but when i placed that
#help-27
slim radish
ok let me restart
y=3cos(x+pi/8)
amp = 3
vertical shift = none
period = 2pi
horizontal shift looks like the problem
its a cos graph so if i plug in -pi/8
it will mark it wrong, compared to a sin graph
devout snowBOT
@slim radish Has your question been resolved?
main gull
its a cos graph so if i plug in -pi/8
How do you know this is wrong?
slim radish
plugged it in
wrong
but if its sin graph
it will work
if y=3cos(x+pi/8)
*sin
vertical shift = -pi/8
cos doesnt
software is weird
devout snowBOT
@slim radish Has your question been resolved?
dire forge
what is ß?
maiden frigate
It is that I copied the function as text and that was copied instead of the bracket, that is why I better send a photo
dire forge
ohhh
maiden frigate
Consider the function f defined on the set of integers
in the following way:
n-1 if n is even, n^2-1 if n is odd
Find all integers n that satisfy the equation f(f(n)) = 8
devout snowBOT
maiden frigate
.reopen
dire forge
Oop
scarlet sequoia
find f(f(n)) firstly
dire forge
Just copy paste the question and post it in another help channel
This one's gonna close since the original message got deleted lol
devout snowBOT
Available help channel!
unreal falcon
f(x+y)=f(x)+f(y)-xy is this easy to solve ?
devout snowBOT
f(x+y)=f(x)+f(y)-xy is this easy to solve ?
unreal falcon
12th
quartz geode
most likely not
there might even be many functions that satisfy that equality at which point the solution is not unique
unreal falcon
okayy thanks
neon aspen
f(x+y)=f(x)+f(y)-xy is this easy to solve ?
Are x and y any real number?
unreal falcon
Are x and y any real number?
yes
neon aspen
Do you want help with the question?
unreal falcon
Do you want help with the question?
I will give another try if not I would like your help
quartz geode
ok i found it online
and yes you have to find f(x) in terms of a parameter
since there are infinite solutions
it's not easy to reach tho without prior knowledge of similar questions
unreal falcon
Do you want help with the question?
I might need it now
unreal falcon
it's not easy to reach tho without prior knowledge of similar questions
knowledge like what
neon aspen
Any progress?
quartz geode
knowledge like what
having solved a similar question before XD
unreal falcon
Any progress?
I got to f(0)=0 and f(x)+f(-x)=-x^2 for all real x
neon aspen
I got to f(0)=0 and f(x)+f(-x)=-x^2 for all real x
You can replace x with -x and y with 2x to get 2f(x) = f(2x) + x^2
unreal falcon
You can replace x with -x and y with 2x to get 2f(x) = f(2x) + x^2
I tried to calculate f(nx) but it won't help me that much ig
neon aspen
Try replacing y with -2x
unreal falcon
Try replacing y with -2x
I got to f(-x)=-f(x)-3x^2
neon aspen
I got to f(0)=0 and f(x)+f(-x)=-x^2 for all real x
If you replace f(-x) with this there's a contradiction
Anyway I tried that and got nothing new
unreal falcon
If you replace f(-x) with this there's a contradiction
yep that's what I thought of
unreal falcon
Anyway I tried that and got nothing new
alrr thanks
devout snowBOT
@unreal falcon Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
tacit wedge
devout snowBOT
tacit wedge
,rotate
woven radishBOT
tacit wedge
is there a way to get an integer solution
im pretty sure there is but idk how
(review, not hw)
I know 5 and 2 satisfy this but
there might be so many possibilities
should i just leave it as 3A + B?
Then again it seems wrong to
Or is it the only?
My brains exploding trying to find out more possibilities
devout snowBOT
@tacit wedge Has your question been resolved?
devout snowBOT
@tacit wedge Has your question been resolved?
devout snowBOT
@tacit wedge Has your question been resolved?
