what if I multiply 3 x 4
#help-0
alpine sable
(base of one of the triangles x the height of the rectangle)
wait
that wouldn't be correct
urghhhhdhfj
HOW DO I DO TH8SS
<@&286206848099549185> can someone help???
outer lodge
@alpine sable tell formula of area of paralleogram
alpine sable
I don't have a formula
outer lodge
okay then area of paralleogram = area of rectangle +2* area of triangle
understood the formula?
outer lodge
can i explain this to you over call?
alpine sable
I don't like calling sorry
outer lodge
.close
lone heartBOT
lone heartBOT
✅
alpine sable
what the hell man
alpine sable
why test it here
outer lodge
alpine sable
can you link a video
outer lodge
just google it , this is a common and easy topic
alpine sable
I don't know what to put man
lone heartBOT
last ether
I can't even understand the shitty Bitmoji videos
The Bitmoji ones suck ass
Khan Academy has a section on geometry
alpine sable
yeah I tried watching that
lone heartBOT
Available help channel!
pseudo ice
.lol
modern sedge
.lol
lone heartBOT
ocean sealBOT
chobu nomu
ivory pivot
what is l.m.c.t.?
lone heartBOT
@plush sierra Has your question been resolved?
plush sierra
what is l.m.c.t.?
Lebesgue monotone convergence theorem
ivory pivot
i think you can say that the integral its $\infty$ for every n
ocean sealBOT
everg
ivory pivot
plush sierra
by Lebesgue integral it is equals to infinity?
ivory pivot
since |sin| its continuous you can use the riemann int. and yes its infinity ...there is obviously infinite area under the graph
i think its a good exercise to formalise this
plush sierra
since |sin| its continuous you can use the riemann int. and yes its infinity ......
oh by reimann int. there's no need to use LMCT?
ivory pivot
no because you can evaluate directly every integral ...are all infinity
and you can use LMCT where the f_n are incrising in n...its not this case isn't it?
plush sierra
and you can use LMCT where the f_n are incrising in n...its not this case isn't ...
ahh yes, increasing and converge for LMCT. I thought i could use it because of the limit outside
ivory pivot
you have the pointwise convergence (the function converge to 0) but not the incrising in n
plush sierra
you have the pointwise convergence (the function converge to 0) but not the incr...
noted, so riemann int. it is thank you! 🫶🏻 can i ask another question for the second problem im working on?
ivory pivot
yes
plush sierra
yes
how about for this problem? do you have any tip on how i can write the proof? I'm considering using LDCT for this one, yet not sure how to start.
ivory pivot
so you have that $g:=\frac{|f|}{M}$ its such that $|g|\le 1$
ocean sealBOT
everg
ivory pivot
and you know that $g_{|E}=\chi_E$
ocean sealBOT
everg
ivory pivot
Are you following me on this?
plush sierra
so you have that $g:=\frac{|f|}{M}$ its such that $|g|\le 1$
ah yes g the integrable majorant |f_n| <= g ?
plush sierra
and you know that $g_{|E}=\chi_E$
im not sure if i understand this part
ivory pivot
p.s. i don't define $f_n$ yet
ocean sealBOT
everg
ivory pivot
sorry maybe its better if i write this $g_{|E}=1$
ocean sealBOT
everg
ivory pivot
?
plush sierra
sorry maybe its better if i write this $g_{|E}=1$
why is it = 1?
ivory pivot
because if $x\in E\implies |f(x)|=M\implies g(x)=M/M=1$
ocean sealBOT
everg
plush sierra
is this how u write it?
plush sierra
because if $x\in E\implies |f(x)|=M\implies g(x)=M/M=1$
ohhh i get it now
ivory pivot
the vertical line means that you constraine your function in E
so you have that $\int g^n=\int_E g^n+\int_{E^c}g^n=\int_E 1+\int_{E^c}g^n=\mu(E)+\int_{E^c}g^n$
ocean sealBOT
everg
ivory pivot
where $E^c$ its the complement of E
ocean sealBOT
everg
plush sierra
what happens to the last integral?
ocean sealBOT
everg
plush sierra
**everg**
ahh same idea from what i was trying to do earlier, i partitioned the integral to E + E - x 😅
wow
ivory pivot
yeah its a good idea to do the integral in some special set with this strong prop
now you can conclude that the last integral goes to zero by dominace convergence
using the function g^1 which dominate g^n for every n
plush sierra
righttt
ivory pivot
gg
plush sierra
wow that was amazing 🥲 i feel like crying thank youuuu
ivory pivot
np ;D
lone heartBOT
ivory pivot
you deserve it xD
lone heartBOT
Available help channel!
floral badge
How do i figure out the value of 'n'?
lone heartBOT
How do i figure out the value of 'n'?
