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hallow saddle
How do I work out Y = mx + c when I don’t have an equation
safe radishBOT
How do I work out Y = mx + c when I don’t have an equation
hallow saddle
I have managed to get my gradient of -1/20 by substituting -5 into the derivative and then doing the reciprocal of 20
However I am stuck with y = -1/20x + c
split ether
You have to pick value of c such t hat y = -x/20 + c has the same value as (x + 1)(x + 3)^2 at x = -5
hallow saddle
Is there no formula to work this out ?
split ether
There is
Generally the equation of a line tangent to y = f(x) at x = a is y = f'(a)(x - a) + f(a)
hallow saddle
But if x = a then wouldn’t I be subtracting from itself
split ether
Wdym?
split ether
Here a = -5
split ether
Nope
hallow saddle
in y = f'(a)(x-a) do i multiply them together and then find the derivate or just find the derivate of a
Im sort of confused on how this equation works
hallow saddle
-5 substituted into f(x)?
split ether
Yup
hallow saddle
So f'(a) is -5 substituted into the derivate of f(x)
hallow saddle
What does this mean
split ether
To get f(-5) you just substitute x = -5 into f(x)
To get f'(-5) you just substitute x = -5 into f'(x)
hallow saddle
Is f'(x) not the derivate of f(x)
hallow saddle
So f'(a) is -5 substituted into the derivate of f(x)
So then why is this wrong
Ob
Oh
split ether
Yeah you were right
hallow saddle
Lol no problem
hallow saddle
in y = f'(a)(x-a) do i multiply them together and then find the derivate or just...
How does this work
split ether
Just evaluate f(a), f'(a) and sub
hallow saddle
Im now confused again
split ether
What did you get as f(a) in this case?
hallow saddle
What did you get as f(a) in this case?
-16
split ether
And f'(a)?
hallow saddle
20
hallow saddle
But my intention is to work out the tangent to the line
split ether
The question is asking you for the equation of the tangent line at x = -5, right?
hallow saddle
Yeah
split ether
Or just 20x + 84
So that's it
hallow saddle
But is the tangent not the reciprocal?
split ether
Slope of the tangent line = f'
hallow saddle
Oh
split ether
You take minus the reciprocal when you are asked for the so-called normal line
hallow saddle
How do I work out Y = mx + c when I don’t have an equation
.
split ether
What can you say about the slopes of lines parallel to each other in general?
hallow saddle
the gradient is equal
split ether
Yup, so we need to find another value of x for which the derivative of f is equal to 20
hallow saddle
So the x coordinate of B would be 1/3
Since that was the other value from -5
When i solved
split ether
Correct
hallow saddle
Thank you very much
new issue has found upon turning my Page
How do I work out the derivate of an equation with a denominator
split ether
The quotient rule:
[
\dv{}{x}\frac{f(x)}{g(x)}=\frac{f^{\prime}(x)g(x)-f(x)g^{\prime}(x)}{g(x)^2}
]
flat frigateBOT
A Lonely Bean
split ether
You can derive it
What you do is simply rewrite f(x)/g(x) as f(x) * g(x)^(-1) and apply product rule + power rule + chain rule
hallow saddle
Oh yeah
Ive learnt about rewriting it using powers
Like 23/x is 23x^-1
But my denominator is 2x
split ether
Then you just do $\frac{x^{-1}}2$
flat frigateBOT
A Lonely Bean
hallow saddle
So if it was x^3/2x ?
split ether
That cancels to x^2/2 for nonzero x
hallow saddle
Would it be x^2 / 2
Question states that x cant be zero
What if I just had -12/2x
split ether
Then rewrite that as -6x^-1
hallow saddle
I see
charred narwhal
no bro it would be x/2/2
hallow saddle
???
charred narwhal
1^x/2
split ether
- That's an invalid expression
- In any way you make it valid, it is not gonna be equal to -12/2x or anything mentioned above
hallow saddle
What do I do with my denominators
Since you can’t find the derivate of a fraction
Do I turn them into the coefficients
split ether
Wdym? I just showed you the way of differentiating a fraction
hallow saddle
I mean
split ether
**A Lonely Bean**
.
hallow saddle
I have x^2 / 2
split ether
Ah
hallow saddle
To differentiate do I make it 1/2x^2
charred narwhal
smth like this
hallow saddle
Half of the derivate?
split ether
Differentiate each term separately and add the results up
charred narwhal
if we had negative number we dividing 1/x
hallow saddle
Differentiate each term separately and add the results up
Yeah i did that
split ether
What did you get?
split ether
You got that from differentiating x^2/2 ?
hallow saddle
No my whole equation
split ether
Ah, so what are you differentiating?
charred narwhal
for example
hallow saddle
x^2 / 2 - 3x / 2 + 2 - 6x^-1
split ether
Everything is correct except instead of +0.5 you should have -1.5
safe radishBOT
@hallow saddle Has your question been resolved?
safe radishBOT
@hallow saddle Has your question been resolved?