woven radishBOT
ninjahuman
sleek island
But each time you are adding $B$ to get the next number
woven radishBOT
ninjahuman
sleek island
The basic idea is
Either $B$ is a multiple of $3$ or one of these numbers divides $3$
woven radishBOT
ninjahuman
sleek island
If $B$ is a multiple of $3$, then you can end up showing that at least one of these numbers is not prime
woven radishBOT
ninjahuman
sleek island
So one of them divides $3$
woven radishBOT
ninjahuman
sleek island
But because they are all prime, one of them must be $3$
woven radishBOT
ninjahuman
sleek island
The one that divides $3$
woven radishBOT
ninjahuman
tacit wedge
so it is 5 and 2
sleek island
Yes $A=5$ and $B=2$ is the only possibility
woven radishBOT
ninjahuman
tacit wedge
why must B be a multiple of 3 tho
sleek island
It can't
That's what you have to show
I'm saying if it is
Then one of them are not prime
tacit wedge
oh
sleek island
One of those numbers
One of them will be an even number greater than 2
if that happens
sleek island
You're welcome!
austere musk
devout snowBOT
winter patrol
no
midnight dirge
u should show some working
hybrid snow
for (ii) domain -2>=x>=0
How does $-2 \geq x \geq 0$ make sense
woven radishBOT
Umbraleviathan
hybrid snow
-2 is not greater than 0
You have the correct numbers
I'd advise you just use function or set notation
austere musk
my bad
devout snowBOT
@austere musk Has your question been resolved?
tawny ruin
my prof didn't do an example like this during class, i can do everything but find the interval where their trajectories are the same.
devout snowBOT
my prof didn't do an example like this during class, i can do everything but fin...
@tawny ruin Has your question been resolved?
devout snowBOT
@tawny ruin Has your question been resolved?
deep cove
In order to have same trajectory for two position equations, we will need $r(t) = R(t)$ for $t \in [c, d]$
woven radishBOT
jimmy1234
deep cove
Now do you see how to proceed?
tawny ruin
actually
devout snowBOT
restive river
what
how is -3 correct
x does not tend to anything
ita Delta x that tends to 0 in the limit defintion
grim burrow
-3 is indeed correct
one way of writing the limit definition for derivative at $x=a$ is $$\lim_{x\to a}\frac{f(x)-f(a)}{x-a}$$
woven radishBOT
waler
devout snowBOT
@gloomy mango Has your question been resolved?
devout snowBOT
@gloomy mango Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
fast junco
Im tasked with finding 3 numbers in an addition that goes as such
VV
UU
AA+
——
VUA
fast junco
Where VV would be 2 of the same number such as 11 or 33 and the same goes for the rest
For VUA the numbers must be one of each of the above
This is the exact problem
I have no idea how to go about it, I thought maybe a matrix or a system of equations but I only have VV + UU + AA = VUA and since this problem doesn’t follow normal arithmetic rules I have no idea how to solve it without just plugging in numbers.
<@&286206848099549185>
winter patrol
since this problem doesn’t follow normal arithmetic rules
wdym
you could express those numbers as sums of multiples of 10
e.g.
VV = 10*V + V
considering properties of addition will also be helpful
think about the information you can get just from looking at the units column
fast junco
But how does that help me create a linear equation?
fast junco
considering properties of addition will also be helpful
And what properties of addition are you referring to?
winter patrol
the ones that should be intuitive and shouldn't overthink
what must happen for the last digit of
U + V + A to be A
fast junco
Well that the addition be less than 10
winter patrol
no
you are told that they're distinct
U and V can't have the same value
and you're still overthinking
U and V must be 5
what led you to that
fast junco
Well U and V must add up to ten then
winter patrol
yes
fast junco
Ah ok, and after that is it ok to just plug in random numbers or should I look for more rules of this type
winter patrol
no
dont plug in randomly
consider the same idea again
note that that'll carry a 1
and then consider when
1 + V + U + A will have a last digit of U
and how much that'll carry over to the next column
fast junco
Ahh ok
I’ll try that out, thx for the help, you’re right I was making this too complicated
devout snowBOT
@fast junco Has your question been resolved?
trail moth
devout snowBOT
trail moth
can someone help me how to simplify this one
devout snowBOT
@trail moth Has your question been resolved?
trail moth
<@&286206848099549185>
trail moth
btw, we are required to use the rules of differentiation
such as the power rule, etc
@dusk umbra
im still on the 2nd derivative and i need to differentiate it up to the third dx
dusk umbra
Have you tried using the neperian logarithmic rule?
That might ease the thinga
Things
You might end up with a much shorter string than what you had earlier
It doesn't shorten every existing derivated ecuation in the earth but try it out see if you get something better
devout snowBOT
@trail moth Has your question been resolved?
dusk umbra
Oh I see....
