Yea I am, I'm graduating highschool next month
#help-49
velvet wraith
W
Lmao yea we tend to just speedrun the syllabus
Man
Yea makes sense but gl on ur exams tho!!
I getting my last 2 exams soon too so yea
Not yet 1st I'm going to Junior College
Then uni
Thxx u too
Yea it's a thing lol
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bleak pier
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bleak pier
i did not understand how they find units?
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candid vector
I am completely lost at probability and can really use some help with these questions
midnight plankBOT
I am completely lost at probability and can really use some help with these ques...
low escarp
do I do percent of it being 18-39, * 873/3550
Seems correct
Chance of 18-39 age group AND belief C means that the probability of both occuring is chance of 18-39 age group * belief C
candid vector
I got 873/6707 is that correct
candid vector
what about this (b) If we draw one individual at random, what is the probability that the respondent has age range 40-59 or 60+
Nvm, managed to get that on my own
but im not sure how to go about this 😭
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candid vector
@stiff heart
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@candid vector Has your question been resolved?
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candid vector
.reopen
midnight plankBOT
✅
candid vector
<@&286206848099549185>
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bleak pier
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silk river
$\mathbb{Q}^c$ is what appears in possible answer (c) and (d)?
grand pondBOT
baseboard
bleak pier
$\mathbb{Q}^c$ is what appears in possible answer (c) and (d)?
Yes
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shy ice
How did they jump from line 1 to line 2?
I tried using u=1+x^2 but it leaves int(x/4u) dx
midnight plankBOT
How did they jump from line 1 to line 2?
I tried using u=1+x^2 but it leaves int...
slender walrus
factor 1/2 out, then long division (or consider x^2 = x^2 + 1 - 1 to decompose that fraction
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thorny oasis
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thorny oasis
howd i do it?
rose cobalt
Normally how do you find the slope of a line with two points given
thorny oasis
delta y / delta x
rose cobalt
Can you find two points that lie on the secant line?
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last slate
need help wit part B
modest fox
i don't undertsand this step..
midnight plankBOT
i don't undertsand this step..
misty gorge
they are skipping a step here, depending on how careful you want to be. To get here, you can divide both sides by 3, on the LHS that cancels with the numerator, and on the right hand side you have the numerator 3^x and the denominator 3, so by your exponent laws you get 3^(x-1) in the numerator.
Then you divide both sides by 4 and do the same thing, the RHS cancels out and the left hand side uses the exponent rules
modest fox
they are skipping a step here, depending on how careful you want to be. To get h...
ah ok
thx
misty gorge
did that help
modest fox
yep
misty gorge
okay great :)
modest fox
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vagrant storm
how can i do the last part easily instead of wasting time factorising it and using the quadratic formula? It says henze so i can use the part before but idk how.
midnight plankBOT
how can i do the last part easily instead of wasting time factorising it and usi...
vagrant storm
Mark scheme
astral garnet
yo
vagrant storm
hi
astral garnet
the equation $2(x+2)^3+x-18=0$ is just $2(x+2)^3+(x+2)-20$
grand pondBOT
Galaxy
astral garnet
which is the same as f(x+2)
and using transformation of functions f(x+2) is just f(x) but shifted to the left by 2
vagrant storm
im trying to see how u realized that lol
astral garnet
hence if a root of f(x) is 2.077 then a root of f(x+2) is 2.077-2 which is 0.077
astral garnet
im trying to see how u realized that lol
it becomes easier the more questions you do
astral garnet
all good
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marsh bolt
Hey guys how do I do this problem
I’m trying to figure out how many times the bird would touch the trains before it dies
Assuming the start is when the bird touches 0
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last slate
uhm so this chapter is about functions and Ive done composite, inverse functions and stuff but i have no idea how to answer application of it cuz im bad when it comes to applications 😭
final answer is RM 4000, RM is currency
midnight plankBOT
uhm so this chapter is about functions and Ive done composite, inverse functions...
lime plover
uhm so this chapter is about functions and Ive done composite, inverse functions...
it's two step
q(n) is the function that gives you the amount of products based on the number of workers
so if you have 20 workers then plugging that into q(n) will give you how many products you get
r(q) if the function that gives you the revenue based on how many products you have
so use q(n) to find the # of products and then r(q) to find the revenue based on that # of products
lime plover
so its q(20)=100 and then r(100)=4000
yeah
last slate
but if u dont mind, my teacher said this one is composite index
last slate
yes
last slate
yes
lime plover
and q is based on n
lime plover
yeah
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last slate
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last slate
What method should I use to differentiate this?
