so based on your understanding
#help-39
sweet cedar
oops one sec lemme
sweet cedar
what is value must the Denominator not be
for 1b?
red sky
yeah
sweet cedar
it cant be a
midnight haven
correct
cosmic garnet
correct, so the domain would be?
cosmic garnet
a to infinity
nop
sweet cedar
oh
sweet cedar
is that interval notation
cosmic garnet
yes
sweet cedar
ohh
cosmic garnet
R denotes real numbers
sweet cedar
wait so could i write it like (negative infinity,a)u(a, infinity)
cosmic garnet
yes
sweet cedar
okayy i dont know how to find the range either
sweet cedar
hmm 0
red sky
hint: there is only 1 value that g(x) can never be
red sky
soo it would be (negative infinity ,0)u(0,infinity)
yes
cosmic garnet
soo it would be (negative infinity ,0)u(0,infinity)
yes
sweet cedar
oh okayokay i think i get that problem then
but for the 1a i dont really get the range cuz
of the b
red sky
or just R\ {0}
cosmic garnet
R-{0}*
sweet cedar
can you put that in anorher form i dont really get this one
cosmic garnet
soo it would be (negative infinity ,0)u(0,infinity)
its the same as this
cosmic garnet
also would the domain be (-infinity,a]
yes
sweet cedar
alrightt
also wanted to clarify that when writing the range of 1a, the variable b isnt included at all?
cosmic garnet
(-inf, b] i think
red sky
which one are yall doing
cosmic garnet
1a
red sky
and whats ur ans?
cosmic garnet
domain is (-inf, a] and range is (-inf, b]
sweet cedar
ya that
pearl pondBOT
pearl pondBOT
Available help channel!
sharp smelt
pearl pondBOT
jolly parrotBOT
Veni, vidi, perii
sharp smelt
which doesn't seem to prove anything to me
sharp vigil
what value of N would make the last implication true?
sharp smelt
Any value greater than ln(M)
sharp vigil
so picking an N for a given M is basically the same as choosing a delta for a given epsilon. so if you use that N it's a straightforward chain of implications
so if we do "let N = ln(M), then,..." and the inequalities you showed earlier then that's pretty much it
sharp smelt
The thing is, it's not clear if N is the length of an interval here
sharp vigil
well unlike the finite case, the interval we are interested in is infinitely long. so we replace "x is sufficiently close to a" with "x is sufficiently large"
so the interval we're interested in is (N, infinity)
sharp smelt
ah
so this is basically $\forall \varpesilon >0 ,\exists \delta>0| x> \delta \implies f(x)>f(N)$
jolly parrotBOT
Veni, vidi, perii
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rare holly
.close
pearl pondBOT
Available help channel!
naive hemlock
pearl pondBOT
naive hemlock
Need explanation for these questions
Anyone help
rough forge
the king is back
pearl pondBOT
@naive hemlock Has your question been resolved?
spare lark
El famoso oppailol
naive hemlock
El famoso oppailol
Yaku the π
rough forge
<@&286206848099549185>
For 15. do you know the mean value theorem?
naive hemlock
!status
pearl pondBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
Also do you know the theorem of Rolle?
rough forge
Why don't send your work then?
rough forge
Need explanation for these questions
Anyone help
.
rough forge
I see
naive hemlock
Like bro in the 14th one
What they have given is the cauchy's mean value theorem
But then they added the extra factor on the right side
π
pearl pondBOT
@naive hemlock Has your question been resolved?
jolly minnow
Why does partially differentiating a pair of straight lines wrt y and x give the lines which intersect at the point of intersection of the pair of straight lines? Is there any simple explanation for this?
jolly minnow
for example (2x^{2}+xy-y^{2}+3x+1)
jolly parrotBOT
Aetherfly
jolly minnow
partially differentiation wrt x
4x + y + 3 = 0
and wrt y
x - 2y = 0
we get x = -2/3
y = -1/3
and that is exactly the point of intersection of the lines
the lines are x + y + 1 and 2x - y + 1
<@&286206848099549185>
pearl pondBOT
@jolly minnow Has your question been resolved?