That's a shame because ln really does ease the things a lot and seeing a so large derivation like before really gives me headaches
devout snowBOT
@trail moth Has your question been resolved?
stone stump
check whether $\lim_{x\to 0} f(x) = f(0)$
woven radishBOT
Denascite
stone stump
if you just plug the numbers in, yes. but you can rearrange and then you get something else
devout snowBOT
@atomic basin Has your question been resolved?
devout snowBOT
@atomic basin Has your question been resolved?
scarlet current
how would you solve this problem? like what would be the best steps to get the answer?
meager blaze
v=lwh, let the new vol be V
V=lwh/8, 8V=lwh, so V=v/8 hence volume is multiplied by 1/8
scarlet current
v=lwh, let the new vol be V
V=lwh/8, 8V=lwh, so V=v/8 hence volume is multiplied...
ohh ok thank you
rugged vortex
idk how to explain thsi properly
devout snowBOT
idk how to explain thsi properly
rugged vortex
this my working out
prime egret
Seems right
rugged vortex
i get how to solve the question just dont know if its right and how to write it in
<@&286206848099549185>
prime egret
Show how you got the length of CB and properly label AC as x.
rugged vortex
CB is just 4 cm right?
prime egret
I meant CD
supple cove
devout snowBOT
supple cove
0
midnight dirge
and derivative of 4x?
supple cove
okok , i get now
supple cove
thank you
supple cove
.close
eternal raft
Use the Pythagorean Theorem to determine the diagonal distance each figure has traveled based on the given translation. Round to the nearest tenth if necessary
(x,y) -> (x - 6, y + 8)
devout snowBOT
Use the Pythagorean Theorem to determine the diagonal distance each figure has t...
@eternal raft Has your question been resolved?
eternal raft
<@&286206848099549185>
supple knot
Use the Pythagorean Theorem to determine the diagonal distance each figure has t...
Did you try plotting it
eternal raft
Nah
eternal raft
Ty
devout snowBOT
@eternal raft Has your question been resolved?
crisp turret
if i have something like
x*tan(a)=5
how do i make a graph so the x-axis represents the value of a
and the y-axis represents the y-coordinate for when xtan(a)=5 is true for that specific a value
scarlet sequoia
I don't understand what you're asking about
lone ravine
if i have something like
x*tan(a)=5
how do i make a graph so the x-axis represe...
So you want a coordinate system where a is on one axis and x on the other?
crisp turret
So you want a coordinate system where a is on one axis and x on the other?
yeah i think so how do i do that
lone ravine
Solve for x in terms of a or a in terms of x
devout snowBOT
devout snowBOT
Available help channel!
midnight dirge
how did this
devout snowBOT
how did this
tiny rain
why are ur questions so difficult
midnight dirge
its
just normal integration
wat
multivariables has 2 integral signs
ill just
resend
..
i lazy del
wooden wraith
Dude what
midnight dirge
an alien invaded :c
wooden wraith
Do we know what the functions f and zeta are?
tiny rain
omg its riemann
supple knot
It follows from bounding the integrand by a constant
midnight dirge
is zeta that c like thing
wooden wraith
yeah
midnight dirge
It follows from bounding the integrand by a constant
but like
f(c(t)) isnt a constant tho?
isit idk
:c
supple knot
Not the whole integrand, just f(zeta)
supple knot
f(zeta(t)) is a function of t
midnight dirge
it takes out n uses max
supple knot
So you just bound it by the max over t
supple knot
like <=
Oh I missed that. Yes it should be <= instead of = unless there's more information about f or zeta
modern token
if someone may please help, desperate need
devout snowBOT
if someone may please help, desperate need
remote meteor
alright what do u know about n
modern token
alright what do u know about n
all the bisectors meet there
remote meteor
alright so whats one conclusion u can draw from this info
remote meteor
Can u identify the radii of the circle from here?
modern token
how would i do that>
remote meteor
HN=GN=NJ
modern token
im not sure how that gives us the radi, but can we use that info to find the missing lengths using sin cos tan?
modern token
i was not no
modern token
but as for LJ?
