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#help-42
calm coralBOT
normal gorge
.reopen
calm coralBOT
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calm coralBOT
@normal gorge Has your question been resolved?
normal gorge
<@&286206848099549185> no help yet plz
normal gorge
<@&286206848099549185>
sly coyote
just draw a squiggly line
it's the motion of the ocean that counts
cos takes value x and spits out a y
cos(0) = 1
so start there
normal gorge
.close
glacial pecan
idk how to do this
calm coralBOT
idk how to do this
pure kayak
didnt you draw a triangle?
calm coralBOT
ion think i did it right cuz my answers were not right
Show your work, and if possible, explain where you are stuck.
pure kayak
is sec the opposite of sin
sec is the reciprocal of cos
pure kayak
nice
valid vine
what does pi/3 + npi mean
pi/3 + any integer multiple of pi
this is because
tan(pi/3), tan(pi/3 + pi), tan(pi/3 + 2pi), tan(pi/3 - pi) etc. are all equal in value
(tan has a period of pi, its values repeat every pi)
glacial pecan
oh
and how do i turn tan sqrt 3 into radians
am i supposed to just know dat cuz its common or what
valid vine
You should know that tan x = sqrt(3) means x = 60 degrees or x = pi/3 (+ integer multiples of pi)
but you can draw a right triangle with legs sqrt(3) and 1
indigo gust
How to find volume of this cylinder?
calm coralBOT
How to find volume of this cylinder?
indigo gust
calm coralBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
dull wagon
,rotate
potent lotusBOT
indigo gust
πR²lsinθ?
dull wagon
yeh
calm coralBOT
@indigo gust Has your question been resolved?
vital plume
calm coralBOT
@indigo gust Has your question been resolved?
pure breach
$$\int_{}^{} \frac{dx}{a + dx}$$
calm coralBOT
$$\int_{}^{} \frac{dx}{a + dx}$$
potent lotusBOT
ItzKraken
velvet osprey
what's this supposed to mean
is this some nonsensical notation à la $\int x^{\dd{x}}$
potent lotusBOT
Ann
pure breach
**Ann**
what..?
No I was asking how do I find (i cant remember the right word) this integral
pure breach
what's this supposed to mean
a is a real constant btw
leaden thunder
No I was asking how do I find (i cant remember the right word) this integral
How are you defining a+dx
pure breach
How are you defining a+dx
'defining'?
leaden thunder
It's not in any standard calculus book
velvet osprey
$\int \frac{\dd{x}}{a + \dd{x}}$ doesnt make sense
potent lotusBOT
Ann
velvet osprey
indeed, it doesnt.
leaden thunder
'defining'?
Define is a pretty common word in math where you give rules for your operation
velvet osprey
i for one have no idea wtf it's supposed to mean.
leaden thunder
a+dx means what?
pure breach
It's not in any standard calculus book
well my teacher never explained properly how and what do I integrate to find the gravitational force between two objects
leaden thunder
...
pure breach
he wrote some weird notation, told us u wont get it, I got stubborn and did some more bull
velvet osprey
garbage in garbage out?
pure breach
lemme draw the diagram and what he wrote
pure breach
garbage in garbage out?
exactly 😂
leaden thunder
Just take a picture of your teacher's integral
pure breach
Just take a picture of your teacher's integral
he didnt even write the integral sign
he fudging told us verbally
its gon take a few mins, can i ping you when am done?
leaden thunder
Nah, doesn't sound promising
pure breach
okay
calm coralBOT
@pure breach Has your question been resolved?
mellow kernel
Let $V:=\mathcal{P}_3(\mathbb{R})$ and let $T \in \mathcal{L}(V)$ be the operator $f(x) \mapsto f(x-1)+f(x+1)$. Is $T$ triangularizable? If yes, is $T$ also diagonalizable? Justify your answers.
potent lotusBOT
sadkid
mellow kernel
I've shown it's triangularizable by putting it in it's matrix representation (it naturally appeared), but how to show it's diagonalizable?