jolly minnow
<@&286206848099549185>
pearl pondBOT
@jolly minnow Has your question been resolved?
jolly minnow
Maybe this is something for you
https://math.stackexchange.com/questions/1872469...
alright
misty gorge
pearl pondBOT
misty gorge
i tried setting up the equation for planes tangent to that surface using any xo, yo, and zo then setting the cross product of the normal vector for that and <4, -2, -1> to 0 but i couldnt get anywhere with those results
plz ping me when / if im answered
pearl pondBOT
@misty gorge Has your question been resolved?
misty gorge
:'(
midnight haven
still need help ?
misty gorge
yes please
misty gorge
thats ok
midnight haven
ill be rly slow and im not sure to be right
rough forge
You wanna solve then for x, y and z
they will be in terms of lambda
Then if you found them, you plug x,y and z into F
and solve for lambda
And then you should get the two points where the tangent plane at those two points is parallel to the other given plane
rough forge
I calculated them out should be fine
rough forge
couldnt go further
You are basically on the right track
Also instead of 5x it should 10x
midnight haven
simplified by 2
pearl pondBOT
@misty gorge Has your question been resolved?
vestal radish
Hi
Im really struggling with problem solving stuff and would like help
I need help on question 18
I understand this is basic algebra but i dont understand how to inverse operations on this specifically
My work is on the 2nd image and every answer that I get is not in the set of options
If someone could break this question down and explain it to me in a way i can understand, that would be great
Im really bad at problem solving stuff and would also like help on how to get better at finding solutions because I do a lot of these practice contests every year and it never helps
vestal radish
Oh thats actually a really cool command
dense jasper
In the future, please rotate your pictures in #bots using ,rotate
anyway, lemme see
vestal radish
In the future, please rotate your pictures in <#488104216678760469> using ``,rot...
Ok thank you i will keep that in mind!
dense jasper
it's fine up to here
you can simplify the right hand side tho
consider ||combining like terms||
nothing you did after that is wrong
it's just not exactly helpful
vestal radish
consider ||combining like terms||
Oh alright! Why is it censored though?
vestal radish
meaning you don't see it immediately
Ohhh ok
vestal radish
consider ||combining like terms||
Is this correct? I havent done algebra since summer break started
vestal radish
addition and multiplication are commutative
Define commutative
dense jasper
dense jasper
Is this correct? I havent done algebra since summer break started
but just write $p \times 3$ as $3p$ and then $p+3p=4p$
jolly parrotBOT
Civil Service Pigeon
vestal radish
https://www.splashlearn.com/math-vocabulary/addition/commutative-property#:~:tex...
Ok thanks π
vestal radish
**Civil Service Pigeon**
Oh yeahhh
Forgot expressions existed
Im going to tweak out
6 isnt an option π«
dense jasper
you need to divide all the terms by 3 if you're going to do that
$\frac{36}{3}=\frac{p}{3}+\frac{3p}{3}$
vestal radish
you need to divide all the terms by 3 if you're going to do that
I do?
jolly parrotBOT
Civil Service Pigeon
dense jasper
why not just do what I said earlier
vestal radish
**Civil Service Pigeon**
Omfd
Im restarting this question hold on
Goodness gracious im stupid
Its 9
Thank you so much
I love you bro
.close
midnight haven
pearl pondBOT
light helm
what's your reasoning for what you entered?
midnight haven
the line hit 1 on y-axis and not sure why i put 2 there
light helm
what's your definition of range
midnight haven
on the x-axis u can see 1 is included for one of the line and not included for the other line
and both lines go to infinity
light helm
what's your definition of range
answer this first
midnight haven
range is all the y values
light helm
why is your range starting from -inf?
cunning veldt
why is my range incorrect?