Thanks, what method is this, how did you get to this conclusion?
Is this quotient
?
Oh ok, when do I use/recognise to use it?
The bottom is squared too no?
g(x)
^2
Ok thnks
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fringe frost
If A and B are points in the plane such that PA/PB= k for all P on a given circle, then the value of k cannot be?
midnight plankBOT
If A and B are points in the plane such that PA/PB= k for all P on a given circl...
fringe frost
Answer is 1
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gloomy nexus
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last slate
use a³+b³+c³ = (a+b+c)(a²+b²+c²-ab-ac-bc) + 3abc
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winter marsh
In robotics competition there are 6 robots arranged in circle each identified from 1 to 6 how many ways are there to arrange the robots such that exactly 3 of them have a number larger than both of their adjacent robots ? Consider rotation and reflection are considered identical
Helpppp
last slate
:/
last slate
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last slate
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last slate
For part e, why is it not just 40 * P(D>5.85) ?
In the markscheme it say 40 * P(D>5.85 I D>5.75)
What is the difference?
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tawny hedge
huh that wording is so weird
steel imp
whats k supposed to be
simple canopy
Constant
simple canopy
Well then we would have the value of both x and k, just need to find y
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vague marsh
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vague marsh
Do I understand the Rational Root Theorem correctly?
Say the constant term was 15
Would the roots then be: ±1, ±3, ±5, ±15 and ±1/2, ±3/2, ±5/2, ±15/2?
slender walrus
with the same leading coefficient?
vague marsh
Yes, stay 2x^5 . . . + 15
slender walrus
then yes those will be the
possible/candidate rational roots
if a rational root exists, it will be in that list
however it isn't guaranteed that any of them will actually be roots
chrome oriole
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chrome oriole
hi i don't know how to solve these
i know for the second one that i have to find a point that joins all of these functions together but i don't know how to start writing that out
and for the first one, i don't know what equation to solve the limit with
marsh grove
i know for the second one that i have to find a point that joins all of these fu...
ok so first take the top two equations
you want to make sure it is defined at x = 3 right
chrome oriole
yea
chrome oriole
okay
marsh grove
then take the second two equations and plug in 9
you get 81 + a = bcos(18pi)+a
then just manipulate then and use systems of equations
chrome oriole
you get 81 + a = bcos(18pi)+a
so i'll be using this equation together with either of the other two equations to solve for a and b?
because there are two variables
marsh grove
mhm
open sedge
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open sedge
I understand a)
but I don't understand why we can't use the same logic as a) for b)
so like 5! are for the boys
but why isnt it still 5^3 for the girls? since each girl has 5 choices
wdym by indistinguishable in b?
i dont understand the girls calculations how did they get those combinations from?
small jasper
this is essentially just casework: either all three get off on diff floors, two get off on one floor and third gets off one a diff floor, or all three get off on the same floor
open sedge
ok no worries
small jasper
this is wrong - it should be $2 \binom{5}{2} \binom{3}{2}$
grand pondBOT
Civil Service Pigeon
small jasper
b/c this is essentially saying pick two floors, then pick two girls out of the three to go out on one of those floors
but let's call the two floors you pick A and B
the pair can go out on A and the third girl can go out on B
or vice versa
but they never accounted for that part
small jasper
**Civil Service Pigeon**
if you fix this, you get 60 + 60 + 5 = 125 = 5^3
small jasper
but why isnt it still 5^3 for the girls? since each girl has 5 choices
which is consistent with this
open sedge
which is consistent with this
could you help me with this one? 🙏
my final is tmrow and its not looking good rn 😭
i don't understand how they found this? the way i did is
i did 12 * 4C3 * 11 * 4C2 for the number of ways possible
cuz the deck goes from 1 to 12 rank and in each of those theres 4C3 ways of picking 3 of the same rank
wait im dumb theres 13 ranks
💀
open sedge
but since the question is asking for probability would you have to divide by 52C5?
atomic solstice
I can’t solve this
midnight plankBOT
I can’t solve this
grand pondBOT
sage olive
if you don't want to simplify it numerically, one nice strategy for this kind of mcq would be plugging in a point
for example i notice that when theta = pi, that expression = 0
automatically eliminating B and C
atomic solstice
Yeah I got it that way, I want to simplify the expression itself tho
Nvm got it I screwed up the formula
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manic bison
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manic bison
what do we do after putting x as 1
summer ravine
Is there a trick to get the values of trignometric functions at different angles?
midnight plankBOT
Is there a trick to get the values of trignometric functions at different angles...