@floral badge Has your question been resolved?
rapid notch
lone heartBOT
rapid notch
How did they obtain the "rsinθ"?
alpine sable
polar coords
worn fox
its the jacobian for spherical polar coords
outer steppe
What's the issue with this?
lone heartBOT
What's the issue with this?
crude shadow
What's the issue with this?
Y= -(x+7)²+44
I did the vertex form
But what is the question?
alpine sable
I did the vertex form
Nice
alpine sable
Yes and after
crude shadow
U need a graph?
crude shadow
Ur welcome
outer steppe
I did the vertex form
Could you work it out for me please? I don't get why you don't have a fraction
crude shadow
Sure
crude shadow
Could you work it out for me please? I don't get why you don't have a fraction
I used 49 bcz 14= 7×2
49= 7²
lone heartBOT
@outer steppe Has your question been resolved?
cloud forum
lone heartBOT
cloud forum
How does the 2^n-1 + 1
become 2^n divided by 2 + 1
Inside of the red box in question 2c
high rapids
Exponent laws
tacit arch
,tex .exp rules
ocean sealBOT
riemann
cloud forum
But wouldn't a -1 divide it by 1
high rapids
Look at the third rule carefully
cloud forum
OHHHHHHHH thank you I understand now
it's a 2^n / 2^1
but if it's to the power of 1 it's just divided by 2
lone heartBOT
@cloud forum Has your question been resolved?
alpine sable
Hey guys, can you guys show me how to find the minimum value of g(x)? I just have no idea at the first part.
tacit arch
find the derivative
alpine sable
find the derivative
I'll try
alpine sable
find the derivative
Already done, how can I make the numerator equal to 0
tacit arch
use log properties to simplify
alpine sable
use log properties to simplify
How can I do it
alpine sable
use laws of logs
I did that but I cannot be sure about it
Like ln (x^6) should be equal to 6 ln x right
oak otter
tacit arch
Like ln (x^6) should be equal to 6 ln x right
yes
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
hearty steeple
Can someone help me with this
alpine sable
when it says p(-3) = 0 does this mean its really a factor or a root? like is it saying (x-3)?
lone heartBOT
solar monolith
its saying x = -3
alpine sable
so the factor would be (x+3) right
lone heartBOT
Available help channel!
mystic coyote
How would I get the axis of symmetry from this table of a parabola?
mystic coyote
alpine sable
Is this channel occupied?
north hemlock
Is this channel occupied?
yes
mystic coyote
yes
pliant cedar
(0+1)/2
north hemlock
so yo- yea
mystic coyote
notice how it has this "bounce"
yeah
north hemlock
it's in between here
mystic coyote
so thats means its 1/2?
pliant cedar
The graph is symmetric
north hemlock
^
north hemlock
so thats means its 1/2?
yes
north hemlock
hmm... I'm not entirely sure but since u have the axis of symmetry so u got that -2b/a = 1/2 and so just select a and b to make this tru then choose another point and try to find c?
the only issue is that the like
curvature of the quadratic depend on a and b
so.. that being said, it may be tedious to find the one that matches perfectly
somebody else may have a better method
north hemlock
mhm
mint lily
In efforts to rehabilitate the local pond, a helicopter is mapping out a triangle to then drop a sulfamic solutuion into. THe helicopter from the starting point flies 4 km then turns clock wise and flies 2 km before making its way back to the starting point. Its 2 paths makes a 45*. What is the area od the triangle the helicopter mapped out
alpine sable
i think its 4 because 4x2/2 =4
mint lily
i think its 4 because 4x2/2 =4
def no
stone pilot
is it specified how many degrees the helicopter turns on the first turn when it turns clockwise
mint lily
yea
stone pilot
oh ok
so do you know about the area of triangle formula that involves sin? (2 bases 1 angle)
mint lily
herons formula?