Well i think its because you used excluded values from 1 to 2 despite them being part of the range
i THINK it shouldve been (-infinity, -2)
wait nvm
i mean
(-2,infinity)
since the lowest value is -2 non inclusive and the function never seems to reach a (global) maximum so the upper bound for the range has to be infinity
midnight haven
why is your range starting from -inf?
cuz thats how one of the line is facing
light helm
you're mixing up x and y values
midnight haven
so where does it start
light helm
are you able to show me any points that negatively large
cunning veldt
so where does it start
-2
the y value never goes lower than -2
so thats where the range starts
and the range ends at infinity since thats where the second line is going in the y direction
midnight haven
what about the other line
cunning veldt
the other line never goes lower than 0
light helm
you can consider the range of each piece, and then take their union
cunning veldt
look it never even goes under the x axis which means the y value is never lower than 0
i think youre thinking about the x valu einstead of the y value
light helm
when considering the range from a graph, you don't care about the x-coordinates. (i deleted the irrelevant values)
cunning veldt
yeah thats when youre talking about the domain
with the range just think of y values
midnight haven
i kinda of get but idk how to write that in interval
light helm
what's the lowest y-value, is it included/excluded?
midnight haven
(-2, inf)?
cunning veldt
yw!
midnight haven
.close
pearl pondBOT
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Available help channel!
gusty prism
Sry i keep practicing these
pearl pondBOT
Sry i keep practicing these
gusty prism
can someone just give me some complex si prefix conversions to make sure i got this down at a good level
becuz i know the exams are the hardest of scenarios
midnight haven
,w d/dx x^x^x^x^x
jolly parrotBOT
sharp vigil
convert 3.54 terahertz to femtohertz
unborn abyss
what would a femtohertz even be lol
calm wing
a VERY deep voice
brisk scarab
what would a femtohertz even be lol
according to wikipedia 3 fHz is "Sound waves created by a supermassive black hole in the Perseus cluster"
gusty prism
uh
velvet wolf
If B is a matrix and I have to find B^4 but I know what B^2 is, can I just do (B^2)^2 ?
pearl pondBOT
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Available help channel!
shy ginkgo
what app do you guys use to solve math problems on mobile? I just can't find a good one π
blissful cloak
WolframAlpha
shy ginkgo
no i mean like draw
autumn fossil
blissful cloak
Solving: WolframAlpha
Graphing: Desmos
Drawing: ibis Paint X or any other drawing app
shy ginkgo
the teacher gives us a pdf with math problems i just need to be able to draw on the pdf and export it
oke lemme try
um ibis paint x how do i enter the pdf
oh i need premium i think
.close
vestal urchin
pearl pondBOT
midnight haven
well this is on roblox
vestal urchin
yup
quartz gazelle
pearl pondBOT
upbeat elm
when it says multiply both sides by 3
did the 3 come from like the common number than can be multiplied by all sides?
keen rain
when it says multiply both sides by 3
the channel is already occupied :3
upbeat elm
oh sorry
keen rain
np
keen rain
but its just a quick question
ys but you'll get fairly quick responses in a new channel, here we just pollute the channel from someone else
quartz gazelle
keen rain
<:wut:1269167408896016394>
had to briefly read in as I may have insufficient knowledge for the task, but the mortality assumption is this right
or replace s with t for time, doesn't matter
mu being the constant force of mortality at age x
l the amount of alive people
and s some time interval
if you have a different context pls mention
note what happens if we try to insert s = 1:
(which is useful since the solution equation contains l_x+1)
then if we divide by l_x:
then the e term is successfully isolated
let's insert that into the original mortality assumption:
I think from here I can let you carry out the rest π
btw junji ito greets
keen rain
and to answer yours, yes to have a common factor for a variable
inthis case they decided to match b
pearl pondBOT
@quartz gazelle Has your question been resolved?
regal herald
y cant equal infinity
versed mica
thatβs not an equation
dusk moat
oh it doesnt exist
regal herald
also those arent the asymptotes (horizontal ones)
hasty galleon
how could you derive sin^2(t) + cos^2(t) = 1 into the identity in the picture?
sharp vigil
divide both sides by sin^2(t)
hasty galleon
that's what i did but im not sure what to do with cot^2(t)/sin^2(t)
sharp vigil
no, i mean divide both sides of sin^2(t) + cos^2(t) = 1 by sin^2(t). if you want to go the other way, you have to multiply both sides of 1 + cot^2(t) = csc^2(t) by sin^2(t)
velvet wolf
Can someone tell me where I went wrong for both of these?