@summer ravine Has your question been resolved?
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neat sandal
In this questions
neat sandal
youre gonna try to gind x values
itll be cuberootx = 1/x
so x = +1 or -1
however in the solution -1 keeps being disregarded
why?
neat sandal
I know im asking why did we neglect -1?
edgy schooner
because x = 8
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edgy schooner
@neat sandal which region are we neglecting?
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flint anchor
second partial derivative
midnight plankBOT
second partial derivative
last slate
second partial derivative
!show
midnight plankBOT
second partial derivative
Show your work, and if possible, explain where you are stuck.
queen ermine
With respect to what?
tiny drum
well you need to calculate them
flint anchor
Wdym
last slate
second partial derivative
Just differentiate it twice considering s as a constant
Right?
Wrt to t*
flint anchor
so im not correct?
tiny drum
you only listed the symbols for the second partials
flint anchor
ok so how do i do it
subtle zinc
Am i correct?
if you're asserting that this diagram commutes then yes 
flint anchor
have you done partial differentiation yet
how do i do that
olive matrix
we did this earlier
d/ds means differentiate the thing, treating the other variables as a constant
tiny drum
Maybe this will help if you aren't familiar: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivatives/v/partial-derivatives-introduction
flint anchor
d/ds means differentiate the thing, treating the other variables as a constant
you only showed me the diagram
olive matrix
yes because i assumed you knew how to differentiate a function
tiny drum
yup
olive matrix
now do that again for each of those -- you'll need the product rule for some of them
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keen seal
how can i determine if this conv
midnight plankBOT
how can i determine if this conv
keen seal
i cant thnk of anything
twilit field
maybe find the limit at $\infty$
tribal temple
Well, what's the $\sqrt{n^2 - 7}$ "basically" like?
tribal temple
Yea, you can effectively "think of" the numerator as n, and then of course, you should know the rest 
keen seal
Yea, you can effectively "think of" the numerator as n, and then of course, you ...
can i put it as ( ) < 1/n^2 - 3
uh idk if im having a memory fog but 1/n^2 - 3
oh to determine 1/n^2 - 3 do i need to do another comparison tets
tribal temple
You could if you wanted (or alternatively, the original denominator is "basically" n^3, and so...)
tribal temple
oh to determine 1/n^2 - 3 do i need to do another comparison tets
(and, well, you may want one if you don't see whether that converges instantly, but as per before-)
keen seal
(and, well, you may want one if you don't see whether that converges instantly, ...
ah so i can do multiple convergence test in a single serie
keen seal
You *could* if you wanted (or alternatively, the original denominator is "basica...
uhm
if original denominator has n^3-3n
i need to remove the 3n no
tribal temple
ah so i can do multiple convergence test in a single serie
I mean, while you can, often there are ways where you don't need to
Matter of fact, what test are you thinking of making use of?
keen seal
keen seal
Matter of fact, what test are you thinking of making use of?
Basically this is what I did
To find Conv
tribal temple
Well, I mean-
The conclusion is right 
That said, here you made the denominator larger, so the whole fraction smaller, so you have the inequality the wrong way around 
tribal temple
Basically this is what I did
The 1/n^2 is something that's quite useful though, and you do want to do some sort of comparison (if you see what I'm getting at)
keen seal
The conclusion is right <:catGiggle:668948717772079128>
wait but
is doing another test i did possible?(if i didnt make a mistake)
tribal temple
is doing another test i did possible?(if i didnt make a mistake)
As in another test to show that your series converges? (or doing direct comparison but in a different way?)
keen seal
As in another test to show that your series converges? (or doing direct comparis...
doing another test
tribal temple
The 1/n^2 is something that's quite useful though, and you do want to do some so...
Yes, another test
keen seal
Yes, another test <:catGiggle:668948717772079128>
so what i did is fine right? ( if i didnt make the mistake)
ill try to redo it this time with limit comp
tribal temple
ill try to redo it this time with limit comp
Yep, if you use limit comparison with 1/n^2, you'll be fine 
keen seal
You *could* if you wanted (or alternatively, the original denominator is "basica...