remote meteor
ok for triangle nlj what type of triangle is it
modern token
right
remote meteor
alright so whats a formula to find an unknown side of a right angle triangle
starts with p
modern token
pythagorean theorem
remote meteor
yes
remote meteor
as we have applied this property, we know that HN=GN=NJ
therefore the length of JN is known as 122
And NL is given as 22
find the unknown which is LJ
modern token
120?
remote meteor
thats right
alright last one
what can you tell about GK and GJ?
whats their relationship
modern token
GK is half of GJ
modern token
so 164 yes?
modern token
yup
remote meteor
alright
devout snowBOT
devout snowBOT
Available help channel!
quartz folio
Resolve into factor
devout snowBOT
Resolve into factor
quartz folio
Yes
loud root
Send your work then
loud root
It's correct
loud root
You want to make (y-x) in the last parentheses become (x-y) like all the other parentheses to factor, right?
quartz folio
Yes
loud root
What you do there is change (y-x) to -(x-y)
So that's where the change in sign comes from
quartz folio
Oh
loud root
+3(y-x)
-3(x-y)
quartz folio
So the minus went out of the bracket?
loud root
What you do there is change (y-x) to -(x-y)
For example, if x=2 and y=4,
(y-x)=4-2=2
-(x-y)=-(2-4)=-(-2)=2
So (y-x)=-(x-y)
loud root
So the minus went out of the bracket?
Yes
loud root
It's like you divided (y-x) by -1 and brought it outside, so (y-x)=-1(-y+x)=-1(x-y)=-(x-y)
quartz folio
Ok thanks
loud root
Np
old spear
help me
old spear
19
How do you take the first and second derivative of a fraction
Quotient rule? If so, how do i Apply it
pulsar phoenix
yes quotient rule
old spear
I kno the formula
pulsar phoenix
That’s a good start aleight
pulsar phoenix
f(x) numerator
old spear
According to my question, t is the f(x)
pulsar phoenix
Yes
pulsar phoenix
yes
old spear
What is it then
pulsar phoenix
t+1*
old spear
Should i simplify or thats the answer?
devout snowBOT
@old spear Has your question been resolved?
pulsar phoenix
Just got back
pulsar phoenix
Is this the second derivative or simplified?
wooden bridge
so i think i solved this problem
i followed this formula i have memorized
on one hand i dont rlly know what it’s asking me to prove
top one is the answer and second one is my work
is that enough for my proof?
E/4
brain go brrrr
devout snowBOT
@wooden bridge Has your question been resolved?
devout snowBOT
@wooden bridge Has your question been resolved?
vale plover
I got stuck on this derivative problem, any tips?
devout snowBOT
I got stuck on this derivative problem, any tips?
scarlet sequoia
you didn't do derivative of inner function
or you did it incorrectly
inner function is sinx/x and its derivative isn't cosx
vale plover
What would it be?
scarlet sequoia
u know quotient rule?
vale plover
Oh yeah I forgot to use that
I’ll try it
Yeah I solved the problem. Thank you for pointing that out
.close
strange tree
helo
old spear
Is this the second derivative or simplified?
My version of the second derivative
Cmiiw
devout snowBOT
@strange tree Has your question been resolved?
short stag
can somebody explain where that -0.1 came from?
devout snowBOT
can somebody explain where that -0.1 came from?
lunar harbor
Decreases at 10% per year
short stag
oh, I've missed that so if it said "increases", this is gonna be positive, am i right?
anyway, thank you so much!
.close
hoary swift
Calculate the probability of winning the host.
- Roulette has numbers from 0-36
- (0),(19),(28) = x3 win (best possible numbers)
- (1) autolose
- Tie=hoster wins
- 2 numerous numbers combine together, Example 11=1+1=2 or 25=2+5=7.