For reference I'm using Axler's text
.close
pure breach
hello
pure breach
so this is what my physics teacher wrote
pure breach
hello
and by considering the mass dM he meant consider a point object with mass dx
and by the F =... he meant u add for lots of tiny l (i.e. i think G times M times the limit as N goes to inifnity of a sum from i=1 to N of dx/l_i)
$F = G \cdot M \cdot \lim_{N \to \infty} \sum_{i=0}^N \frac{dx}{L_i}$
potent lotusBOT
ItzKraken
pure breach
this should be it, I think
calm coralBOT
@pure breach Has your question been resolved?
pure breach
WHATS UR QUESTION? IS F THE GRAVITATIONAL POTENTIAL?
its the force
calm coralBOT
its the force
pure breach
.close
calm coralBOT
calm coralBOT
Available help channel!
feral spear
Is it possible to obtain the power reduction formula for $\int\tan^{n}x{dx}$ using integration by parts?
potent lotusBOT
R(icky)
calm coralBOT
@feral spear Has your question been resolved?
feral spear
<@&286206848099549185>
nocturne scaffold
The power reduction formula for that could be obtained using integration by parts, where the integral is expressed in terms of a lower power of the tangent function and the natural logarithm of the cosine function. It's technically possible
feral spear
there is a $\int\tan^n(x) \ln(\sec x) dx$ term which makes me think that I'll continue integrating forever
potent lotusBOT
R(icky)
feral spear
hey @nocturne scaffold I've watched some bprp and I've seen there is no need for natural logs
he made this rearrangement
instead of $ \tan^{n-1}x \times\tanx $
he used $\tan^{n-2}x \times \tan^{2}x$
potent lotusBOT
R(icky)
feral spear
.close
broken crow
calm coralBOT
broken crow
Help.
remote mural
!status
calm coralBOT
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
limpid coral
have you played around with the hint 
calm coralBOT
@broken crow Has your question been resolved?
fallow saffron
question on einstein notation, we've been using it the first time, really...
does s_ij * s_ij mean what I think it means?
with there not being a s_12 * s_23 for example?
fallow saffron
$s_{ij} , s_{ij} = \sum^i \sum^j s_{ij},s_{ij} =s_{11},s_{11} + s_{12},s_{12} + s_{13},s_{13} + s_{21},s_{21} +s_{22},s_{22} + s_{23},s_{23}+ s_{31},s_{31} +s_{32},s_{32} + s_{33},s_{33}$
potent lotusBOT
Untitled7
torn gorge
wooooww
fallow saffron
well... <@&286206848099549185>
calm coralBOT
@fallow saffron Has your question been resolved?
calm coralBOT
@fallow saffron Has your question been resolved?
fallow saffron
maybe again <@&286206848099549185>
leaden thunder
question on **einstein notation**, we've been using it the first time, really......
They explain your example around 5m
fallow saffron
so yes?
calm coralBOT
@fallow saffron Has your question been resolved?
fallow saffron
i guess
queen pendant
any french person that could help with maths?
calm coralBOT
any french person that could help with maths?
remote mural
I need help
upper sparrow
I need help
!occupied
calm coralBOT
I need help
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
stoic oyster
any french person that could help with maths?
C'est pas impossible mais faut voir la gueule du problème d'abord
calm coralBOT
@queen pendant Has your question been resolved?
drifting vortex
why does the b contain a modulus?
glass heart
well given that you have a +- it doesnt really matter anyway
drifting vortex
well given that you have a +- it doesnt really matter anyway
but why did they use it
like whats the point
glass heart
with your course I am asking myself that quite often
upper sparrow
Because $\sqrt{b^2} = \abs{b}$, most likely
potent lotusBOT
@upper sparrow
glass heart
well you still wanna write correct stuff
the only reason you can leave it out is because the +-
remote mural
calm coralBOT
remote mural
how do i pull out a factor so that 27 turns into 1?
i only need to know how to pull out a factor
is it possible to pull out like this?