Also I’m not too sure what you meant by this
tribal temple
I mean it feels a bit messy no? @_@
As in, you can compare the original series with 1/n^2, is what I meant
tribal temple
Also I’m not too sure what you meant by this
The highest power of the numerator is n, the highest power of the denominator is basically n^3, and so...
keen seal
The highest power of the numerator is n, the highest power of the denominator is...
So it’s just 1/n^2… but there’s still the -3
Which I’m not too sure how to remove unless I do another test
tribal temple
So it’s just 1/n^2… but there’s still the -3
You do limit comparison 
that already accounts for it because you'll get a finite limit
keen seal
You do limit comparison <:OathLove:698213874125766717> that already accounts for...
ah so basically what i did right
keen seal
wait so what i did here is correct? ik the answer is but the steps i did
idk if its correct
tribal temple
Well, you don't need any of the inequalities
keen seal
OH
tribal temple
Literally work out the limit $\lim_{n\to\infty}\frac{ \frac{\sqrt{n^2 - 7} }{n^3 - 3n} }{ \frac1{n^2}}$
grand pondBOT
@tribal temple
keen seal
ohhhh
i didnt know thats what you meant omg
wait honestly yeah that works LOL
tysm!
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green crag
Hi
green crag
can someone explain to me what is circled?? context: ellipsoid
this is the equation as we defined it
zealous schooner
it means that if you replace x by -x, y by -y, z by -z or any combination of those transformations, it doesn't change the equation
this means that the locus will be symmetric about all three planes (xy, yz and zx)
safe relic
zealous schooner
Read #❓how-to-get-help, don't type here, another helpee is using this channel
and don't mention helpers specifically.
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sharp coral
because (-x)² = x², yes
note that replacing x with -x reflects about the yz plane, and similarly for the other two coordinates
river scarab
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tidal token
express the volume of water in terms of h
V = 20 x 10 x h = 200h
so dV/dh = 200
Now use the chain rule to find dh/dt
midnight plankBOT
whole oyster
donde esta el chat de algebra
en español
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last slate
Hi
queen ermine
You'd think the mother of dragons would know how to handle an integral
last slate
What did I do wrong
@queen ermine ?
queen ermine
I'm trying to figure out what you did here
last slate
I translated it up by 4
Then found the area under the quadratic between 0 and 6
And then made a rectangle and a triangle for the area under the straight line
And then did the rectangle + triangle - area under quadratic
queen ermine
Rookie mistake kido
last slate
Omg what did I do
Is that wrong
I don’t understand how that doesn’t work
I’m not integrating to find the integral between those points I’m trying to find the area
last slate
If I integrated upper - lower here I’d get some negative area which would not be the area
queen ermine
Wait, actually this should be right
you sure it's wrong?
bruh
Do you even math
last slate
Omg how embarrassing
midnight plankBOT
last slate
Bruh
queen ermine
lmaoo
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keen seal
does (n+1)! = (n+1)n!?
midnight plankBOT
does (n+1)! = (n+1)n!?
keen seal
lavish venture
yes
lavish venture
because (n+1)! is just (n+1)(n)(n-1)(n-2)… and n!= (n)(n-1)(n-2)….
notice that it is just n! after the n+1
keen seal
notice that it is just n! after the n+1
ngl idk why it took me 20m to understand
anyway tysm!
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cunning bobcat
$ln(y)=2x$, then $ln(y)'=?$
midnight plankBOT
$ln(y)=2x$, then $ln(y)'=?$
grand pondBOT
Joeller
tawny hedge
oh that looks fun
cunning bobcat
doesn't it 
last slate
Just derive 2x no?
still nacelle
agreed
last slate
very cursed
Very real
cunning bobcat
Just derive 2x no?
no
last slate
Just derive 2x no?
Or js it composed ?
cunning bobcat
this notation is cursed
wdym
marsh grove
is it asking for the derivative of ln(y)?
still nacelle
**Joeller**
I'm more confused as to if that's derivative of ln(y) wrt. x or y
cunning bobcat
yeah same
queen ermine
I hate ' notation, why can't people just use the d
cunning bobcat
fr
last slate
I hate ' notation, why can't people just use the d
Physics issue
cunning bobcat
f'(x) is the only acceptable one
queen ermine
no, just snobby physicists not wanting to learn math
marsh grove
f'(x)
cunning bobcat
AH
queen ermine
so would that be (ln(y))'
cunning bobcat
I'm assuming so
queen ermine
since y is y(x) is this then (ln(y(x)))'
with respect to x?