stone pilot
herons formula?
no
like uh
theres a formula involving these 1 sides and theta to find the area
stone pilot
in this case a,b = 2,4 and theta = 45
mint lily
yea
stone pilot
cosine law?
technically you could do it that way and use herons
but theres actually another formula
stone pilot
its a*b*sin(theta)/2
its also where the original b*h/2 formula comes from because sin90 = 1
mint lily
oh ic yeah that makes sense thx
simple spire
Need help with this I found the derivative what do i do next?
simple spire
<@&286206848099549185>
void hornet
I'm not sure if this is the best method, but you could construct an equation for the tangent line and set it equal to f(x).
void hornet
equation for the tangent line?
The derivative of the function is the slope of the tangent line
simple spire
right
so with the slope of the tangent i can create another equation is what you are proposing?
Just a question why would i set it equal to f(x)
void hornet
Using the derivative (which is the slope of the tangent line) and the point (3, -3) you could construct an equation for the tangent line
You would set it equal to f(x) because the question is asking for the other point which the tangent line intersects
void hornet
Hold on
simple spire
wait i have the derivative 3x^2-12x+8
and the point (3,-3)
i need it in form y = mx+b
what is the slope (m)?
i have x and y but i need m to find b
void hornet
Here
If you have the function f(x) and are looking for the tangent line at the point (1, 1)
The derivative at x = 1 would be equal to f'(1)
Which would be m in your tangent line
simple spire
Kinda confused
void hornet
what is the slope (m)?
For this problem specifically, m would be equal to f'(3) since it is at the point x = 3, y = -3
simple spire
wait i did that
void hornet
And as you stated before, you already have x and y from the point provided
void hornet
You plug 3 into the derivative
void hornet
Since the derivative is equal to the instantaneous slope at the point, and m is in y = mx + b is also equal to the slope.
simple spire
So i should get -59
when the derivative is -12x^2+16x+1
right
o wait wrong eq
-1
is what i get
plugging into 3x^2-12x+8
simple spire
y = -x
void hornet
Now you can set -x equal to the original equation
simple spire
I have to expand this equation right?
sorry nvm
i keep looking at the wrong q./
once im left with 0 on one side
it becomes quadratic correct?
void hornet
You should end up with this
And you can just move everything to one side and solve for x
void hornet
x((x-3)(x-3)-2) = 0
simple spire
where did the minus 2 come from?
void hornet
Yeah
void hornet
You can try verifying if your solution is correct by plugging in the x value that you find into both the tangent line and the original function
In this case, x = 3 also works because that was the x value of the original point
If they don't match up it means that you likely made an arithmetic mistake
simple spire
I think where i went wrong
was the factoring
how did u get this x((x-3)(x-3)-2) = 0
void hornet
x^2-6x+7 doesn't factor into (x-3)^2
a
void hornet
x^2-6x+9 does
a
simple spire
it would be x(x-3)^2 right?
void hornet
x^2-6x+7 turns into (x-3)(x-3)-2
simple spire
but its x^3
void hornet
(x-3)(x-3) = x^2-6x+9, you would end up with -2 leftover
simple spire
-6x^2
void hornet
You factored out the x correctly, I'm talking about the inside part which you messed up.
simple spire
xd
void hornet
So anyways it would be x(x-3)^2 = 0
simple spire
but then will i still get x = 0?
void hornet
Yeah
simple spire
how so?
void hornet
You can leave this in factored form
simple spire
oh
void hornet
So anyways it would be x(x-3)^2 = 0
This is the same as (x+0)(x-3)(x-3) = 0
void hornet
So the solutions to the equation would be x = 0 and x = 3
void hornet
And we can ignore x = 3 because it is from the original point
void hornet
@x = 0 y = 0
Correct!
simple spire
i can just find the y by plugging it into um the original equation?
void hornet
Yeah, you can find y by plugging the new x value into f(x).
simple spire
rightt,
void hornet
In short:
- Find f'(3)
- Construct a tangent line using f'(3) and point A
- Set the tangent line equal to f(x)
- Plug the new x value into f(x) to find your point (x, y)
simple spire
Thank you so much man.
this question was acc giving me trouble
i couldnt solve like 10 of the exact same q's but with diff wordings
Sorry to be a bother, if you have time may i ask another question?
void hornet
Yeah sure
void hornet
Do you know the chain rule?
simple spire
yes
void hornet
Alright, so try solving for H'(x) in terms of f(x) and g(x)
simple spire
but like i can apply it when im given like a numerical problem
simple spire
Alright, so try solving for H'(x) in terms of f(x) and g(x)
ok
so it would be f'(g(x)) times g'(x) right
void hornet
Yep!