27(1+6/27x) ^ -1/3
upper sparrow
(almost, but the -1/3 also needs to be applied to the 27)
upper sparrow
Yep like that 
remote mural
Yep like that <:SCgoodjob2:750436894915166321>
but why
i dont understand it
can u explain it with simpe numbers?
upper sparrow
Well in this case note that you can factor $27 + 6x = 27(1 + \frac{6}{27}x)$, but then as you have $(27 + 6x)^{-1/3}$, you turn that into $\pqty{ 27(1 + \frac{6}{27}x) }^{-1/3}$
potent lotusBOT
@upper sparrow
upper sparrow
using rules of exponents that becomes $27^{-1/3}\pmqty{1 + \frac{6}{27}x}^{-1/3}$
potent lotusBOT
@upper sparrow
upper sparrow
Awww, why thank you 
remote mural
calm coralBOT
remote mural
ok so i got b i
but imm not sure about b ii
for bi i got
it was same as the mark scheme but im not sure about b ii
hello??
whys everyone ignoring my question 😢
.close
proud kite
calm coralBOT
leaden thunder
Can you upload this again
leaden thunder
What did you even do here
proud kite
What does "took z" mean
Factorized
leaden thunder
Yea still don't know what you mean. You're not being detailed enough
proud kite
Yea still don't know what you mean. You're not being detailed enough
They both have z
X + 2x = x(1+2)
leaden thunder
What about the line after that
leaden thunder
They both have z
The first line is equal to 18+6i, how did you conclude z=18+6i
Be specific
leaden thunder
X(x+1)=0
This only applies when one side equals zero
Not when it's nonzero
Also you don't have just x+1
You have z + zbar
calm coralBOT
@proud kite Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
rustic solstice
Calculate the result of
lim ( 1-cos(3x) / x^2 ); with x tending to 0
fallen whale
do u have an idea of where to start
rustic solstice
Ye, adding the value x tends to
(forgot to type it)
First of all trying to calculate it as I would do usually
And it comes out as a indetermination form of type 0/0
Then I have to find a workaround
Which I don't know how to
fallen whale
do u know a rule where if u get an indetermination form u can use said rule
rustic solstice
The first that comes to mind in this case is 1-cos(x) / x^2 = 1/2
fallen whale
(its called l'hopitals)
rustic solstice
(its called l'hopitals)
Never heard that name
remote mural
The first that comes to mind in this case is 1-cos(x) / x^2 = 1/2
Yeah and u will divide and multiply by 3
And u will solve it
rustic solstice
Result is supposed to be 9/2
remote mural
My bad wait
fallen whale
basically l'hopital is if u get indetermination form, then differentiate numerator and denominator and plug x=0 in that
remote mural
Lemme write it so
remote mural
U should have everything root
remote mural
I wanna learn hopital rule
Are u in high school ?
rustic solstice
Ye
remote mural
Cuz I’m in high school and teacher says that I can’t use it
But it’s easy with hospital
Lemme write it
fallen whale
l'hopital is really easy u can learn it in primary school
rustic solstice
Bro my teacher opened the book and spit random exercises numbers, as when I asked for help with another exercise he had to put glasses on to actually read (things that he doesnt while giving out exercises)
fallen whale
but since u never learnt it im assuming whoever gave u that question wants u to do it another way
rustic solstice
He never even mentioned it so I'll assume I can just use it
fallen whale
u know differentiation?
rustic solstice
No
fallen whale
oh ok he defo doesnt expect u to use it then
rustic solstice
Then how should I solve this
potent lotusBOT
remote mural
Do u understand
rustic solstice
I think so
Basically the expression is still the same
As if I do the calculus normally at the second row I simplify the two 9 together
And it turns out to be the original
Then I use the rule I mentioned earlier and it works out
Dam it was this easy?
remote mural
Dam it was this easy?
Yeah bro u just need a good teacher that’s a basic limit
depends on how old are u tho
rustic solstice
17
remote mural
Oh same
rustic solstice
Probably my teacher's fault I suppose
Can I ask for supervision with another exercise I had sort of the same problem with in this channel?
remote mural
Can I ask for supervision with another exercise I had sort of the same problem w...
Send
rustic solstice
lim sqrt( 1-cos(x) ) / x ; with x = 0+
remote mural
It’s 1/2 I supposed
rustic solstice
Ye
remote mural
But lemme write it to make sure
cuz it’s a usual limit
Do u know how I solve it ?
rustic solstice
I would divide the x by sqrt(1-cos(x)
And multiply everything by the same
So that the expression is unvaried
rustic solstice
What
Ye I see it now
Everything is hence under square root
But what about the numerator ?
remote mural
yeah my fault it will be 1/sqrt2
rustic solstice
Im not understanding
remote mural
Are u American ?
remote mural
French
remote mural
You asked me if I'm american cuz I'm dumb
NOO 💀 mate me too I was dumb at limits last year
I guess ur not familiar with limits
remote mural
Yeah if u need any help I’m here for it and if U need some challenging limit I can send them to u
rustic solstice
Like here rn or in dms?
remote mural
Like here rn or in dms?