is this a chain rule problem?
cunning bobcat
The formula should be in your class mate
I've never seen one like this before
last slate
I've never seen one like this before
Ah i apologize then
cunning bobcat
I'm pretty sure its (ln(y))'
queen ermine
Right, let's assume we got that right, how would you approach this now?
cunning bobcat
we're gonna use chain rule ?
last slate
since y is y(x) is this then (ln(y(x)))'
does it want dln(y)/dy or over dx?
last slate
It doesn't know what it wants
That’s actually cursed
queen ermine
ikr
last slate
Good luck 😭
cunning bobcat
alright
marsh grove
idk thats what i did and i got 2x + ln(2)
grand pondBOT
Joeller
queen ermine
so you get y = e^2x
queen ermine
ln(e^2x) with respect to x?
marsh grove
just e^2x wrt x
i think
thats what i did then i reformatted it to fit the ln(y) after
cunning bobcat
2e^{2x}
queen ermine
huh
marsh grove
wait nvm
queen ermine
what?
queen ermine
lmaooo
cunning bobcat
damn
queen ermine
ok I got it
this is stupid
and the notation is stupid
and all about this is stupid
cunning bobcat
so you got it ?
queen ermine
y' = 2 * e^(2x)
ln(y') = ln (2 * e^(2x)) = ln(2) + ln(e^(2x)) = ln(2) + 2x
this is stupid
like, actually bonkers
I don't see how else they got this answer
cunning bobcat
I see
queen ermine
but why is the ' in the brackets
cunning bobcat
ye this question is stupid
queen ermine
are you sure you wrote it correctly with texit?
cunning bobcat
it wasn't in brackets
queen ermine
no brackets at all?
cunning bobcat
nope
cunning bobcat
its confusing cause it can be interpreted both ways, ln(y') or ln'(y)
cunning bobcat
report to police
yeah
I'll file a police report
Alright
thank you so much
I'll ask my teacher next session about this
thanks y'all fr
have a nice day 
.close
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acoustic temple
Graph y=4(3)^x. How does this graph compare to the graph of y=4(1/3)^x? Explain completely.
midnight plankBOT
Graph y=4(3)^x. How does this graph compare to the graph of y=4(1/3)^x? Explain ...
acoustic temple
I know that they are reflections about the y-axis
but why is this true/how does that work
sharp coral
because you get the same thing when replacing x with (-x)
shell vapor
Whats the difference between the black function and the other 3 functions that make the other functions not equal the black one?
midnight plankBOT
Whats the difference between the black function and the other 3 functions that m...
shell vapor
my bad
i mean these
blue and red are equal
and black and green are equal
but blue and red doesnt equal black and green?
sharp coral
well you could make blue match green if the right sides were equal
shell vapor
i think its because i added to the right side incorrectly
after completing the square
now black blue and green equak
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flint anchor
find a taylor series for the function f(x)=lnx centered at c=1
midnight plankBOT
find a taylor series for the function f(x)=lnx centered at c=1
queen ermine
Do it, Rony, I believe in you
flint anchor
i am at the part where
lnx=((x-1)/1)-(((x-1)^2)/2)+(((x-1)^3)/3)-(((x-1)^4)/4
after this what do i do
queen ermine
you keep going forever
queen ermine
or at least for as long as taylor let's you
flint anchor
You need to find the general form
how
hard shard
who is taylor and why is he stopping you
ivory crescent
or at least for as long as taylor let's you
Taylor will come and stop most people by the tenth term
queen ermine
Taylor will come and stop most people by the tenth term
ivory crescent
how
For example, if you have the series $1+x+x^2+x^3+\cdots$, you could say the general term is $x^n$
grand pondBOT
otheol
flint anchor
my brain rn
ivory crescent
It's just about finding a pattern in your terms
flint anchor
ohhhh
but how can i find that here
or do i just leave it as is
i think i found a pattern
ivory crescent
What is it
flint anchor
((x+1)^n+1)/n+1
flint anchor
what
ivory crescent
You need to account for the changing signs
flint anchor
true
ivory crescent
Because the terms go +-+-+-+-...
flint anchor
-1^n
queen ermine
Because the terms go +-+-+-+-...
