the denominator?
native briar
do I write it is x^4/x^2 - 3/x^2?
boreal karma
- not - but yes I would start there
native briar
oh ok
boreal karma
then I would simplify the first fraction to just x^2 and the second one I would write as 3x^-2
can you follow that?
boreal karma
and then the second term i just took x^2 out from the denominator and changed it to x^-2
boreal karma
do you know that 1/x = x^-1
native briar
Yea
boreal karma
so in this case 3/x^2 = 3x^-2
its the same rule
you can move it up but you gotta make the power negative
native briar
I get it yea
boreal karma
okay so we have x^2 + 3x^-2
boreal karma
negative 2 power on the second term sorry
i keep mistyping
anyways, now we take the second derivatives. we can do one term at a time which do you want to start with
native briar
So do we differentiate now ?
boreal karma
yep
native briar
wait was that all to get the 1st derivative ?
boreal karma
nope
native briar
Oh ok
boreal karma
ok so do you want to start by derivating x^2 or 3x^-2
boreal karma
perfect
native briar
I think I have to rewrite it
would it be
Since it’s a negative exponent
2+18/x4?
boreal karma
yep
native briar
aye thanks
boreal karma
sure
native briar
hold on it’s 2
boreal karma
do you understand what its asking
native briar
wait which question are we doing first
boreal karma
we can do whatever one you want to do
native briar
can we do 21 first
native briar
is it asking to find y’’
boreal karma
yep but what does that mean
i gave you a hint earlier that y' is normally the first derivative
so then what would y'' be
boreal karma
yep exactly
so the problem is just asking whats the second derivative of -4cosx
do you know what the derivative of cosx is?
native briar
No
boreal karma
hmmmm
native briar
is it -sinx?
boreal karma
im not sure how to teach it by proofing it but the derivative of cosx is -sinx
native briar
I read up on it before
boreal karma
yes thats perfect
native briar
fr?
boreal karma
the first question is to find y'' for y= 4sinx correct?
that would not be the answer
native briar
no?
boreal karma
you made a mistake somewhere
the first derivative will have cos in it
so the second derivative must have sin it
without doing any math i know that
native briar
yea
boreal karma
the first derivative would be 4cosx
native briar
yea
boreal karma
yeah i know
native briar
it’s ok so would it be
4 cos x
yea
but the derivative of cos x is -sinx
so is the answer -4sinx?
boreal karma
okay this one is similar to the last one but with one extra step basically
you can change theta (the weird o thing) to x btw if you want so its more in line with the other problems we've been doing
native briar
it’s 0 right
boreal karma
well no, we have to use the product rule because we have -x^8 * cosx
native briar
Ah
native briar
no
boreal karma
basically its (f x g)' = (f' x g) + (f x g')
native briar
kk
boreal karma
so the derivative of x^8 times cosx plus the derivative of cosx times x^8
ok i wrote it properly now sorry about that
so do you think you're able to do that?
native briar
wait so