c) We need to find coefficients c1 and c2 such that:
x = c1x^2 - 4c1 + c2x + 2c2
Equating coefficients give us the following system of linear equations:
c1 = 0
c2 = 1
-4c1 + 2c2 = 0
Subbing in c1 and c2 into the third equation gives us -4(0) + 2(1) != 0
Thus, the system is inconsistent and x is not in Span(S)
d) We need to find coefficients c1 and c2 such that:
3x^2 - x + 6 = c1x^2 - 4c1 + c2x + 2c2
Equating coefficients give us the following system of linear equations:
c1 = 3
c2 = -1
-4c1 + 2c2 = 6
Subbing in c1 and c2 into the third equation gives us -4(3) + 2(-1) != 0
Thus, the system is inconsistent and 3x^2 - x + 6 is not in Span(S)
regal herald
seems fine
velvet wolf
Oh?
Apparently the answers are they are in the span for both of them but I was thinking that's a typo cuz I couldn't see why
regal herald
you can tell x isnt just by looking so thats certainly not true
your work is all fine
pearl pondBOT
pearl pondBOT
Available help channel!
opal urchin
I need help understanding whats wrong with this,
pearl pondBOT
I need help understanding whats wrong with this,
opal urchin
wait...
-1/2 hmm
y axis, is +3, so up 3.
|x+1|
would mean left 1 aka -1 since abs value
versed mica
do you know what |x| looks like
fresh jetty
hi, im new but i want to try to help you!
versed mica
why the π€
opal urchin
why the π€
a bit confused now.
opal urchin
yes
opal urchin
youβre simply applying transformations to |x|
So whats the steps i need to do to get this problem right?
huh. is -a, reflect?
versed mica
english brother
fresh jetty
so i noticed when we plug in -3 we get:
f(-3) = (-1/2)| (-3) + 1 | + 3
f(-3) = (-1/2)| -2 | + 3
f(-3) = (-1/2) * 2 +3
f(-3) = 2
opal urchin
or is it a stretch?
fresh jetty
but your graph shows it as ( -3 , 4 ) because its not accounting for the absolute value
opal urchin
so i noticed when we plug in -3 we get:
f(-3) = (-1/2)| (-3) + 1 | + 3
f(-3) = (...
-3 from where?
random number used?
fresh jetty
-3 as a value for x !
i chose -3 to demonstrate because it fits nicely into the function and is showing how the left side of the graph isnt reflecting the outputs of your function like you want it to
opal urchin
i chose -3 to demonstrate because it fits nicely into the function and is showin...
ah
fresh jetty
the graph for the absolute value of x aka | x | is kinda funky!
because when we take the absolute value of something we're only interested in the distance from 0 on the number line, not the direction, so you get a mirrored affect
opal urchin
ok
fresh jetty
i hope this is helpful and not confusing! let me know if im not making sense bc i tend to ramble lol
opal urchin
its alright lol
versed mica
peter singer
opal urchin
oh... -_- I see what the issue was
fresh jetty
i could explain it better in a voice channel probably but yeah! when we graph f(x) = | x | we know its gonna be a "V" shape. when we make a function negative, we flip it down, so itll become a "^" shape
fresh jetty
oh... -_- I see what the issue was
YIPPEE
fresh jetty
yeah!!
pearl pondBOT
fresh jetty
my pleasure :)
pearl pondBOT
Available help channel!
pearl pondBOT
jolly parrotBOT
kisnar
chrome plank
Since you're not familiar with basis transformations, I'd suggest looking into the Jacobian matrix, which is used to transform between bases.
yes, but you won't need it anywhere near as complicated to transform between two orthornormal bases.