They go brrrrrrrrrr
flint anchor
(-1^n)((x+1)^n+1)/n+1
ivory crescent
(-1^n)((x+1)^n+1)/n+1
Indeed
Just make sure to put the -1 inside the base
like $(-1)^n$
grand pondBOT
otheol
ivory crescent
Just making sure
ivory crescent
Go ahead
flint anchor
when i derivate the lnx in the beginning do i just derivate 4 times or is it just how much i want
flint anchor
ohhh i see
sage olive
it's actually sometimes easier for this to recognize that the derivative of lnx is 1/x, write 1/x as a geometric series, and then antidifferentiate with respect to x
than to keep finding derivatives of lnx
flint anchor
how about these cases
green crag
Hi
green crag
from wherre did they get this to start with??
midnight plankBOT
@green crag Has your question been resolved?
green crag
<@&286206848099549185>
viscid phoenix
wow nice handwriting
midnight plankBOT
@green crag Has your question been resolved?
final monolith
from wherre did they get this to start with??
that's the distance from a point to the origin
(with the square root taken away because it's simpler and leads to the same answer)
green crag
oh so whendistance is max, distance^2 is max
midnight plankBOT
@green crag Has your question been resolved?
midnight plankBOT
green crag
thanks
tired gyro
hiiiiii may someone help meee
midnight plankBOT
tired gyro
oops
midnight plankBOT
Available help channel!
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grand pondBOT
dice
worthy wing
Ok so what do you have in the first one
() * ()
You have something u already know
Because u have x^4 and y^4
@last slate
Before continue
Ur exercise is factor that or u need to factor that for other exercise?
Ok so if u look at the coefficients
U can see they are 1, -2, 3, -2, 1
Dont u have anything in mind aboit these?
This comes from (a-sqrt(ab)+b)^2
If u expand this u will see u get the same coefficients
So i just need to find a and b, which are trivial
Expand it and before simplifying
Do the factors
It is a bit hardworking and i have to sleep now but i think u can do it
grand pondBOT
dice
late roost
idk what you want me to tell you
Using the expansion of (a-sqrt(ab)+b)^2 then finding a and b is probably your best bet, but they really doesn't tell you how you could have gotten it on your own if you've never seen the expansion of (a-sqrt(ab)+b)^2
Like we said yesterday, it's more of a pattern recognition thing than any actual lack of knowledge on your end
Pretty much the same way you did an expansion yesterday?
No?
What did you get when you expanded $(a+(ab)^{1/2}+b)^2$?
robust flint
**dice**
take x^2y^2 common in this expression
then set t = x/y
then it factorises easily
wdym
sorry idk how to use latex but
when you take x^2y^2 common it will become x^2y^2[(x/y)^2 -2(x/y) + 3 - 2(y/x) + (y/x)^2]
then set t = x/y
basically we exploit the symmetry of this expression
if you set t= x/y , it will become
$x^2y^2[t^2 -2t + 3 -2/t + (1/t)^2]$
grand pondBOT
Diborane
grand pondBOT
Diborane
robust flint
this become $x^2y^2(t + 1/t -1)^2$
grand pondBOT
Diborane
robust flint
then put value of t = x/y and simplify
simple canopy
**Sehtnar**
Expand this and if you compare the values with the question you will find that it’s is actually (-x² + rt(xy) -y²)²
robust flint
i dont think i understood the question
are you asking why i set t=x/y
$x^2y^2[(x/y)^2 -2(x/y) + 3 - 2(y/x) + (y/x)^2]$
grand pondBOT
Diborane
robust flint
you understood this right ^
robust flint
**Diborane**
when i set t = x/y, it gives me an expression like this
i mean
idk how to explain this but
this is kind of a standard method to factor palindromic polynomials
grand pondBOT
dice
robust flint
**Diborane**
this
grand pondBOT
Diborane
dawn kindle
y=2x+4 change the subject to x
question
huuh
y=2x+4 change the subject to x?
how does this work
how dis server work..
yes
change y to x
hmm
ok sry
unreal fjord
!da2a
midnight plankBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
nimble copper
!15m
midnight plankBOT
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viral dagger
you already have a channel that you pinged helpers 4 times 8j a row
then why did you do it 😭
nimble copper
Doubtful
midnight plankBOT
nimble copper
<@&268886789983436800>
analog vine
what a child
nimble copper
Many such cases
grand pondBOT
dice
last slate
well
@last slate
Take xy out
Common
Leave that then,
In orginal expression do this:
@last slate clear nowM
?
grand pondBOT
dice
midnight plankBOT
@last slate Has your question been resolved?
last slate
Greetings, is there any recommended website to plot points for 3d geometry?
midnight plankBOT
Greetings, is there any recommended website to plot points for 3d geometry?
tawny hedge
Greetings, is there any recommended website to plot points for 3d geometry?