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@hallow saddle Has your question been resolved?
knotty viper
Should i solve this as a logistic growth function?
safe radishBOT
Should i solve this as a logistic growth function?
knotty viper
Like this?
safe radishBOT
@knotty viper Has your question been resolved?
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@knotty viper Has your question been resolved?
knotty viper
<@&286206848099549185>
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@knotty viper Has your question been resolved?
tepid epoch
need help plz how do i do this
safe radishBOT
need help plz how do i do this
green bane
find the slope
green bane
pick two points subtract the y and the x divide
modest robin
do you see how the line goes through the point (6,5)
tepid epoch
ok
tepid epoch
do you see how the line goes through the point (6,5)
yes
modest robin
you could use that point and (0,0)
green bane
y change/x change
tepid epoch
ok thats 0.83333333333
green bane
fraction
tepid epoch
ok 5/6
green bane
yep
tepid epoch
alright
i dont think it takes a fraction as an answer
it says equation that represents therelationship for the graph
so the relation ship is 6,5 and 0,0 i think
ok im just gonna try to figure it out with the video it gives me but have a good one
.close
safe radishBOT
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quiet briar
hi i dont understand this
safe radishBOT
hi i dont understand this
junior smelt
,calc sqrt(7500/250)
flat frigateBOT
Result:
5.4772255750517
Might be a mistype or a miscalculation, is there any more context to this?
quiet briar
yep
its basically this
given values of k and m
for a question
hang on
here's something similar
if i use the value of 20 in my calculations here i get the correct graph
,calc sqrt(10000/250)
flat frigateBOT
Result:
6.3245553203368
when i use this
graph is wrong
i feel like im doing something illegal when calculating natural frequency
flat frigateBOT
Result:
20
gusty inlet
if you put in extra zero you get your result
so maybe a zero has been forgotten somewhere
quiet briar
Ahh
Hm
Interesting
I think the question must have missed out the extra 0
Makes sense
Thanks .close
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prisma condor
A = "5327"
B = "4839"
C = "25xy7353"
5327*4839 = 25xy7353
Where x and y are mystery digits that i have to figure out without straight up multiplying A and B.
How do i figure out the sum of x and y using the modulus 9 rule?
-
Adding up the digits of a number will give you the remainder of the number when dividing by 9
-
(A % 9) * (B % 9) = C % 9
Where a b and c are numbers produced by adding the digits in the number up
safe radishBOT
A = "5327"
B = "4839"
C = "25xy7353"
5327*4839 = 25xy7353
Where x and y are my...
prisma condor
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crude star
@junior smelt when u say test the convergence at x = 1 and x = -1
crude star
do I straight up plug x = 1 and x = -1
and then find the lim?
both converge no?
its 0.
for both
junior smelt
Pretty much check whether the series
[
\sum_{n=1}^{\infty} \frac{1}{\ln(n+5)}
]
and
[
\sum_{n=1}^{\infty} \frac{(-1)^{n}}{\ln(n+5)}
]
converge or not
flat frigateBOT
@junior smelt
flat frigateBOT
crude star
OH WHAT
crude star
shit now im tripping
crude star
wont this converge accoridng to the nth term test doe?
oh brah
I might need to use another test
right
oh
wit ratio test
I get L = 1
do I use another test again
junior smelt
You could e.g. try comparison for this one
junior smelt
wont this converge accoridng to the nth term test doe?
if by nth term you mean "the sequence converges to zero, so the series must converge", then that isn't quite true (e.g. $\sum_{n=1}^{\infty} \frac{1}{n}$ doesn't converge despite $\lim_{n\to\infty} \frac{1}{n} = 0$)
flat frigateBOT
@junior smelt
crude star
You could e.g. try comparison for this one
do I compare it with 1/n?
junior smelt
do I compare it with 1/n?