The executive summary is, suppose we consider the basis vectors as a matrix. Then, transforming between bases, A to B, is as simple as finding the matrix, M, such that B = MA.
you'll need to do a little more for you bases
yes
well, kinda
actually
B = MA <=> M^{-1} B = M^{-1} M A <=> M^{-1} B = A
you need to make sure you left-multiply by the inverse
if B = MA, then C(A,B) = M
where C(A,B) is the matrix which transforms basis A into basis B
though this only works for orthonormal bases.
@midnight haven Ah, I posted the wrong video. This is better π
https://youtu.be/bpuE_XmWQ8Y?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG
well worth a watch!
actually, both eiganchris' "tensors for beginners" and 3blue1brown's "essence of linear algebra" are a must watch for anyone serious about intuitively understanding linear algebra π
eiganchris: https://youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG
3blue1brown: https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
watch essence of linear algebra to get a feel for what is actually going on when you just do calculations.
tensors for beginners does an excellent job of going through the basics of everything.
they're basically the "why", not necessarily the "how".
pearl pondBOT
@midnight haven Has your question been resolved?
eager moss
How would this be done without natural log?
pearl pondBOT
How would this be done without natural log?
sharp vigil
product rule and pain
eager moss
since there are two functions in the numerator how would you deal with that first?
eager moss
you can differentiate numerator then use quotient rule?
versed mica
just when you take the derivative of the numerator it also entails using the product rule
versed mica
you can differentiate numerator then use quotient rule?
no sir
eager moss
oh wait can the product rule be extended to more than 2 terms?
versed mica
yes
versed mica
no.
eager moss
wdym by being able ti extend it to more than two
but whats meant by this still
versed mica
itβs not relevant here
for product rule of more than two
this is all you need: $\left(\frac{u}{v}\right)^{\prime} = \frac{vu^{\prime} - uv^{\prime}}{v^2}$
jolly parrotBOT
knief
versed mica
u and v are taken to be functions of x
howβd you manage to own an entire bakery btw
very impressive
eager moss
and that being there is related to the fact two functions are in the numerator?
eager moss
howβd you manage to own an entire bakery btw
i started by owning half of one
versed mica
i started by owning half of one
crazy work
versed mica
and that being there is related to the fact two functions are in the numerator?
this is just the quotient rule sir
eager moss
but quotient rule uses two functions g(x)/h(x) in the problem theres three
two of which are already being multiplied
oh maybe substitution?
or am i reading too much into it
versed mica
but quotient rule uses two functions g(x)/h(x) in the problem theres three
no sir
quotient rule is used for quotients
which we have
just because thereβs more than one x term doesnβt invalidate it
versed mica
**knief**
it just means when using the quotient rule to find uβ youβll have to use the product rule
eager moss
so set the entire numerator equal to something h(x) and itll work
yes that right i think i hope
versed mica
i think iβm interpreting you correctly
eager moss
this
versed mica
,rotate
jolly parrotBOT
eager moss
oh i accidentally rewrote the entire thing instead of assigning one to another
its not supposed to be there
thats kinda cool to know ive never done a practice problem with that kind of thingy
versed mica
math is cool
eager moss
i was gonna manually solve it but then realized how long it is
anyways thank you for ur help π
pearl pondBOT
@eager moss Has your question been resolved?
hoary ridge
pearl pondBOT
hoary ridge
i dont fully understand how to rotate it
i couldnt make it to my most recent MVC lecture as i have covid
do u know any good resources?
fair
thats my next one
no lin alg
in courses
this is calc 3
π
interesting :0
math I-IV???
lin alg before calc 1?!
that sounds rlly confusing
im ngl
idk i think the system at my school is more to like
weed out people who wouldnt do well in linear and higher classes
so those ones are smaller
college first year
hs?
huh
math intended major at liberal arts school
r u in USA?
that would make sense
USA education is wack
liberal arts is more like
smaller school that have a big mix in subjects
so im doing a double in visual art and math
oof
that does not sound very enjoyable tbh
anyways thank you for trying :3
.close
pearl pondBOT
pearl pondBOT
Available help channel!