Now you can say that H'(1) = f'(g(1))*g'(1)
The values for g(1) and g'(1) can be found in the graph
void hornet
Correct
simple spire
and the derivative
How would i find that
its just the slope of the tangent?
at that point?
void hornet
Remember that the derivative is just equal to the instantaneous slope at that point.
So pretty much just the slope
void hornet
Correct!
simple spire
2 * 2 ?
void hornet
f(x) is non-differentiable at that point.
void hornet
f'(f(1)) = f'(2) because f(1) = 2
void hornet
f(x) is non-differentiable at that point.
Functions are non-differentiable at a point when there is a cusp or corner at that point.
simple spire
Functions are non-differentiable at a point when there is a cusp or corner at th...
also i believe a right limit DNE at that point right?
void hornet
The limit as x --> 2 from the right = 4
simple spire
wait the left lim DNE then right
not the right
o no it does
Alright man, i dont wanna take up so much of your time, I really appreciate your help!
void hornet
No problem!
simple spire
sorry are you still here?
wide marlin
lone heartBOT
drowsy scroll
The question gave you a point on the graph
The lowest point in time t = 0 and the bottom is 5 feet
wide marlin
I already did it
drowsy scroll
You can just plugin those values into each equation to see if the Left side equals to the right side
wide marlin
can you help me with a different one
drowsy scroll
Sure
drowsy scroll
Amplitude is max - min / 2
wide marlin
ok so 6
drowsy scroll
Yes
wide marlin
and how do I get period
drowsy scroll
Period is the time it takes to repeat
wide marlin
so just 3 minutes
drowsy scroll
Vertical shift would be 8 flowers
wide marlin
so 30?
wide marlin
180/6
drowsy scroll
Keep it in minutes
drowsy scroll
I can do one more
drowsy scroll
H is true
wide marlin
what else
simple spire
@wide marlin why are you asking for test answers?
wide marlin
<@879855894849028106> why are you asking for test answers?
its not a test
drowsy scroll
G is true
simple spire
What is it then..
wide marlin
What is it then..
practice
simple spire
Right.
wide marlin
ok ty
wide marlin
<@879855894849028106> refer to <#486128019652476939>
it says I can do homework
leave a brotha alone
This is my last one
wide marlin
Read the Guidelines under <#486128019652476939> i'm sure you haven't read them.
"are for homework type questions/problems"
simple spire
That is not what i asked you to read.
drowsy scroll
This is my last one
- Gives the height of wave from midline to crest
- Nothing
- Nothing
- Gives number of sections between crests
- Nothing
simple spire
Read #6 under guidelines refer to #rules Also if you are not sure I strongly advise you to take a look at #❓how-to-get-help
wide marlin
1. Gives the height of wave from midline to crest
2. Nothing
3. Nothing
4. Gives...
thanks
drowsy scroll
@wide marlin You should close the channel using .close if you're not going to ask another question any time soon
wide marlin
.close
drowsy scroll
What is the proper form of derivative notation?
lone heartBOT
What is the proper form of derivative notation?
drowsy scroll
$y^1$
ocean sealBOT
christan
ocean sealBOT
christan
drowsy scroll
I see many
last ether
There's no "proper"
last ether
There's a fuck ton
drowsy scroll
There's a fuck ton
oh
last ether
Especially when you do partial derivatives
Then shit goes out the window with notation
drowsy scroll
oh please i only just started learning this 😭
inland aurora
dy/dx also works
Imo this takes too long to write and is too small on paper
inland aurora
I do y' or dy
So I stick with these
last ether
$\dv{y}{x} = y' = f'(x) = f^{(1)}(x) = f_x(x)$
ocean sealBOT
Umbraleviathan
drowsy scroll
i like f prime x
drowsy scroll
what is the fourth derivative
last ether
And then I resort to f^(5)
last ether
what is the fourth derivative
Derivative of the derivative of the derivative of the derivative
drowsy scroll
is it too late to forget calculus
last ether
So the fourth derivative of x^4 will be 4!, or 24
last ether
is it too late to forget calculus
Nah it ain't too much
Just the notation may be ass
But the concepts themselves are bite sized
last ether
x^4 derivative is 4x^3 then 12x^2 then 24x?