You can 
crude star
shit then it does diverge
but on the exam lets say
because I always end up usin ratio/root/nth term test first most of the times
and lets say with one of them.
it shows that it converges but with others
its inconclusive
like for instance the question we just did
with nth term test I got 0 but with ratio test I got 1. how would I know that that is not rnough to prove a series convergence
gusty inlet
there is no way a test would show that the harmonic series converges
you probably used it wrong
crude star
I used the nth term test and got 0
gusty inlet
describe the nth term test
crude star
i took the limit
of the series
as n approaches infinite
and got 1/inf
which is 0 isnt it
gusty inlet
you mean the limit of 1/n right ?
crude star
no
crude star
,w sum 1/ln(n+5), n from 1 to inf
this
gusty inlet
so you calculated the sequence of partial sums ?
how did you prove that it converges
is my question
then we can work on whether or not something was wrong in the solution
crude star
i took the limit
i literally just did this
i thought since the denom gets larger and larger and the top doesnt change then the limit would approach 0.
gusty inlet
you mean you took the limit of 1/ln(n+5) ?
crude star
ye
gusty inlet
and does that prove that the whole series converges ?
what does the nth term test say, specifically
write it down in words
gusty inlet
yes yes exactly what i wanted to to arrive at.
gusty inlet
the test is a divergence test not a convergence test
gusty inlet
you can't
crude star
Oh my god
gusty inlet
you can only test for divergence xD
crude star
im acc so slow this whole day
I been thinkin dat
if its L = 0
then it means
it converges
gusty inlet
it's okay mate, it happens
look
I want you to think like charbit told you
first, don't believe stuff in text book just because they are written by someone of higher authority
justify everything you read for yourself
and the way to justify this is through what charbit said
does it really test for convergence ?
lemme try to find a series
that diverges
and the nth term test gives zero
the most famous one is the harmonic series
lim 1/n is zero
but the series diverges
this means that the nth term test cannot test for convergence otherwise the harmonic series would converge
and that would lead to contradiction
crude star
ty man.
gusty inlet
you welcome buddy ^ ^
crude star
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gilded scroll
Why is it negitive
safe radishBOT
Why is it negitive
gilded scroll
alrighty
so I jsut put it as negitive when i solve these?
lol yeah
oh wait
the formula is a/1-r
so it has to be negitive
mk ty
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✅
gilded scroll
how did they get that formula?
the one i have up there?
ah
right
just somthing to memorize
ty
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fickle talon
can someone explain this to me? why aren't we doing D < 0 for the quadratic in t but |t| < 2?
safe radishBOT
can someone explain this to me? why aren't we doing D < 0 for the quadratic in t...
fickle talon
split ether
Where |t| < 2 is coming from is unclear yeah
Especially considering that’s invalid since t can be imaginary
Not really useful
You usually can’t tell if the roots are imaginary by only looking at their product and sum
So setting discriminant to be a negative number should be the way
fickle talon
can someone explain this to me? why aren't we doing D < 0 for the quadratic in t...
the teacher says that we dont need a condition for D since if D < 0 then automatically x is imaginary so we only need |t| < 2
the range of x+1/x is (-inf, -2] U [2, inf)
toxic stratus
because for real values of x you can't have |x + 1/x| < 2
fickle talon
so it makes sense ig
split ether
Actually what I think you could also do it replace x with some ki where k is a real number and set real and imaginary parts of the polynomial equal to zero
toxic stratus
x + 1/x >= 2 for positive x is a result of AM-GM
if you have that it is <2 in magnitude then x must be complex
split ether
Actually what I think you could also do it replace x with some ki where k is a r...
That results in ak - ak^3 being equal to zero
I believe
fickle talon
if you have that it is <2 in magnitude then x must be complex
alright makes sense
thanks
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potent solstice
Does anyone know how exactly this is a systems of equations?
safe radishBOT
Does anyone know how exactly this is a systems of equations?
potent solstice
I tried working out what the first iteration was but it just got dumb complicated and I think I did it wrong.
For iteration 1 I inserted the variables and then I simplified each element in the matrix
I am not sure how exactly to work this out as a systems of equations because I thought those were just
27 = 2x - y
y = 2x + 3
safe radishBOT
@potent solstice Has your question been resolved?
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@potent solstice Has your question been resolved?
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@potent solstice Has your question been resolved?
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pine dove
Can someone explain how they got 20 in question c)?
safe radishBOT
Can someone explain how they got 20 in question c)?
pine dove
<@&286206848099549185>
safe radishBOT
@pine dove Has your question been resolved?
fickle abyss
safe radishBOT
fickle abyss
how come they add a +C on LHS but not on RHS?
green bane
?
thin bridge
both sides will still differ by a constant,
there's no need to have two arbitrary constants
fickle abyss
both sides will still differ by a constant,
there's no need to have two arbitrar...
so then the equation would be wrong no?
thin bridge
wdym
fickle abyss
if one side have a constant, wouldn't it equal to the other side since that side haven't got a constant
thin bridge
not sure what you mean
suppose
f'(x) = g'(x)
integrating both sides
f(x) + C = g(x) + D
f(x) = g(x) + (D-C)
(D-C) is just another constant
f(x) = g(x) + k
fickle abyss
$ln(k) - ln|1-y^2|$ = $ln|1+x|$ \ $ln(k) - ln|1-y^2|$ ≠ $ln|1+x| + ln(k)$
flat frigateBOT
yomiko
fickle abyss
suppose
f'(x) = g'(x)
integrating both sides
f(x) + C = g(x) + D
f(x) = g(x) + ...
so does that mean that it doesn't matter which side i put the constant at ?
thin bridge
yes
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prime mason
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prime mason
so if x approaches 1 from the left hand side is f(x)=dne?
pure agate
If the limit was from both sides, it would be DNE.