Whatever u want I don’t mind
rustic solstice
Ill ask in a few days thru dms then to prepare for a test, right now I'm just making homeoworks days before the actual due date so I have less work later
remote mural
Ill ask in a few days thru dms then to prepare for a test, right now I'm just ma...
Alright mate good luck
vale mantle
can someone help me with this question?
calm coralBOT
can someone help me with this question?
vale mantle
this is the methods of question 4
you have to use the 2cos(theta) = e^itheta + e^-itheta
or smth like that
mortal orbit
Here's a nudge in the right direction : Show that $(e^{i\theta} + e^{-i\theta})^6 = ...$
potent lotusBOT
rafilou2003
vale mantle
Here's a nudge in the right direction : Show that $(e^{i\theta} + e^{-i\theta})^...
$(e^{i\theta} + e^{-i\theta})^3 * (e^{i\theta} + e^{-i\theta})^3 = ...$
potent lotusBOT
rego22o
mortal orbit
$(e^{i\theta} + e^{-i\theta})^3 * (e^{i\theta} + e^{-i\theta})^3 = ...$
no I was thinking of using binomial formula directly
mortal orbit
"super long" Idk there's like 7 terms so it's not that bad
mortal orbit
**rego22o**
and I guarantee you that doing this is NOT a better way
because you'll get twice as many calculations for just the same result
vale mantle
because you'll get twice as many calculations for just the same result
fair enough
i'm just confused as to what they want us to use from question 4 then
mortal orbit
First of all (a) will be important
then, how did you find $(e^{i\theta} + e^{-i\theta})^3$ in the first place?
potent lotusBOT
rafilou2003
vale mantle
I didn't do that question but I assume you just expand and group like terms
mortal orbit
I didn't do that question but I assume you just expand and group like terms
well yes, expanding
using newton's binomial formula
and you're gonna do the same here in 9)
Expand
vale mantle
alr
mortal orbit
and then group terms alike
vale mantle
yeah whoops
mortal orbit
and now you can regroup terms alike
calm coralBOT
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Available help channel!
steep marsh
<@&286206848099549185>
calm coralBOT
<@&286206848099549185>
steep marsh
<@&286206848099549185>
hasty fiber
You're supposed to ask your question and then ping helpers (only once, and only after 15 minutes)
!help
calm coralBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
steep marsh
Oh
so basically
I’m getting a keyboard with a height of 15cm
but I have a laptop which covers like 25cm of the desk
will that keyboard fit??
since this is taking an while please @ me when u want to respond
shadow tendon
will that keyboard fit??
We would need more info
steep marsh
wym
shadow tendon
Like how big is the desk
steep marsh
Like how big is the desk
about 38 cm
cold crow
help
calm coralBOT
cold crow
.reopen
calm coralBOT
✅
cold crow
help
oblique current
!noclopen
calm coralBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
cold crow
bro could have just told me if its 50 or 100
leaden thunder
bro could have just told me if its 50 or 100
!patience
calm coralBOT
bro could have just told me if its 50 or 100
Please wait patiently, and do not interrupt other channels with your question. Helpers in this server are volunteers, and the server cannot guarantee that someone will be able to help you. By being impatient or begging, you will only turn potential helpers away.