24x is the 3rd derivative of x^4
But yeah you get the gist
drowsy scroll
Holdup how would be the fourth derivative exist tho
last ether
It'll make more sense when you learn Taylor series
drowsy scroll
$y^1 = n(f(x))^n-1$ Where n is the exponent
ocean sealBOT
christan
drowsy scroll
oops the -1 is supposed to be part of the exponent too
last ether
#❓how-to-get-help delete your post
last ether
**christan**
y^(n)
The parentheses matter
But yeah
The notation gets real fucked up
Just kinda be familiar with them
drowsy scroll
Would the taylor series be in grade 12 calc
last ether
I don't know your curriculum
They're generally covered in Calc 2
Maybe previewed in pre calculus as some identities but never proven
grand fable
im a bit confused on how to start for this
lone heartBOT
im a bit confused on how to start for this
grand fable
i have cycle = 0.5L
but im a bit stuck on whether i should have a reserve and a residue term or just a term for both of them
like
i currently have either
cycle = 0.5L
residue = 2L
reserve = 2L
or
cycle = 0.5L
reserve + residue = 2L
would this be a question for my professor?
im also thinking that i might need to use sine in the final function due to the periodic nature of respiration
<@&286206848099549185>
limpid field
Yes
slate monolith
im a bit confused on how to start for this
is this calc 2
grand fable
this is new zealand
slate monolith
is it calc
grand fable
not really
its just forming a function
no differentiating or integrating
first year first semester university math paper
.close
vale wigeon
we don't give out solutions.
grave cedar
they explain so that you get it
regal parcel
Hi! Could someone help me out on this one
lone heartBOT
Hi! Could someone help me out on this one
mellow grail
Hi! Could someone help me out on this one
A) What dimensions are you given?
B) What is the Volume you are given?
regal parcel
15 by 25 with volume of 400
mellow grail
How do you calculate the other dimension?
regal parcel
I was thinking it would be just left as x
regal parcel
I’d like to mention it’s an open planter box, so there’d be more to it:(
acoustic cedar
Could someone pls tell me what to do
uncut glen
Hello! I need help with a question. It's a proof in which we need to Use contrapositive to prove the following:
Suppose 𝑥,𝑦,𝑧∈ℤ and 𝑥≠0. If 𝑥∤𝑦𝑧, then 𝑥∤𝑦 and 𝑥∤𝑧. (Hint: Recall “∤” means “does not divide.”)
ocean sealBOT
CT
serene junco
Hello! I need help with a question. It's a proof in which we need to Use contrap...
Hey, have you made any progress so far?
uncut glen
tbh no, I don't really know where to start :C
serene junco
Do you know what contrapositive means?
uncut glen
yeah
serene junco
And do you know the definition of 'divides'
uncut glen
yeah
serene junco
Okay great, so what would the contrapositive of your statement be?
uncut glen
If x divides y and x divides z, then x equals zero?
wait sorry
I got the lsat part of it wrong
hold on
If x divides y and x divides z, then x divides yz, for x is any nonzero integer
serene junco
Close, but remember demorgan's law
The negation of (not A) and (not B) is actually A or B
uncut glen
ah right
so then If x divides y or x divides z, then x divides yz, for x is any nonzero integer?
serene junco
Yeah, you can even leave the suppositions to the beginning
Like, assume x,y,z are integers and x is not 0
Then state that we'll prove $(x\not\mid yz) \implies (x \not\mid y \wedge x\not\mid z)$ by proving the contrapositive
oof
My ∤ signs are screwed up, but hopefully you get the point lol
uncut glen
yeah I think I get it
ocean sealBOT
tatpoj
serene junco
yes, sorry my latex preamble must not be set like I thought lol
uncut glen
ah okay nah its all good lmao was just curious
serene junco
the slash is supposed to go through it
uncut glen
alright I think I got it from here thank you so much for helping me!