In this case, because it is from the positive side, the limit does have a value.
mortal sandal
positive?
pure agate
It does say lim x->1^+.
pure agate
It will only be one of those values.
pure agate
Trace the curve from x=2 to x=1. At what value of y does it end at?
granite idol
from +2
pure agate
Trace the continuous part of the curve. Do not jump across discontinuous parts.
Probably the most difficult part of limits to understand is that we are not concerned with the value of f(x) at x = 1, we want to know the value of f(x) as x gets close to x = 1 while approaching from the positive side.
pure agate
It is not 2.
prime mason
so how is it 0 then
pure agate
Because the left end of the curve stops at (~1, 0).
(1.00000000000001, 0.000000000001) to be more "precise" which is close enough to y = 0 that we say the limit as x approaches 1 from the positive side is 0.
pure agate
No.
When it comes to limits, we are not concerned with the actual value at f(c), we are only concerned with the value it approaches.
granite idol
key word here is "approaches"
pure agate
While f(0) does not exist, the curves do approach the same value of y as they get infinitely close to each other.
prime mason
I see
pure agate
This is an important definition to understand when you start talking about continuity and if a point is continuous.
prime mason
so if it doesnt have a closed or open circle will that be the only time that the its considered DNE?
pure agate
A limit will be DNE if the limits from either side do not equal each other.
ie. limit as x-> 1
prime mason
well like I was thinking that since x-> doesnt have any open or closed circles it would be dne
but its approaching the value of 0 at this instance then correct?
pure agate
This is another thing that often confuses students. The open and closed circles only give you information about the intervals. They do not describe anything about the actual value of a limit.
prime mason
what is the y value at x=2?
0
pure agate
So the curve from x=1 to x=3 is on the interval (1, 3]. Everything on that interval exists because f(x)) on the interval (1, 3] is implied to exist by the curve in the graph.
The limit from the left side of x=2 approaches y = 1, the limit from the right side of x=2 approaches y=1, and f(2) = 1.
That right there is the definition of a continuous point.
upbeat marsh
Find the scope of the function definition:
In response, write down the largest entire solution
pure agate
Find the scope of the function definition:
You need to open your own Help channel. #❓how-to-get-help
prime mason
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safe radishBOT
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lean otter
i am confused about how to find the sum of a series
safe radishBOT
i am confused about how to find the sum of a series
lean otter
like what would the steps be for this
empty gyro
taylor series?
Replace -1/4 with x
Then let f(x) be your sum
Find f'(x)
That sum should be easier (I think)
I could be way off
lean otter
wait so i take the first derivative with respect to n?
empty gyro
no
with respect to x
Oh
This is also a series of a known function
But if you don't recognize it, maybe the derivative idea will help your recognize it
lean otter
This is also a series of a known function
what is it?
empty gyro
log
But I'll leave the details for you to find
I'll give you this is a hint, since it's the only series I remember
lean otter
isnt 1/1-x only for finding an expression for a power seres
empty gyro
I'll give you this is a hint, since it's the only series I remember
Take integral of both sides here
empty gyro
and x^n+1/n+1
You see how close this is to your original series?
lean otter
yes...
empty gyro
In short, your series is ln(1-x)
lean otter
but i need to plug in something right
lean otter
yeah i just suck at series
lean otter
im actually just incredibly bad at calc 2 n gl
like once we got to series and sequences, all hope has been lost
empty gyro
Yeah. I forgot everything from calc 2
I just recommend you review your taylor series and see which one gives you your sum
lean otter
I just recommend you review your taylor series and see which one gives you your ...
i find that there is just so much to remeber in calc 2, do you have any advice for that i guess
lean otter
yes thats in my notes
empty gyro
And I can get sin and cos using e^ix=cos(x)+i*sin(x)
lean otter
this series stuff is so confusing to me lol
this and discrete
actually going to die
empty gyro
I remember this one
And get ln(1-x) by integrating it
Those are really the only ones I have memorized
lean otter
like what would the steps be for this
can we go over this from the beginning
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raven snow
For b, I am not sure why the integral is less than or equal to S. I thought the point of the integration test is that we can make the integral greater or equal then the sum, since we can use left or right Riemann sums. In this case, since it converges, wouldn't we want the integral to be greater or equal to S?