6.Bigger number always wins example: 8>25
onyx echo
devout snowBOT
@hoary swift Has your question been resolved?
hoary swift
This game is played at casino, so u bet money against the hoster/coupier.
devout snowBOT
devout snowBOT
Available help channel!
digital spade
hi
digital spade
how would i do this https://media.discordapp.net/attachments/761641569010188308/1021418844553756672/IMG_1422.jpg?width=702&height=936
devout snowBOT
@digital spade Has your question been resolved?
digital spade
You can use a rule of 3
could you walk me through this as im unfamiliar
digital spade
sure
dusk umbra
Oh and sorry I forgot a comma, result is not 255 but 25,5
dusk umbra
is there some kind of rep system
Wdym?
digital spade
like reputation
digital spade
only thing i found confusing is your 1s looked like 7s
dusk umbra
Because there is a common mistake where people thinks 14,4 would be long triangle's lines length, but it's not
dusk umbra
only thing i found confusing is your 1s looked like 7s
I always put a line in the sevens
digital spade
yeah i noticed whe i thought about it
dusk umbra
Because there is a common mistake where people thinks 14,4 would be long triangl...
Anyways be careful with that
digital spade
Because there is a common mistake where people thinks 14,4 would be long triangl...
yes i thought that at first
dusk umbra
So you know how long would the big line be?
digital spade
lemme try rq
dusk umbra
Oh sorry wait you might have misunderstood me
digital spade
would it be 17.6
dusk umbra
The line we are comparing in the big triangle isn't 14,4 cm's long
digital spade
oh
dusk umbra
would it be 17.6
Sorry but that's not the correct answer
dusk umbra
could you walk through it
Yeah of course! I am going to explain it to you
digital spade
cheers
dusk umbra
digital spade
i see
dusk umbra
So now with that in mind how much is y?
dusk umbra
Lmao
digital spade
there we go lol
dusk umbra
Yes!!!
That's it
Oh waiit
No o
That's the kine
Line
But not Y
The excersise is asking you for y
Remember the rule of 3
dusk umbra
Well not exactly but yeah, we'll take that
digital spade
so what would the final calculation be
dusk umbra
That's what you have to figure out using the rule of 3 I showed you earlier
digital spade
so i would do
dusk umbra
Go ahead
digital spade
first
digital spade
so you said `x = 15.17/10 `
why is there a decimal point
dusk umbra
Because this rule is at comparison
Look
First of all what line in the small triangle corresponds to big triangle's 23,4?
digital spade
9
dusk umbra
And the small triangle's equivalent to big triangle's y?
digital spade
11
digital spade
11
dusk umbra
Great so there we have our first comparation.
9 ----- 11
(When right is 9, bottom is 11)
Then when right line is 23,4 what does bottom line equal to?
digital spade
x
dusk umbra
Exactly, so we have our second comparison
23,4 ----- x
Now we put one on top of the other
9 ----- 11
23,4 ----- x
Do you understand until there?
Or are you missing anything?
digital spade
9 * 11 /23.4?
digital spade
ah ok
dusk umbra
As it is in the picture
digital spade
23.4 * 11/ 9
digital spade
28.6
digital spade
which one
dusk umbra
The one where i explain the rule of 3
dusk umbra
Nope
dusk umbra
Numbers are related diagonally
The pair goes on top of the division and the one that is single goes underneath
digital spade
why are the 11 and 9 swapped
dusk umbra
Oh
Sorry my bad
Oh then you were right I had it wrong in my paper
I'm so sorry 😔🙏
I made you loose time
Ok so your answer is in fact correct
dusk umbra
My god I'm so sorry
digital spade
23.4 * 11/ 9
also this is right also i just realised
dusk umbra
Don't forget to type .close when you're done
dusk umbra
also this is right also i just realised
Yeah your answer was ok from the beginnign
digital spade
also this is right also i just realised
wait nvm
dusk umbra
I'm real sorry
digital spade
Yeah your answer was ok from the beginnign
thanks i understand it now
dusk umbra
Good ok bye!
digital spade
.close
graceful canopy
Hello, so the math problem is "The triangle has corners in points: A(-2,4), B(7,1), C(2,6). You have to get the equasions for the carriers of the height and the coordinates of the height points of the triangle." I have the answer to the problem, but I really have no clue how to get it.
devout snowBOT
Hello, so the math problem is "The triangle has corners in points: A(-2,4), B(7,...
graceful canopy
answer:
devout snowBOT
@graceful canopy Has your question been resolved?
graceful canopy
<@&286206848099549185>
devout snowBOT
@graceful canopy Has your question been resolved?
devout snowBOT
@graceful canopy Has your question been resolved?
graceful canopy
<@&286206848099549185>
timber pebble
Hello, so the math problem is "The triangle has corners in points: A(-2,4), B(7,...