In the meantime, please make sure your channel contains the original question, clearly describes what you have already tried, and states exactly what you are having trouble with. This increases your chances of getting a good response.
cold crow
just tell me if its 50 or 100 its not that hard please man
latent steeple
Maybe ask chatgpt
leaden thunder
Maybe ask chatgpt
bad
calm coralBOT
@cold crow Has your question been resolved?
cold crow
u guys arent helping with anything
calm coralBOT
it is 100
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.
formal pumice
chat gpt said it was 50
.....
chat gpt doesn't know math
lol if the arc is 100 degrees, then the angle of the two points with vertex of the center is also 100
calm coralBOT
@cold crow Has your question been resolved?
calm coralBOT
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Available help channel!
chilly garnet
calm coralBOT
chilly garnet
How do I find the limit of this sequence
I tried using Lhopitals rule but I get stuck in a loop of e^x
Where have I messed up? Or what other techniques should I do?
upper sparrow
I would suggest working with that ln(1 + e^n), there's a way you can make it something a bit nicer to work withh...
chilly garnet
Is there a way to take out the n?
upper sparrow
Well, there's a way to get an n out of that, somehow 
upper sparrow
Maybe think of a way of factoring 1 + e^n, then log rules 
back to your l'opitals, you could also work with this to get something that's nicer too
chilly garnet
Hmm
chilly garnet
back to your l'opitals, you could also work with this to get something that's ni...
I realized I multiplied by 2x instead of dividing
But now I get an answer of 1 and it’s supposed to be 0
upper sparrow
But now I get an answer of 1 and it’s supposed to be 0
How do you get the answer of 1?
upper sparrow
Nice nice 
upper sparrow
So how are you saying to factor the 1 + e^n
For that, you could write it as $e^n(1 + e^{-n})$ then split that up with log rules so you get $\ln(1 + e^n) = n + \ln(1 + e^{-n})$
potent lotusBOT
@upper sparrow
upper sparrow
From there, working the limit out should be alright
chilly garnet
That makes sense actually ok
upper sparrow
perfect
chilly garnet
Woaahhhhhhhh wait omg I forgot about that lol
Ok I am getting this! I have a test tomorrow and I have been studying allllll day and it’s clicking for me
upper sparrow
Awww best of luck for the test! Happy it's starting to set in 
vapid nova
for intermediate value theorem, ik that for some value x = c to exist, f(a) < f(c) < f(b)
but can the order be switched around? f(a) > f(c) > f(b)
vapid nova
is this a valid?
wanton wave
if I'm understanding you right, yes
if f is continuous and u is some value between f(a) and f(b), then there exists some c between a and b such that f(c) = u
but it could be f(a) < u < f(b) or f(b) < u < f(a)
upper sparrow
[in fact, between a and b, f will attain a maximum value and a minimum value (which could be greater/less than f(a) and/or f(b)) and you can attain any value between that maximum and minimum]
vapid nova
so if i picked some arbitrary interval [a,b]
it doesnt matter if f(a) > f(b) or f(a) < f(b)
as long as f(a) != f(b) then there is some number f(c) that is in between f(a) and f(b)
wanton wave
yes, with c being between a and b
halcyon ore
calm coralBOT
modest pebble
are u supposed to solve for 'x' ?
crystal forge
well you were on the right track with that step ln(9) = 1-5x, now finish solving for x
crystal forge
what did you get, x = ?
crystal forge
yeah
crystal forge
$\frac{\ln 9 - 1}{-5} = \frac{1-\ln 9}{5}$
potent lotusBOT
Soosh
calm coralBOT
calm coralBOT
Available help channel!
solemn steeple
Any clue? All I was able to do was find the actual sequence but I have no clue how do I approach it further
humble ivy
Did you find a closed form for a_n?
solemn steeple
Isn't that just an arithmetic progression
it isn't
solemn steeple
Did you find a closed form for a_n?
you mean generalizing an nth term? I failed to do so, just formed a sequence
humble ivy
The the trick is to apply the recursive formula to the sum
calm coralBOT
@solemn steeple Has your question been resolved?
solemn steeple
The the trick is to apply the recursive formula to the sum
I wasn't really able to go about it
solemn steeple
For me it worked
I still couldn't get to a conclusion about how do I generalize a nth term in this
potent lotusBOT
Jelle
calm coralBOT
Available help channel!
hollow sphinx
calm coralBOT
hollow sphinx
I saw a thing where if you have a polynomial you can ignore the rest of the terms and just look at the highest power
so 3x^2 and x^2 but that doesn't work here
merry python
that's only for limits at infinity
terse marlin
Is this allowed in the integration for moment of inertia of a uniform density sphere?
still marlin
Yup
burnt phoenix
Is this allowed in the integration for moment of inertia of a uniform density sp...