safe radishBOT
For b, I am not sure why the integral is less than or equal to S. I thought the ...
plucky elk
draw the picture
raven snow
I honestly dont know how to draw the picture of this
plucky elk
,w plot log(x) / x^2 for 2 < x < 10
flat frigateBOT
plucky elk
you just need to know that log(x) / x^2 is decreasing
so compare the integral with the series
raven snow
I understand that, and if I calculate the integral I will get a finite value 5(ln(2)/(8)+1/16). Thus it converges. But when comparing, since the integral converges, dont I want to the sum to be less then the integral?
plucky elk
draw the picture
.
raven snow
by comparison test we then know S converges if the integral is bigger and converges
plucky elk
so compare the integral with the series
compare as in draw the area of the series
raven snow
I thought we use Riemann sums to compare the care, and depending if we use left or right would depend if the area is greater or less?
we know ln(x)/x^2 decreases, so using right riemann sums to draw it we would get a lower area, using left riemann sums we would get a greater area. Is my understanding flawed somewhere?
plucky elk
pick whatever endpoint that represents your series
you know from (a) that I converges, and from integral test that S is also convergent
raven snow
But since the integral test is the same as I, dont we need I to be greater then or equal to S to show that S converges?
safe radishBOT
@raven snow Has your question been resolved?
teal oracle
i need help
safe radishBOT
i need help
teal oracle
can someone help
granite idol
empty gyro
It takes longer than a minute to read the whole thing
empty gyro
also what do you need help with
granite idol
given that info, how can you represent the length? look at the colors
empty gyro
This whole measurement is the length
And you see it broken into bits here
x is a length of unknown quantity. A variable
teal oracle
so i am susposed to find the length by comping all the spaces in between ?
granite idol
combine everything you're given to cover the whole length
your teacher color-coded it to help you see
empty gyro
all the green segments add up to your total length
granite idol
yes I assume that's what the colors are for
granite idol
I don't think you can without more information
the instructions just say to create the polynomial
teal oracle
but there is no number to plug in
granite idol
yes, you are only asked for the expression for the length
teal oracle
yes but how can i get find the x to find the rest of the length
granite idol
you aren't asked to find the x
empty gyro
you're usuing x just as it is
If I told you to add 1 and x, that's just 1+x. You don't need to do anything else
safe radishBOT
@teal oracle Has your question been resolved?
tight sentinel
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granite idol
cancel the exponentials
stray socket
Yeah you can just cancel the e^yln(x)
They're common factors
Otherwise you're fine
tight sentinel
oh
granite idol
it might have been easier to see if you changed it to x^y
midnight patio
safe radishBOT
solar hazel
idk it kinda sounds like you're just repeating the given information
and the problem is pretty much that simple but...
idk what to say about it tbh
midnight patio
yeah I agree, I'm just not sure how i can frame it
to show that it is transistive
It is so hard for that reason
solar hazel
something like let p be a prime divisor of x, then p is also a prime divisor of y (by assumption that x star y), so p divides z (by assumption that y star z)
midnight patio
something like let p be a prime divisor of x, then p is also a prime divisor of ...
Does this seem right?
This is my slight improvement one
solar hazel
the language reads a little funky to me but it's probably fine
midnight patio
midnight patio
the language reads a little funky to me but it's probably fine
This is like a similar quesiton, seems easy but language kind of off
solar hazel
wdym by divides itself?
midnight patio
divides into itself
solar hazel
what does that matter for?
midnight patio
trying to prove that it is reflexive
I'm just saying that every part of its prime factor divides itself, so it is related to tself
solar hazel
x star x is true if every prime divisor of x is a divisor of x
which is clear
for any natural number x
midnight patio
midnight patio
for any natural number x
Is this fine thanks?
solar hazel
i would put a period here instead of a comma but yea haha
midnight patio
the language reads a little funky to me but it's probably fine
how would I be able to imrpove the language, I could see it as well.
solar hazel
ummm
since ... then ... doesn't sound good to me and i don't think it's grammatically correct
i'd probably write
since y star z, we have that every...
there are some things i'd structure differently but i'm probably just being picky
midnight patio
there are some things i'd structure differently but i'm probably just being pick...