sterile turtle
im taking the derivative of this
pearl pondBOT
im taking the derivative of this
sterile turtle
this is what i wrote
naive hemlock
Yo
naive hemlock
I am back fr
naive hemlock
im taking the derivative of this
Bro is there tan alpha both in num and denom
sterile turtle
the 2tanx derivative isnt 2sec^2x on the top
sterile turtle
Bro is there tan alpha both in num and denom
yea
jolly parrotBOT
sterile turtle
,w expand (2tana+1)^2
thats cursed aint no way im doing that
sterile turtle
yea
sterile turtle
double cursed
sterile turtle
imma have a sqrt in the fraction
sterile turtle
im only confused why the 2 in the denom when diffed doesnt go to the top
sterile turtle
yea
naive hemlock
apply it
Wait imma send some explanation
In written
,w rotate l
,rotate l
, rotate p
jolly parrotBOT
naive hemlock
Now see
Sho they directly cancelled one step
Instead of clearly writing the first
Which is leading to your confusion
sterile turtle
im a fucking idiot
sterile turtle
i was doing it like
naive hemlock
This is because 2 is separate from the f(a)
naive hemlock
Welcome
pearl pondBOT
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Available help channel!
dim wren
This is a compound interest question, the 2nd image is my attempt/solution but my answer is always not right compared to the solution on Graphic Calculator.
dim wren
or this might be easier to see for you (the 2nd image)
pearl pondBOT
@dim wren Has your question been resolved?
dim wren
<@&286206848099549185>
pearl pondBOT
@dim wren Has your question been resolved?
pearl pondBOT
@dim wren Has your question been resolved?
pearl pondBOT
@dim wren Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
limpid tiger
this my first time seeeing this
pearl pondBOT
this my first time seeeing this
limpid tiger
how does it work ?
random ermine
multiply and divide by this
sinful nebula
how does it work ?
Multiply/Divide by the conjugate of both numerator and denominator.
versed ledge
how does it work ?
They skipped one step and went to final step directly
2 times multiplication has been done in numerator and denominator
pearl pondBOT
@limpid tiger Has your question been resolved?
limpid tiger
They skipped one step and went to final step directly
2 times multiplication ha...
so like multiply conjugate of numerator then multiply conjugate of denominator
?
limpid tiger
oh alr thank you guys
pearl pondBOT
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Available help channel!
ivory storm
Hello, may I get help on question 20?
pearl pondBOT
Hello, may I get help on question 20?
versed mica
,rotate
jolly parrotBOT
versed mica
integrate both sides of the first equation
ivory storm
I donβt really know how to do it
Oh wait I got it, thank you so much π
.close
pearl pondBOT
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Available help channel!
brisk nacelle
pearl pondBOT
versed ledge
I think the question is wrong
brisk nacelle
I think the question is wrong
No
versed ledge
Left side of both equations are same if you multiply 2 in first equation
But right side will change
That's not correct
First equation 3x-2y=5
Can be written as
6x-4y=10
2nd equation is
6x-4y = 5```As far as I know you can't have different RHS for same LHS but maybe I am wrong
jolly parrotBOT
faiyrose
brisk nacelle
Yes
Ooooyhhhhh
Okay
y* the last one
0
Then what?
Bro
Theres no way
Im doing sum wrong
Ill try the other way
After that?
brisk nacelle
What is a contradiction
So again no solutions
I hope its not wrong
Or else im gon get an ass whopping from my teacher
.close
warm echo
how do i solve this?
pearl pondBOT
how do i solve this?
latent quail
how do i solve this?
First of all, do you agree 10^2log2 = (10^log2) *(10^log2)
Why do not?