serene junco
awesome, np 👍
uncut glen
.close
wheat crag
lone heartBOT
wheat crag
can anyone help with this
i was thinking it had ot do something with lower rectangle area < exact area < upper rectangle area
lone heartBOT
@wheat crag Has your question been resolved?
lone heartBOT
@wheat crag Has your question been resolved?
heady pollen
your thought is good, however look at what area Hn gives us
Hn actually gives us the upper rectangle area
the exact area would be ln(n)
although i am not getting anywhere with this task
im trying induction right now
wheat crag
oh alright
idk its weird i think ill wait for my teacher to explain it
ill just leave it
thanks
.close
tardy nebula
I have to study the monotony of $f:\mathbb{R}-{\frac{1}{2}}\to\mathbb{R}, f(x)=\frac{x+4}{2x+1}$
ocean sealBOT
roentgen
tardy nebula
-1/2 should be in brackets, like {-1/2}
I have used the formula our teacher gave us, $\frac{f(x_1)-f(x_2)}{x_1-x_2}}$
ocean sealBOT
roentgen
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
tardy nebula
and after some algebra I got to $-\frac{7}{(2x_{1}+1)(2x_2+1)}$
ocean sealBOT
roentgen
tardy nebula
I don't know where to go from here. I tried making x1=x2, because after that I end up with (2x+1)^2 in the denominator, which is always positive, so the function must be strictly decreasing
but the graph doesn't look like that to me
some help?
(i haven't got to calculus yet, I'm in 9th grade)
tardy nebula
i know what it is
heady pollen
oh nice
tardy nebula
but I can't use it in class
tardy nebula
I know that if you take the derivative of a function you can figure this out pretty easily
tardy nebula
it would make this really easy
yes, but I have to use only what we've been taught so far
wait
if I let x1=x2
heady pollen
this is what i get
so now about this formula you used
if it is <0 for all x, then the graph is always decreasing
(this implies that x2>x1 obviously)
if it is >0 for all x then the graph is always increasing
tardy nebula
if I let x1=x2
then the equation becomes $-\frac{7}{(2x+1)^2}$
ocean sealBOT
roentgen
heady pollen
which is exactly the derivative of the function
almost
btw, what values did you put in there? just any variables?
tardy nebula
if it is <0 for all x, then the graph is always decreasing
(this implies that x2...
yes, he told us this
tardy nebula
btw, what values did you put in there? just any variables?
x1<x2
heady pollen
uh
aha
just as a side note, that will not prove that the whole graph is monotonous then
tardy nebula
hm, I don't know
this is the only formula he gave us
oh, nevermind
I just read the question again
I don't have to prove the whole graph is monotonous, I need to work out in which intervals it is
heady pollen
still this won't work
in this graph we used your formula
your formula basically gives us the average slope between two points
which can be positive, however that does not mean that the slope is positive on the whole interval
tardy nebula
our book says this
let me try to translate it into english
methods to prove that a function $f:D\to\mathbb{R}$ is strictly monotonous on an interval A \subset D
ocean sealBOT
roentgen
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
heady pollen
if we want to show that f is strictly monotonous on an interval, we have to show that it is for all possible x values in this interval
we can do that though
tardy nebula
how?
heady pollen
if we substitute in we get this
tardy nebula
yes
heady pollen
we want to show that it is strictly monotonous
so we either assume it is strictly decreasing or increasing
let's say it strictly decreases
now the important question:
assuming the graph is strictly decreasing, will the fraction at the top be negative or positive?
ocean sealBOT
~Martin
heady pollen
ok one second, im confused a bit myself
tardy nebula
it should be negative I think, it says this in my book as well
heady pollen
yeah that makes sense
tardy nebula
if it is >= 0, it is increasing
<= 0, decreasing
heady pollen
but i get a wrong answer that way
tardy nebula
what way do you get a right answer?
heady pollen
im looking over my calculation again, i must have made a mistake
tardy nebula
what do you get when you take the derivative?
heady pollen
the idea is that we set this all to be <0
then show that the statement is true by rearranging it
then we proved it
tardy nebula
im looking over my calculation again, i must have made a mistake
I got $-\frac{7}{(2x_1+1)(2x_2+1)}$
ocean sealBOT
roentgen
tardy nebula
I did all the possible calculations except expanding the brackets in the denominator
heady pollen
how did you get the 7?