But it is good that you are picky
solar hazel
lol
midnight patio
solar hazel
no i feel bad commenting on people's writing a lot
midnight patio
Don't feel bad, I am happy that you are
solar hazel
what if you just wrote something like
Suppose x, y, z in N and x star y and y star z. We will show that x star z. Let p be a prime divisor of x. Then ............... Thus p divides z. Therefore x star z.
do you think you need all of that at the start and then to say suppose x, y, z in N after?
like if you do that's fine
solar hazel
what if you just wrote something like
Suppose x, y, z in N and x star y and y st...
but this is probably more how i would write it
midnight patio
But I feel like you need to show for all prime factors p
solar hazel
ya
p is an arbitrary prime factor of x
and we showed p divides z
ie we have it for all of them
midnight patio
midnight patio
p is an arbitrary prime factor of x
Is this good?
solar hazel
sure that's fine
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solar hazel
np ^^
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misty panther
hi guys what's the order of the identity element in a group
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hi guys what's the order of the identity element in a group
@misty panther Has your question been resolved?
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@misty panther Has your question been resolved?
plucky elk
hi guys what's the order of the identity element in a group
Use the definition of order
Trial and error works too
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scenic holly
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scenic holly
Anyone help
sweet basin
can u translate the question please
scenic holly
can u translate the question please
I need to solve inequality using the graphs
How to solve the example like that?
It's occupied channel man
scenic holly
can u translate the question please
Could you help?
@sweet basin
Understood
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orchid wave
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orchid wave
how do I even start this ?
pastel verge
Whatsvthe probelm
You have to find where both s and x are positive or negative at same time
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orchid wave
sorry about that
orchid wave
You have to find where both s and x are positive or negative at same time
yea I did that
and I got t=2, t=5/3 and t = 1
but how do I find the range of values for t ?
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leaden cypress
$ln[(1-x²/π²)(1-x²/(4π²))(1-x²/(9π²))⋯] = -ln(1/x²) - π²/6
(1-x²/π²)(1-x²/(4π²))(1-x²/(9π²))⋯ = e^(-ln(1/x²) - π²/6) = x² e^(-π²/6) / (1-x²/π²)
(-1/π²) (1-x²/π²)(1-x²/(4π²))(1-x²/(9π²))⋯ = (-1/π²) (x² e^(-π²/6) / (1-x²/π²)) = e^(-π²/6) (x² / π²) ∑ (1/n²)
(1-x²/π²)(1-x²/(4π²))(1-x²/(9π²))⋯ = (-1/π²) π²/6 = -1/6$
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$ln[(1-x²/π²)(1-x²/(4π²))(1-x²/(9π²))⋯] = -ln(1/x²) - π²/6
(1-x²/π²)(1-x²/(4π²))...
flat frigateBOT
Caffu
leaden cypress
Just trying to see something
$ln[(1-x²/π²)(1-x²/(4π²))(1-x²/(9π²))⋯] = -ln(1/x²) - π²/6$
flat frigateBOT
Caffu
leaden cypress
$(1-x²/π²)(1-x²/(4π²))(1-x²/(9π²))⋯ = e^(-ln(1/x²) - π²/6) = x² e^(-π²/6) / (1-x²/π²)$
flat frigateBOT
Caffu
leaden cypress
$(-1/π²) (1-x²/π²)(1-x²/(4π²))(1-x²/(9π²))⋯ = (-1/π²) (x² e^(-π²/6) / (1-x²/π²)) = e^(-π²/6) (x² / π²) ∑ (1/n²)$
flat frigateBOT
Caffu
leaden cypress
$(1-x²/π²)(1-x²/(4π²))(1-x²/(9π²))⋯ = (-1/π²) π²/6 = -1/6$
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small breach
Hello!!!
small breach
I have this problem that I can't seem to solve
A simple assignment with me needing to find how to explain why the triangles are similar and to find x
split ether
Q17?
small breach
Yep
Here's my first solution(sry for the handwriting)
But then after, i need to find x
split ether
Mirrors reflect with the same angle, kinda hard to explain but basically the angles ABT and SBG are equal (B being the point on the mirror)
small breach
Yep yep
They're the same angle and so is angles TAB and GSB
Since theyre right angles
split ether
Yeah there seems to be info missing
small breach
No answer for x then?
split ether
Yeah
undone umbra
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raw garden
Try computing the integral, think that equation gets you what you need to show
proven stag
I am a tad lost on how i am incorrect, I am trying to find the volume of the like y=2x-x^2 rotated around the x axis and bounded by y = 1 and x = 1
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I am a tad lost on how i am incorrect, I am trying to find the volume of the lik...
pallid nymph
I know that a continuous function need not map closed to closed. I wonder about the converse: let f be a function that maps arbitrary closed set to closed sets; must f be continuous?