You just need to see it as two entities, get the result of 10^log2, multiply it, done
warm echo
First of all, do you agree 10^2log2 = (10^log2) *(10^log2)
i get 2 * lg 2
pearl pondBOT
Please read the channel description before posting, and stay on topic.
latent quail
not exactly
Hm
wraith vessel
Whats the equation for deja vu?
latent quail
Let me carry out another example
pseudo oxide
badk please remain on topic.
warm echo
Whats the equation for deja vu?
can you leave
latent quail
Do you agree 10^5 = (10^3) x (10^2)
jolly parrotBOT
warm echo
Do you agree 10^5 = (10^3) x (10^2)
yes
warm echo
Do you agree logx + logx = 2 logx
yes
pseudo oxide
<@&268886789983436800>
solid pier
keep it on-topic in the help channels
pseudo oxide
check logs
latent quail
First of all, do you agree 10^2log2 = (10^log2) *(10^log2)
Here
latent quail
Great
warm echo
what now
warm echo
Do you agree 10^(logx) = x
yes
latent quail
Congrats, you have the access to the solution now
warm echo
10^lg p = p
warm echo
Do you agree 10^(logx) = x
that formula right?
latent quail
Yes
warm echo
or?
latent quail
Itβs more like an identity
latent quail
Correct, the answer is 4
latent quail
Yes, youβre correct
pearl pondBOT
latent quail
No problem
unkempt yacht
pseudo oxide
No problem
bro this BadK dude
pearl pondBOT
Available help channel!
arctic carbon
when graphing cosx, and sinx graphs i understand how to find the period but how do you find each individual point inbetween
arctic carbon
for example cos(2/3x)
it's (2pi)/(2/3) which is 3pi
but in the period in between how do i find each individual point on the x-axis
0, ?, 3pi/2 , ?, 3pi
rough forge
divide 3pi/2 by 2
arctic carbon
alright, and for the one after 3pi/2?
rough forge
and between 3pi/2 and 3pi is 3pi/2 + that quarter
basically if you want to find your quarter interval divide your period by 4
then it's
period/4 * 0
period/4 * 1
period/4 * 2
period/4 * 3
(period/4 * 4)
rough forge
and that works with every kind of reduction you wanna make
pearl pondBOT
pearl pondBOT
Available help channel!
rich jolt
hint?
pseudo oxide
hang on
acoustic path
oh it's one of these questions
inland ivy
you need to use inequalities
pseudo oxide
idts
inland ivy
yes
acoustic path
yes
pseudo oxide
you can just treat it as a constant
inland ivy
you do
inland ivy
you can just treat it as a constant
treat what as a constant
pseudo oxide
the integral?
inland ivy
integration by parts doesn't work here
pearl pondBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #βhow-to-get-help for instructions).
pseudo oxide
integration by parts doesn't work here
lemme check rq
inland ivy
integration by parts doesn't work here
because you will get int f(x) terms inside the integral
rich jolt
yea
inland ivy
@rich jolt use the inequality $$\sqrt{\int_0^1 f(x)g(x)\dd{x}}\le\left|\int_0^1 f(x)^2\dd{x}\right|\left|\int_0^1 g(x)^2\dd{x}\right|$$
inland ivy
now the important part is knowing where the equality part of this holds
first choose an appropriate f(x) and g(x)
inland ivy
we cant just write the integral like that
what?
inland ivy
it's a continuous version of the cauchy-schwarz inequality
inland ivy
wait a second
i messed it up a lil bit
missed the squares
hmm this makes it a little tougher actually
oh my god what am i doing
let me just rewrite the whole thing
rich jolt
hmm this makes it a little tougher actually
yeah cuz i think i just used the inequality once before
that too for some algebra part
inland ivy
$$\left|\int_0^1 f(x)g(x)\dd{x}\right|\le\sqrt{\left(\int_0^1 f(x)^2\dd{x}\right)\left(\int_0^1 g(x)^2\dd{x}\right)}$$
jolly parrotBOT
kheerii
inland ivy
there now it's right
inland ivy
how is it gonna help
you need to build a series of inequalities
inland ivy
the idea is that you will eventually get to an inequality where you know for sure equality has to hold
acoustic path
i do not think this is intended solution
inland ivy
which means the equality conditions for all the previous inequalities also hold
inland ivy
i do not think this is intended solution
what do you suggest
I thought $xf(x)=\sqrt{f(x)\cdot x^2 f(x)}$ looked promising
acoustic path
consider first integral + second integral + third integral = 0
jolly parrotBOT
kheerii
rich jolt
ohh
acoustic path
consider first integral + second integral + third integral = 0
force a sol
rich jolt
they just simply
inland ivy
consider first integral + second integral + third integral = 0
???