tardy nebula
i'm going to send a picture
wait a second
it's going to be hard for me to type this all out
heady pollen
ok i found my mistake
tardy nebula
alright
heady pollen
let's go through this
the idea is that we never substitute in any value for x1 and x2
that way we prove that this statement is true for all x
this is what we last had
tardy nebula
the idea is that we never substitute in any value for x1 and x2
yes
heady pollen
assuming it is strictly decreasing
tardy nebula
yes
tardy nebula
I would probably try to figure out what x1-x2 is
heady pollen
good idea
we have x1-x2 on both sides
so we can cancel it out
however, we have to consider something here
we are assuming that x1<x2
tardy nebula
them being negative
heady pollen
therefore x1-x2<0
tardy nebula
yes
heady pollen
and if we multiply both sides by a negative number, the < switches and becomes a >
tardy nebula
yep
heady pollen
that is what my mistake was
now we have two cases
let's look at x1, x2 > -0.5
that way we can get rid of the fractions
tardy nebula
yep
heady pollen
now we just rearrange further
the rest should be simple
once you are done with that, also look at x1, x2 < -0.5
heady pollen
we assumed it is strictly decreasing
tardy nebula
oh yeah i forgot about the restriction lol
heady pollen
if at the end we get a true statement, then our assumption is correct
btw, i edited my messages a bit
we assumed x1, x2 < 0
however we actually assume
x1, x2 < -0.5
this is because x=-0.5 is the point where 2x+1 changes from negative to positive
tardy nebula
yeah
tardy nebula
**roentgen**
and also the function is defined like this
in the domain
all numbers except -1/2
heady pollen
this is how i did the rearranging
and x2>x1 was something we fundamentally assume
so the statement is true
we now have to also check for x1, x2 < -0.5
in that case 2x+1 becomes negative on both sides
so the > switches to a <
however since we multiply by 2 negatives, it switches back
thus the equation will be the exact same
tardy nebula
yep
heady pollen
so in the end we proved our statement for these two subsets
and for x=-0.5, f is just not defined there
heady pollen
👍
solemn junco
Hello, could someone help me with number 2 of the first exercise ?
solemn junco
I need to solve the non linear differential equation and find on which interval it is a maximal solution
gusty gorge
looks separable
pseudo ice
I always have to look at my formula sheet for the integral of sec, honestly 
gusty gorge
I don't remember the last time I properly did an integral by hand instead of asking ,w
limpid spade
Balls
sec can be done by weierstrass then partial fractions I think
,w integral of 1/cosx
ocean sealBOT
solemn junco
I got this ? @limpid spade @gusty gorge @pseudo ice
solemn junco
Y here is a "composed function" i think is the term in english ?
So like integrating u(x) by x
Integral of u(x) dx
If that makes sense ?
solemn junco
Dy/secy ?
solemn junco
I might be wrong but when deferentiating sec(y) by x we get y’/cos(y) right ?
pseudo ice
You'd be integrating sec(y) = 1/cos(y), and wrt y
solemn junco
@pseudo ice @limpid spade
Sry had a problem with the wifi, so you agree with this ?
Oh wait no
😦
So dumb haha
Derivative of sec(x) is sec(x)tan(x) ?
pseudo ice
it is [but we're not, or at least shouldn't be, differentiating it]
pseudo ice
With that said, to do the antiderivative $\int \sec(y) dy$, you could multiply that by $1 = \frac{\sec(y) + \tan(y)}{\sec(y) + \tan(y)}$ and get
[
\int \frac{ \sec^{2}(y) + \sec(y) \tan(y) }{\tan(y) + \sec(y)} dy
]
from where you can notice the inside is of the form $\frac{f'(y)}{f(y)}$
ocean sealBOT
@pseudo ice
solemn junco
Woooow 🤯
Beautiful but i’m trying to integrate y’*sec(y) i’m afraid 🙁
Or less compact : y’(x)*sec(y(x))dx
No sorry let me correct that
keen plinth
<@788085606483361802>
biggest ass pull in integration ever
pseudo ice
As in your differential equation is basically
[
y' = \dv{y}{x} = \sin(x) \cos(y)
]
which on separation becomes
[
\frac{1}{\cos(y)} y' = \sec(y) y' = \sin(x)
]
ocean sealBOT
@pseudo ice
solemn junco
pseudo ice
biggest ass pull in integration ever
[and this is why for the most part, I never bother remembering them 
]
solemn junco
I don’t follow ? How are we integrating the same function ?