Errrr.. i don't think you can simply convert a triple integral into a product of three single integrals line that 
still marlin
It works in this instance tho
terse marlin
It works out, just wanted to make sure it’s valid, thank you
still marlin
Cus the bounds are independent
It's kind of like with a single integral u can take out the constants
burnt phoenix
Cus the bounds are independent
Interesting. learns
terse marlin
Can I do this in general for simple shapes?
still marlin
Since the bounds don't depend on each other and when integrating u treat the other variables as constants
Hmmmm
There's a theorem I forget the exact conditions
But if the bounds aren't independent probably not
terse marlin
Do you remember the name of the theorem?
still marlin
nope I can Google it tho
OK it doesn't have a specific name but u can prove it by spamming fubini's theorem twice I think https://en.wikipedia.org/wiki/Fubini's_theorem#%3A~%3Atext%3DIn_mathematical_analysis%2C_Fubini's_theorem%2Cby_Guido_Fubini_in_1907.?wprov=sfla1
There's a section for rhe product of 2 integrals case
So then ud use it a 2nd time for 3 integrals
2nd*
calm coralBOT
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Available help channel!
hollow sphinx
calm coralBOT
upper sparrow
Well you don’t exactly “plug in” 0 - hold on a moment 
Is that supposed to be a trick question, or did they write that wrong(?)
upper sparrow
tried plugging in 0 and equating them but I get sin0/0 = -2
Just going to assume they meant what they wrote, but what’s sin(0)/0?
wanton bobcat
virus
hollow sphinx
Just going to assume they meant what they wrote, but what’s sin(0)/0?
undefined?
wanton bobcat
do you know u sub?
wraith sand
Some one help me
hollow sphinx
do you know u sub?
Yes but I don't see where I'd use that here
wraith sand
Can someone help me?
wanton bobcat
look i think the question is badly worded and we mus assume that sin(0)/0=1
hollow sphinx
this is the solution but I'm so confused
wraith sand
In math
hollow sphinx
why are they deciding by ax then multiplying by a
wraith sand
hollow sphinx
Is this guy serious lol
wanton bobcat
!occupied
calm coralBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
upper sparrow
[
f(x) =
\begin{cases}
\frac{\sin(ax)}{x} & x < 0 \
x^2 + x - 2 & x\geq 0
\end{cases}
]
potent lotusBOT
@upper sparrow
wanton bobcat
yep^
upper sparrow
<@788085606483361802>
The question they actually asked has answer “no values”, but I think they wanted this here haha
wanton bobcat
virus does this change anything?
upper sparrow
At which point, working out the limit from both sides and all (shall leave this to you @wanton bobcat 
)
hollow sphinx
even then I'd just think to plug in 0 and equate them to each other thats what I saw in a vid
hollow sphinx
but I'm not actually sure how to check for differentiabilty and continuity
wanton bobcat
to check for continuity at a point you do the limit from the left at said point and from the right
wanton bobcat
<@788085606483361802>
in this case
what would the limit from the left be? and from the right?
hollow sphinx
do you use lohpitals on the top one?
wanton bobcat
do you use lohpitals on the top one?
you can! well get to that
hollow sphinx
so acos(ax) / x
wanton bobcat
/x?
hollow sphinx
1**
wanton bobcat
so the limit from the left is
hollow sphinx
0 from both the right and left?
wanton bobcat
virus
you found and expression using lhopital cor the left limit
what is that expression
dont skip steps
hollow sphinx
what is that expression
the derivative of the top and bottom
wanton bobcat
what does that yield in your case
hollow sphinx
a?
wanton bobcat
the whole expression virus
hollow sphinx
acos(ax)/1 if you plug 0 into that you get a
wanton bobcat
perfect
that is the limit from the left
to prove continuity the limit from the left must be the same as the limit from the right at said point
so lets do the limit from the right
hollow sphinx
Also a?
wanton bobcat
limx—>0+ x^2+x-2
wanton bobcat
oh I thought u meant for the same function
note it is the same function!
when going from the left however you coming from -0.000000001 which applies to the top and from right from 0.0000001 which applies to the bottom
wanton bobcat
🤞🏽
hollow sphinx
and for differentiability do I differentiate the top and bottom and equate to each other?