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I know that a continuous function need not map closed to closed. I wonder about ...
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crimson jewel
B is 25% less than C. what does that mean?
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B is 25% less than C. what does that mean?
quasi bison
0.75C = B ?
this
final halo
Maybe enlightening to view B as C - 0.25C highlighting the 25% less
crimson jewel
so answer is 0.75C =B ?
before I close this channel, someone tell me I can't chat in general lounge. I don't see the box where you type message instead it guides me to diff channel
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inner lintel
"Per Cent" means "of one hundred". You have 25 less of a full hundred. 100/100C - 25/100C = 75/100C = B.
crimson jewel
"Per Cent" means "of one hundred". You have 25 less of a full hundred. 100/100...
thanks
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inner lintel
B = 0.75C in it's reduced form (0.75 over 1) is correct. Your welcome.
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B = 0.75C in it's reduced form (0.75 over 1) is correct. Your welcome.
@inner lintel Has your question been resolved?
fiery olive
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fiery olive
I see the multiple choice answers and could get it right with enough guesses, but how would I get one of these answers without the multiple choice available?
Like what’s the method to decide which expression to try the limit comparison test with?
rough gazelle
the method to decide is mostly intuition based
it's the reason practicing the method is important
once you do it enough, you'll be able to figure it out
fiery olive
Damn that’s rough ok
rough gazelle
it isn't actually that bad
it should make intuitive sense which ones work and which comparisons don't
fiery olive
the ln vs n or 2^n connection is very unintuitive for me
Maybe it’ll help if I can find practice problems without potential answers
rough gazelle
that's because it's probably not right
rough gazelle
the comparison between ln and 2^n makes no sense because it doesn't work
rough gazelle
but the comparison to 1/n makes sense because it's harmonic
if you really struggle with it, harmonic is one of the easiest ways to tell
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wintry radish
Find the possible values of q if the constant terms in the expansions of (x^3+q/x^3)^8 and (x^3+q/x^3)^4 are equal
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Find the possible values of q if the constant terms in the expansions of (x^3+q/...
wintry radish
<@&286206848099549185>
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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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
use the binomial expansion
lean otter
constant in this context means the term with no x
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spiral topaz
Hi, can someone help understand how this simplification was achieved?
mortal sandal
Plugging in values for r and h I would assume
though I don't see any values they're probably part of the problem
spiral topaz
You kind person, is absolutely correct
compact ferry
woops
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mortal sandal
no prob
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heavy glade
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mortal sandal
domain is the set of points on which the function is defined
it's the set of inputs it can take
granite idol
why did you give the answer that you gave? you must have some idea how to answer it, right?
heavy glade
why did you give the answer that you gave? you must have some idea how to answer...
because the bottom part cannot be zero
granite idol
yes, look at what your teacher circled
granite idol
while x^2 + y^2 > 0 is true (well, it can equal 0 as well), that is not correct for the domain
what is the domain of y = 1/x
mortal sandal
I mean ig it works right
heavy glade
what is the domain of y = 1/x
all real number but 0
heavy glade
while x^2 + y^2 > 0 is true (well, it can equal 0 as well), that is not correct ...
i know
isnt the domain all in input it can be
if its zero
its undefined
granite idol
all real number but 0
yes, so for that the domain is $x \neq 0$
flat frigateBOT
cwatson
heavy glade
yes, so for that the domain is $x \neq 0$
why does that not apply to y?
heavy glade
so {(x,y)|x^2+y^2>0} is the domain
but dat what i said and he said i wrong 😦
my friend said this and it was right
but ours means the same thing no?
granite idol
I assume your teach wanted you to use the not equals to sign
i think they are the same in this case
mortal sandal
I assume your teach wanted you to use the not equals to sign
eh that's dumb though if it's true
granite idol
I agree, I'd argue for those points back
mortal sandal
yeah
heavy glade
Sorry guys one more question
safe radishBOT
Sorry guys one more question
granite idol
I guess it looks right, but yea why did you change x and y to H and I
heavy glade
I wanted to say HI
i dont think i should argue this
my techer might get angry adn grade me harsher
ty tho
.close
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obtuse plover
<@&268886789983436800> said the n word but it got insta filtered
crystal fulcrum
use series to approximate the definite integral with an error of magnitude less than 10^(-5)
0.5
∫sqrt(1+x^9)
0
I just started this in class and I still dont completely get it
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use series to approximate the definite integral with an error of magnitude less ...