keen plinth
substitute u = sin and pfrac
pseudo ice
Note that the integral there is basically $\int \frac{\dv{y}{x}}{\cos(y)} dx = \int \frac{1}{\cos(y)} dy$
ocean sealBOT
@pseudo ice
keen plinth
what don't you follow
solemn junco
<@788085606483361802>
This neither
solemn junco
substitute u = sin and pfrac
Partial fraction ?
pseudo ice
Ways to find the antiderivative of sec
keen plinth
like
molten pivot
biggest ass pull in integration ever
I prefer the partial fractions method
Because it actually makes sense haha
keen plinth
1/cos(y) = cos(y)/cos^2(y) = cos(y)/(1 - sin^2(y))
molten pivot
Yes exactly
keen plinth
and now you can do a substitution of u = sin(y) to get 1/(1 - u^2) which you can pfrac
molten pivot
But I think your form of the integrand ends up being complex somehow so you have to do more work to show its a real function iirc
Could be wrong on that
solemn junco
Daaamn i see
Ok o think i got ot
Y’all are so smart @keen plinth @pseudo ice
Thank you so much
Take care ❤️
.close
tidal badge
@slender marten
lone heartBOT
<@234339303944224768>
slender marten
Oh good. I couldn’t eliminate the arbitrary constant.
tidal badge
Here’s where I’m stuck now tho 💀
It works out for the horizontal component but not for the vertical
slender marten
Your general solution is wrong.
slender marten
,w y’’’’ - k^4y= 0
ocean sealBOT
tidal badge
Oh shet
I forgot
You get 4 solutions
I’m dumb
Stupid mistake lol lemme fix that
slender marten
It’s because we have m^2 = -k^2 is a option. Hence there’s a imaginary root.
tidal badge
Yeaaaaa I gotcha
lone heartBOT
@tidal badge Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
civic tide
hi
civic tide
had a doubt in algebra
question: I need to find HF in terms of angle DCE. DEC is 90 degrees btw
CD is 1
DEC is 90
89.9 which is 90
civic tide
89.9 which is 90
diagram error 👀
lone heartBOT
@civic tide Has your question been resolved?
alpine sable
lone heartBOT
fringe sleet
$u=e^{3x}$
ocean sealBOT
Duh Hello
fringe sleet
its just a substitution
proven remnant
fringe sleet
$e^{6x}=(e^{3x})^2$
ocean sealBOT
Duh Hello
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
so 6u^2 - 38u + 40?
then div by 2?
then just quad formula
to find u
then sub back e^3x
find x using logs/ln
and done?
rotund jolt
function question
lone heartBOT
function question
wild trail
This is just function composition
rotund jolt
plain flame
did they say x = 2?
rotund jolt
no
vale wigeon
are you sure you copied the instructions correctly
rotund jolt
are you sure you copied the instructions correctly
yes,i sure
plain flame
then the instructions are wrong and you are right
tulip hound
how do I solve this
lone heartBOT
how do I solve this
outer lark
raven hill
how do I solve this
Hmm maybe notice that a^x is convex
So 3.16^x… this function is convex too
Thus it is monotonically increasing
Maybe try to find the roots first?
Set =0
Not sure tho
tulip hound
what about If I divide everything on 81^x
tulip hound
what about If I divide everything on 81^x
yeah works like that
raven hill
what about If I divide everything on 81^x
Why 81 lol
raven hill
Urm, would dividing by 5.36 ^x help too? As you would get (3.16/5.36)^x+(2.81/5.36)^x < 1
weak bison
I have the linear transformation T(x, y, z) = (x-y-z, x-z,0) and I’m trying to find the image
opaque hull
could someone explain this to me? thank you.
weak bison
I have the linear transformation T(x, y, z) = (x-y-z, x-z,0) and I’m trying to f...
I got that image(T) = (a, b 0) where a and b are just any real number but in general how would I compute this?
My method right now is just set
T(x, y, z) = (a, b, c) and then try to simplify with the 3 equations I have
.close