@wanton bobcat
sry for ping
wanton bobcat
i am not 100% sure bc i never actually used diferentiability but im pretty sure it means if the gunction is continuous and its derivstive exists for all points
calm coralBOT
@hollow sphinx Has your question been resolved?
pulsar bear
did I do this polynomial division right?
calm coralBOT
did I do this polynomial division right?
pulsar bear
glad plover
the answer is right
calm coralBOT
pulsar bear
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remote mural
how do you undo an inverse
calm coralBOT
how do you undo an inverse
potent igloo
depends on f 
muted vale
f'(x) = -1-2sin(x)
calm coralBOT
f'(x) = -1-2sin(x)
muted vale
I need to find local min/max
So I took second derivative
f''(x) = -2cos(x)
So for this, would it just be cos(x) = 0/-2, or in other words cos(x) = 0?
So 3pi/2 and 1pi/2?
then test those in the f(x) function
oh wait thats for concavity
My bad not local min / max
I've got the min/max done
calm coralBOT
@muted vale Has your question been resolved?
calm coralBOT
@muted vale Has your question been resolved?
fluid musk
I understand that this requires the fundamental theorem of calc, and that -15 = g(9), and f(9)=g'(9), but I have no idea what my first step should be in solving this
fluid musk
oh!!
i'll give it a try rn
i'm still lost...
i'm here ^^
it should be h'(u)=f(u), oops
zenith ginkgo
you don't need the fundamental theorem of calculus for that one
As stephen suggested, you should let u = 3t and do an u-substitution
fluid musk
but then what about the different bounds?
astral mural
Why not just use FTC?
strange lichen
u = 3t
du = 3 dt
1/3 du = dt
strange lichen
but then what about the different bounds?
U get that from the u-sub
fluid musk
is there a way to do it using FTC? sorry,,,
zenith ginkgo
No
zenith ginkgo
yes!
fluid musk
okay, thanks sm for the help! i'm glad i wan't j going crazy that FTC wasn't working
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calm coralBOT
calm coralBOT
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misty hound
calm coralBOT
thorny stump
!status
calm coralBOT
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
1
thorny stump
I guess it's assumed that the cost of the fence is proportional to its length
misty hound
yeah
thorny stump
You have a rectangle, can you pick two letters for its side lengths?
misty hound
x and y
thorny stump
Can you give me the total length of fence in terms of x and y?
misty hound
I don't know that. It's part of what I'm trying to figure out
thorny stump
Isn't that how it would look like?
misty hound
yeah. Perimeter would be 3y+2x
thorny stump
Well that's the total length of fence
misty hound
oh I thought you meant the total length in numbers
thorny stump
I said "in terms of x and y"
misty hound
oh fck. Dunno how i missed that
thorny stump
Anyway, can you now give me the area in terms of x and y?
misty hound
x*y
thorny stump
RIght, and that equals 1.5 million, right?
misty hound
yeah
thorny stump
With square feet as a unit but that's unimportant
Actually let's just make the unit "million square feet", so that x*y = 1.5
You want to minimize 3y+2x
Can you simplify this to keep only one variable?
misty hound
x*y=1.5 so x=1.5/y. Then it's 3y + 2(1.5/y)
thorny stump
Ok, can you simplify?
misty hound
3y+3/y
misty hound
yeah
thorny stump
Can you find this one?
misty hound
3-3/y^2
misty hound
y=3
thorny stump
No
thorny stump
Yes, though that's not the only root
misty hound
-1
thorny stump
Yes
Now since y is a distance, we know it's positive, so we can ignore this one
But now we know y=1
So what is x?
misty hound
1.5
thorny stump
Yes, and now the total length of fence?
misty hound
6 cause 1.5x2 + 1x3
potent lotusBOT
misty hound
probably a coding bug. Am computer science major so I run into this occasionally
potent lotusBOT
thorny stump
Ok that's better
misty hound
so would the final answer be 1000ft by 1500ft cause it's 1.5 million
thorny stump
Yes
If the unit of area is "million square feet" then the unit of length is "thousand feet"
icy flame
Not sure how Im suppose to solve this
calm coralBOT
Not sure how Im suppose to solve this
keen pike
what question are you stuck on?