carriers?
height point?
graceful canopy
yes sorry i translated it from my language and didnt know exactly what its called
devout snowBOT
@graceful canopy Has your question been resolved?
glad osprey
Hi, I need help with 3 questions, starting with this one
devout snowBOT
Hi, I need help with 3 questions, starting with this one
glad osprey
I'm just confused with how I'm going to show the limit of f(x) as x approaches a equals 0 with the given information
devout snowBOT
@glad osprey Has your question been resolved?
inland seal
Hint:
$\lim_{x \to a} f(x) = \lim_{x \to a} g(x) \cdot \frac{f(x)}{g(x)}$
woven radishBOT
RedstonePlayz09
inland seal
And no, you can't use limit arithmetic like you wrote, since g(x) approaches 0.
When g(x) does not approach 0 and both limits exist, you can.
glad osprey
hi, I tried it again and this is what I came up with. I'm not sure if this is a proper way to do it though
inland seal
This is false:
$\frac{\lim_{x \to a} f(x)}{\lim_{x \to a} g(x)} = \lim_{x \to a} {\frac{f(x)}{g(x)}}$
woven radishBOT
RedstonePlayz09
inland seal
Since g(x) approaches 0.
inland seal
**RedstonePlayz09**
Start from this
Show that the right hand side is 0, and that will mean that f(x) approaches 0.
Another hint: ||use the product rule for limits||
glad osprey
can I do it this way?
inland seal
No
Close
$lim_{x \to a}{g(x) \cdot \frac{f(x)}{g(x)}} = \lim_{x \to a} (g(x)) \cdot \lim_{x \to a} \frac{f(x)}{g(x)}$
woven radishBOT
RedstonePlayz09
glad osprey
ohh did I just need to distribute the limit and then that's it?
also no worries! I appreciate the help
devout snowBOT
@glad osprey Has your question been resolved?
devout snowBOT
@glad osprey Has your question been resolved?
glad osprey
also this one, did I do it right?
devout snowBOT
@glad osprey Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
stone axle
devout snowBOT
lone ravine
Use the formula for the sum 0 to x^n
acoustic siren
Yes, you can use the first formula here (because the sum is finite)
stone axle
and when i look at the solution, they use the power of 8, not 7
lone ravine
Yeah, I meant the 1st one
acoustic siren
and when i look at the solution, they use the power of 8, not 7
yes, cause note that the sum is to n-1
so n = 8
lone ravine
Yes
regal vector
devout snowBOT
low nexus
add up the side lengths
crimson plinth
Yeah
low nexus
and express them in a reduced form
cosmic jacinth
You basically could even find out x and y, since opposite sides are equal
Form two equations
regal vector
So I know I'm supposed to write them like 2y-x=x+2 x+y+1=3x-4
obtuse oxide
So I know I'm supposed to write them like 2y-x=x+2 x+y+1=3x-4
Yes.
regal vector
But Im stuck on what to do next
obtuse oxide
Solve the system of equations.
low nexus
ohhhh they want an actual answer
i thought they just want it expressed in terms of x and y
@regal vector do you know how to solve systems of linear equations?
regal vector
Somewhat
low nexus
$2y - x = x + 2$
woven radishBOT
aguaman
low nexus
let's start with this one
what do you want to do first
(hint: make it in the form of ax + by = c)
regal vector
Eliminate x?
low nexus
Eliminate x?
you can't eliminate without a second equation, focus on getting it into a proper form
regal vector
Oh
low nexus
because right now, this shit ugly
so you wanna make it pretty y'know
@regal vector what's the first step
regal vector
2y=2x+2
low nexus
yeah.. you're right but...
move the x on the right to the x on the left
we want it in a form of ax + by = c
this saves us a step
low nexus
good!
so that's equation 1
we need to make equation 2
what's equation two gonna be (look at the opposite side lengths)
regal vector
X+y+1=3x-4
regal vector
-2x+y+1=-4?
low nexus
mhm
what's the next step
we want a constant on the other side remember, so move the 1
regal vector
-2x+y=-5
low nexus
good!
so we have two equations now
2y-2x=2 and -2x + y = -5
lets solve this using substitution
what would you do first
hint: use equation 2 because that's easier to substitute with
regal vector
y=-5+2x?