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prisma acorn
use series to approximate the definite integral with an error of magnitude less ...
just a question is the error supposed to be less than 10^-5 or 0.5
and was there any other info on what series you are supposed to use?
crystal fulcrum
Ill send a pic of the problem
prisma acorn
ok
crystal fulcrum
yes
prisma acorn
ok
Ok IDK what series they want you to use
So I am gonna assume it is a tailor series
Do you know how to make one for this series?
crystal fulcrum
no i do not
prisma acorn
Do you know what they are?
crystal fulcrum
yes i kind of know what series are
crystal fulcrum
yes!
prisma acorn
Cool
crystal fulcrum
I totally forgot about that formula thing
prisma acorn
Ok
so the basic idea is to
make a taylor series or whatever
and prove that you only need a certain amount of terms
crystal fulcrum
yeah a taylor series
prisma acorn
so that the error is less than 10^-5
then you can use the series to find the integral approximetly
I can't spell sorry
crystal fulcrum
its fine, i cant ether
prisma acorn
Ok so try doing this and see if you can figure it out
crystal fulcrum
how would i get it into the formula?
prisma acorn
Ok
prisma acorn
you can use a=0 to make your life easier
sqrt(1+x^9) first find the taylor series of this function
to find the first term
plug in 0
sqrt(1+0^9)=1
crystal fulcrum
oh,
crystal fulcrum
ok
crystal fulcrum
no i dont
prisma acorn
ok never mind then
(1+y)^n = 1 + n*y + (n(n-1)/2!)y^2 + (n(n-1)(n-2)/3!)y^3 + ...
have you seen anything like this?
crystal fulcrum
yes i have
crystal fulcrum
ok it would be (1+x^9)^1/2?
prisma acorn
ok it would be (1+x^9)^1/2?
yes
crystal fulcrum
so is where i would plug them in?
prisma acorn
1 + n*y + (n(n-1)/2!)y^2 + (n(n-1)(n-2)/3!)y^3 + ... whever there is a n you can plug in 1/2 to get
crystal fulcrum
okay i see now
prisma acorn
1 + 1/2(y) + (1/2(1/2-1)/2!)y^2 + (1/2(1/2-1)(1/2-2)/3!)y^3 + ...
and you can do the same for y
that math is a bit tedious
prisma acorn
i can simplify it, its just the part of me getting there
could you elaborate
?
is the difficulty in plugging in the formula or understanding where it came from
or anything else
crystal fulcrum
I just dont understand series at all
prisma acorn
Do you know veratasium?
crystal fulcrum
no
prisma acorn
he made a great video explaning the series
crystal fulcrum
is he the one with a blue V
crystal fulcrum
Thanks
prisma acorn
go
to the 5:20
mark that is the explanation of the series
but honestly in my oponion the whole video is amazing
it gives the reason behind why it is all done
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next trout
Is this proof correct?
F2 = {(x, y) ∈ R^2, x^2 = y^2}
To show that F2 is a vector subspace of R^2, we must verify that:
The null vector (0,0) belongs to F2.
F2 is closed under addition.
F2 is closed under multiplication by a scalar.
The null vector (0,0) belongs to F2 because 0^2 = 0 and therefore (0,0) is a solution of the equation x^2 = y^2.
Let (a,b) and (c,d) be two vectors of F2. We must show that their sum (a+c, b+d) belongs to F2, that is to say that (a+c)^2 = (b+d)^2. Expanding this expression, we get:
(a+c)^2 - (b+d)^2 = a^2 + 2ac + c^2 - b^2 - 2bd - d^2
= (a^2 - b^2) + 2ac - 2bd + (c^2 - d^2)
Since (a,b) and (c,d) belong to F2, we have a^2 = b^2 and c^2 = d^2. Therefore, (a+c)^2 - (b+d)^2 = 0, which shows that (a+c, b+d) belongs to F2. So F2 is closed under addition.
Let k be a scalar and (a,b) a vector of F2. We must show that k(a,b) = (ka,kb) belongs to F2, that is to say that (ka)^2 = (kb)^2. This condition is clearly satisfied because (ka)^2 = k^2(a^2) = k^2(b^2) = (kb)^2. So F2 is closed under multiplication by a scalar.
As the three conditions are satisfied, we can conclude that F2 is a vector subspace of R^2.
safe radishBOT
Is this proof correct?
F2 = {(x, y) ∈ R^2, x^2 = y^2}
To show that F2 is a vec...
@next trout Has your question been resolved?
vast obsidian
Is this proof correct?
F2 = {(x, y) ∈ R^2, x^2 = y^2}
To show that F2 is a vec...
For the closed under addition thingy you stated this is 0. But it is still unclear for me why this has to be true as there is 2ac -2bd remaining. Do you know for sure it is a supspace, because (1,-1) + (4,4) looks like a counterexample
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