There is desmos
I think WA and maybe geogebra have a 3d plot
tawny hedge
WA stands for?
Wolfram Alpha
astral garnet
western australia
tawny hedge
Does nobody abbreviate it
last slate
Ok thank you
bleak pier
midnight plankBOT
bleak pier
Should I use the Riemann integration or sandwich theorem?
sage helm
Doesn't look like it turns into an integral
Squeeze theorem it is
wait or does it
[\lim_{n \to \infty} \sum_{k = 1}^n \f{k}{k + n^2} ]
grand pondBOT
Sadie Carnot (η = -1)
sage helm
nah i don't think it does
hard umbra
its both
bleak pier
What can i do next?
bleak pier
I have solved ot by sandvich
bleak pier
Becauae of n^2
cobalt sigil
,w integrate from 0 to 1 (x/(x+1))
grand pondBOT
hard umbra
that is wrong
cobalt sigil
Answer ?
hard umbra
,, \sum_{i = 1}^n \f i {n^2 + n} \le \sum_{i = 1}^n \f i {n^2 + i} \le \sum_{i = 1}^n \f i {n^2}
grand pondBOT
cobalt sigil
Whats the answer ?
hard umbra
not what you got
ionic thicket
**Sadie Carnot (η = \-1)**
can this be done with riemann integral
hard umbra
technically the RHS here is a riemann sum, although you'd probably never evaluate it as such
cobalt sigil
not what you got
Then actual answer please !
its the reverse process , this example may help !!!
Anyone here ?
Ping if anyone replies !
midnight plankBOT
@bleak pier Has your question been resolved?
manic escarp
.close
midnight plankBOT
Available help channel!
tidal turret
midnight plankBOT
tidal turret
,rotate
grand pondBOT
twilit field
notice e^x is never zero
tidal turret
so
twilit field
so find if any points exist such that x^2-x-5=0
tidal turret
,w solve x^2 -x -5 =0
grand pondBOT
still nacelle
so find if any points exist such that x^2-x-5=0
isn't the question solving for f(x) = 1/2, not f(x) = 0?
tidal turret
true
still nacelle
you can't do that
tidal turret
okay
still nacelle
x(x-1) = 5 doesn't not mean x = 5 or x-1 = 5
that's only true if the right hand side is 0
tidal turret
that's only true if the right hand side is 0
okay
still nacelle
to solve a quadratic that doesn't factorise, either use quadratic formula, or complete the square
tidal turret
,w solve x^2 -x -5 = 1/2
grand pondBOT
midnight plankBOT
@tidal turret Has your question been resolved?
midnight plankBOT
@tidal turret Has your question been resolved?
midnight plankBOT
@tidal turret Has your question been resolved?
midnight plankBOT
@tidal turret Has your question been resolved?
tidal turret
Consider ((a_n){n \in \mathbb{N}}) a sequence of positive terms that satisfies (\lim{n \to \infty} \sqrt[n]{a_n} = 4) and ((b_n)_{n \in \mathbb{N}}) a sequence such that for all (n \in \mathbb{N}) it holds that (b_n > \left(\frac{3n+2}{3n+1}\right) \ln(a_n)).
Calculate (\lim_{n \to \infty} b_n).
midnight plankBOT
Consider \((a_n)_{n \in \mathbb{N}}\) a sequence of positive terms that satisfie...
grand pondBOT
938c2cc0dcc05f2b68c4287040cfcf71
tidal turret
!status
midnight plankBOT
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
@tidal turret Has your question been resolved?
tribal temple
Think about what happens to this, from what you know
tribal temple
Think about what happens to this, from what you know
Well, that does tell you that the first bracket here would go to 1 (you can equivalently see that by dividing numerator and denominator by n)
You may want to multiply by 1 in a certain way, to use something you know about a_n 
tribal temple
You know that $\sqrt[n]{a_n}$ has a limit of 4 - can you think of a way to relate that to $\ln(a_n)$?
grand pondBOT
@tribal temple
tribal temple
Yep, that’s it - now, can you make a manipulation to make the latter ln(a_n)/n appear in the expression?
tidal turret
Wat do i needt do