regal vector
2(-5+2x)-2x=2
regal vector
2x=12 x=6?
regal vector
-12+y=-5
Y=-5+12
Y=7?
low nexus
good
now back to the original question
finding the perimeter
sub in those values back into the other ones
and add them up
regal vector
7+7+6+6=14+12=26
sharp sparrow
I close it by accident
devout snowBOT
I close it by accident
wooden veldt
sharp sparrow
thx
I know the top one is euler constant
Im stuck on how to solve the denominator
wooden veldt
you can try taking logs
sharp sparrow
Question, since x is tending to infinite what is the explanation 1\x is not going to 0?
midnight dirge
it is
woven radishBOT
ΣAC
sharp sparrow
Ok, so why is this equivalent to the euler constant
midnight dirge
i think its defined as such
soft shore
what’s pi
sharp sparrow
if 1/x goes to zero, how (1+1\x)^x=e?
sharp sparrow
Right
soft shore
same for e
wooden veldt
if $f(x) \to 1$ and $g(x) \to \infty$ this does not mean that $\lim_{x\to\infty} f(x)^{g(x)} = 1$
sharp sparrow
So how would i solve for the denominator?
woven radishBOT
ΣAC
sharp sparrow
Oh i got
But i still have no idea on how to solve for the denominator
Ill get e over (1-1/x)^x
arctic field
do you know any other things related to the limit (1 + 1/x)^x?
not that its actually needed here i dont think
sharp sparrow
nope, the question just ask to solve the limit
wooden veldt
you might know a general formula for the limit of (1+a/x)^x for some number a
arctic field
wait nvm i think you do need to know that
yeah
no matter what you do
you cant avoid
midnight dirge
ca
woven radishBOT
arctic field
thats the limit definition of e
midnight dirge
yep definitionally
sharp sparrow
im trying to fatorate here
arctic field
fatorate? 
midnight dirge
is hard
midnight dirge
anw, u can split to num n denom n apply
sharp sparrow
fatorate? <:what:561568026210730004>
yeah, multiply the denominator on the numerator and try to use a notable product
midnight dirge
this twice
sharp sparrow
take out those negatives numbers
midnight dirge
:0
arctic field
oh nvm just take e^ ln
i have no idea what you're talking about
it all needs proof
and its all part of real analysis
midnight dirge
to find lim, dont we just take e^ln (eq)
arctic field
doesnt help if you dont know what the limit of x ln(1 + a/x) is
arctic field
well
midnight dirge
:0
arctic field
just a lot of analysis
midnight dirge
which is the subject
sharp sparrow
Can someone at least give me a hint where should i start?
arctic field
this is a good place
arctic field
apply it to this
however youd like
one way is to do the numerator and denominator separately
wooden veldt
if you can prove this, then you have dealt with the denominator
you can begin to try and prove it by starting with the limit definition of e and substituting x with x/a
midnight dirge
you can begin to try and prove it by starting with the limit definition of e and...
thats taking a lot for granted
wooden veldt
well we're not going to start getting epsilons and deltas out are we
you have to take something for granted somewhere or else its overkill for just a computation question where the idea is to use limits you know
sharp sparrow
you have to take something for granted somewhere or else its overkill for just a...
This question is part of an acedemy application previous test is something you can solve by paper
Im trying rn what you told me
arctic field
i think this limit is very often taken for granted
but since you dont know it it would be a good idea to see how it works
devout snowBOT
devout snowBOT
Available help channel!
restive river
Can someone please help
I'm doing fourier series
From -pi to pi integral sin(mx) dx
I got
f(x)= 2sin(m pi)/ (pi (m^2-n^2)) summation from n=1 to infinity n(-1)^n sin (n pi)
The answer however is 0
Did I do sth wrong? Or should I just now say that sin (n pi)=0 so f(x)=0?
stone stump
well yes sin(npi)=0 so what you have is f(x)=0
restive river
Um, wait
Actually I got
Bn= (2sinm pi)(n cos n pi)/(pi (m^2-n^2)
Then I got
F(x)= summation (n=1 to inf) bn (sin n x)
Now when I plug my bn in it
I should have sin (nx) but the youtuber somehow wrote it as sin (n pi)
Why did he transitioned from x to pi?
devout snowBOT
@restive river Has your question been resolved?