icy flame
3
keen pike
the triangles are both congruent
which means if you have an angle on one triangle you can find it on the other
keen pike
yup
keen pike
np
icy flame
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calm coralBOT
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frosty marsh
Can someone help me solve this
calm coralBOT
Can someone help me solve this
calm coralBOT
@frosty marsh Has your question been resolved?
calm coralBOT
@frosty marsh Has your question been resolved?
crimson cliff
calm coralBOT
crimson cliff
how did we get this?
calm coralBOT
@crimson cliff Has your question been resolved?
winter loom
Chain rule really.
potent lotusBOT
! What the hell am I doing here?
calm coralBOT
calm coralBOT
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sweet totem
How do I prove limit as x approaches 3 of x/(x-2) = 3?
calm coralBOT
How do I prove limit as x approaches 3 of x/(x-2) = 3?
sweet totem
I tried checking f(x) - 3 and it’s 2|x-3|/|x-2|
Which is less than 2delta/|x-2| but idk how to go from here
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calm coralBOT
sweet totem
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cloud topaz
Choose delta to be a minimum of some number and the thing
sweet totem
Wdym
cloud topaz
$$\delta=\frac{1}{2} \implies -\frac{1}{2} < x-3 < \frac{1}{2} \ \implies \frac{1}{2} < x-2 < \frac{3}{2}$$
Blah
potent lotusBOT
$Pure$
sweet totem
Don’t get it why can we say delta is 1/2
cloud topaz
Because delta can be any number we’re just choosing it to work and I’m not saying delta is definitely 1/2
But we can use the fact that delta is 1/2 to bound 1/|x-2|
Then if you solve for delta that makes the expression less than epsilon you can just say choose delta to be the minimum of 1/2 and that value
ancient thistle
lol
ancient thistle
calm coralBOT
@sweet totem Has your question been resolved?
stuck raptor
What formula do i use to find angle A?
calm coralBOT
What formula do i use to find angle A?
winter loom
Sine, cosine, either would work.
You should get a good understanding of when to use what.
This is your second time for the same problem. Not belittling you, just saying.
Observe when you use cosine formula and when the sine formula.
calm coralBOT
@stuck raptor Has your question been resolved?
stuck raptor
im sorry, im still trying to understand, but i got it with cosine for now, still trying to get the sine rule to work
calm coralBOT
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dense cedar
Hello again, I wanted to ask a question on how do you simplify this expression
dull geyser
Combine the two fractions
fringe reef
again, denominators are the same
just add the numerators
unlike the last time though, you are not done after doing that
dense cedar
unlike the last time though, you are not done after doing that
So like I have to cancel?
fringe reef
what do you have so far
dense cedar
wait
fringe reef
So like I have to cancel?
just to confirm
dense cedar
9x-6
3x-2
dense cedar
Dont think so
fringe reef
well
you can
can you factor something out of the numerator?
what's the common factor of 9 and 6
dense cedar
3
potent lotusBOT
artemetra
fringe reef
but yeah
fringe reef
because we just factored it out
fringe reef
yes
dense cedar
Ty ty ty
fringe reef
np
dense cedar
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desert storm
hi i solved for this and got these answers but it says one of them is wrong, don't know which one
calm coralBOT
hi i solved for this and got these answers but it says one of them is wrong, don...
desert storm
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astral mural
Hello
astral mural
I differentiated twice using LH
and got
$\frac{-\frac{2}{9}\left(27x\right)^{-\frac{4}{3}}}{\frac{5}{9}\left(27x\right)^{-\frac{1}{3}}}$
potent lotusBOT
LE SSERAFIM
astral mural
What do I do after?
cloud topaz
Simplify power of x
astral mural
Simplify power of x
How?
calm coralBOT
cloud topaz
Np
calm coralBOT
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rapid axle
calm coralBOT
rapid axle
This question is greens theorem, i understand everything just not how to get the bounds for X,Y
for the double integral
This is what i have so far
i have the integrand
just am not sure how to get the bounds for the question
whole hinge
(Moderator ping answered)
leaden thunder
maybe draw a picture
rapid axle
oh wait
jesus christ
0 <= x <= 1, x^2 <= y <=sqrt(x)
@leaden thunder appreciate it
how do i close channel?
grand dragon
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waxen talon
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