pseudo oxide
first int + second int + third int isn't 0
acoustic path
i mean multiply each integral by a constant then add them to get 0
pseudo oxide
it's 7
pseudo oxide
...
rich jolt
thats what i saw
acoustic path
for a specific choice of these constants, this problem becomes trivialized
rich jolt
u get this ultimately
acoustic path
u get this ultimately
what does that on the left say
inland ivy
so the answer is 0?
acoustic path
ok so not ur work
rich jolt
why is fx not valid?
acoustic path
because f(x) is positive
rich jolt
ok so not ur work
yea
acoustic path
therefore f(x) > 0
rich jolt
therefore f(x) > 0
yeah and
acoustic path
and you know (x - c)^2 > 0
rich jolt
yea
inland ivy
$\int_0^1 (x-2)^2f(x)\dd{x}=0$ with $f(x)>0$
jolly parrotBOT
kheerii
rich jolt
ohhh
acoustic path
but you have right side = 0
rich jolt
got it
rich jolt
why is fx not valid?
im not sure how they infered this
acoustic path
what inference did they make?
inland ivy
Mqnic_ just explained it to you..
rich jolt
alpha-x ^2 is always positive
acoustic path
that is true
rich jolt
alpha-x ^2 is always positive
what if it was zero tho?
inland ivy
it's only zero at a single point
inland ivy
you mean f(x)=0?
pseudo oxide
i mean guys we can just notice that both x and x^2 will reduce the values of f(x) on the interval
hence no such functions exist?
inland ivy
it's not valid because it doesn't satisfy the original equations
inland ivy
i mean guys we can just notice that both x and x^2 will reduce the values of f(x...
this is also true
rich jolt
thnx guys
inland ivy
nice
rich jolt
i mean guys we can just notice that both x and x^2 will reduce the values of f(x...
what does this mean again
inland ivy
$$\begin{aligned}
0\le x&\le 1\
\implies x^2&\le 1\
\implies x^2f(x)&\le f(x)\
\implies\int_0^1 x^2f(x)\dd{x}&\le\int_0^1f(x)\dd{x}\end{aligned}$$ which isn't satisfied by the values given
rich jolt
what about that third line
rich jolt
i think i got it
jolly parrotBOT
kheerii
keen shell
@cedar bough u still there?
pearl pondBOT
<@886475675479978024> u still there?
cedar bough
yeah
keen shell
yeah
I got a different factor question
im struggling on this one
can you help me out
cedar bough
yup
keen shell
x^3+3x^2-16x+12
rich jolt
take x common and see
cedar bough
ok so this is a bit different
keen shell
what would you recommend doing?
cedar bough
i can't recommend the thing i'm about to say
but this is one of the first methods you learn to solve a cubic
try for some simple values of x and pluf=g that in the expression
to see if it becomes zero
rich jolt
yea lmao
cedar bough
like x=1, -1, 2 or -2
rich jolt
do u need to actually solve a cubic manually?
cedar bough
wdym manually
rich jolt
i mean like on paper
cedar bough
so what else will you do?
pearl pondBOT
rich jolt
i mean like on paper
id use wolfram alpha
cedar bough
i suggest you do not take help of search engines or apps before trying on your own
rich jolt
tru but the cubic formula is too long
cedar bough
yeah that's a long ass formula
cedar bough
Ill try figure this one on my own thanks for helping me earlier
good luck
pearl pondBOT
Available help channel!
brisk nacelle
pearl pondBOT
brisk nacelle
This correct?
cloud zephyr
,rcw
jolly parrotBOT
cloud zephyr
looks good
brisk nacelle
Okay
cloud zephyr
Shouldnt i do
?
brisk nacelle
y= 5/5
cloud zephyr
y = (-5)/5
brisk nacelle
y = (-5)/5
Can i do the same on here?
cloud zephyr
Can i do the same on here?
which one?
oh
we need to use "the other equation" to get solution for x
brisk nacelle
Coz like someone previously said that its has no solution