Wait so the derivative is the red ones or the blue
#help-17
elfin fiber
tidal mesa
Woops have it backwards, its graph to derivatives. Derivatives in red
I might be able to do it now, I had my understanding backwards
elfin fiber
Ah okok if you need help you can @ me and I’ll try my best to
tidal mesa
No, please help, thought I had it and immediately got lost
elfin fiber
Ah okok
So if you have a linear function it’ll be y=x right
So what would the derivative be of y=x
tidal mesa
The derivative would also be linear, right? I know the derivative of a constant is infinity
elfin fiber
So that’s not true though
The derivative of a constant is 0
But it wouldn’t be linear actually
So the derivative x^2 is 2x because of the power rule right
tidal mesa
Yes
elfin fiber
So then what would the derivative of 2x be
tidal mesa
2
elfin fiber
Not quite it would be 2
So you can use the power rule to see it
So 2x^1
That’s the same as 2x
tidal mesa
I got it, said 1 because x^0 forgot to multiply it by the 2
elfin fiber
Ah okok
So that means it would be a constant
So if you get the derivative of a linear function such as Y=x would be a constant
tidal mesa
Oh, so B would match to I, right?
elfin fiber
Yes
Because the derivative of y=5x would be y’=5 so just y would be 5 for all of x
Do you get that part?
tidal mesa
Yes, the power rule ensures that all derivates of x^1 will be a constant
elfin fiber
Exactly so when you graph it it’ll be a constant as well
Okay so let’s move on to the parabola one
A parabola is a y=x^2 function right
tidal mesa
Yes, so the derivative would be linear instead of constant
elfin fiber
Exactly
tidal mesa
I get it now
elfin fiber
And if it’s a cubic function then the derivative would be a x^2 type function
tidal mesa
C belongs to II as its degree is greater than 2, and A and D belong to III
elfin fiber
Sii
tidal mesa
Thank you! I have a lot of trouble relating between evaluating equations and translating that to graphs
This has made it much clearer!
elfin fiber
Ah I’m glad I could help
stuck mesa
Hello everybody, my name is Max and I kind of fucked up. I have a NY Geometry regents at 8:30 am tomorrow and I have been slacking off in class around about all year, can someone please help me get the basic knowledge to secure atleast a 65 on this test? Your help would be greatly appreciated.
vocal sleetBOT
Hello everybody, my name is Max and I kind of fucked up. I have a NY Geometry re...
outer warren
try khan academy
stuck mesa
https://tenor.com/view/flightreacts-school-math-gif-10331778363403279731
this might be me ‼️
hybrid flicker
Jesse I need you to cook math outside <@&268886789983436800>
inner osprey
by asking the <@&268886789983436800>
vocal sleetBOT
@stuck mesa Has your question been resolved?
stuck mesa
no bro
outer warren
you need to post specific problems you're stuck with
outer warren
try khan academy
and
vocal sleetBOT
@stuck mesa Has your question been resolved?
sudden compass
vocal sleetBOT
sudden compass
Any ideas on evaluating either one of these integrals?
Came across them while trying to evaluate another integral using Feynman (hence the alpha)
mellow oyster
out of curiosity what was the original integral?
half imp
x=cos(u) maybe idk
mellow oyster
trig sub is definitely the move here
vocal sleetBOT
@sudden compass Has your question been resolved?
sudden compass
trig sub is definitely the move here
Can't find a suitable one tho
sudden compass
~~x=cos(u) maybe idk~~
Nope doesn't work
mellow oyster
out of curiosity what was the original integral?
^
sudden compass
out of curiosity what was the original integral?
Uhh its integral from 0 to 1 of x sin^(-1)(x)/(1+x^2)
sudden compass
U parameterize inverse sine function (sin^-1 ax), differentiate, do some substitutions, it becomes this - same integral but with (sqrt(1-a^2)/sqrt(1+a^2)) inside the arctan
sudden compass
<@&286206848099549185>
vocal sleetBOT
@sudden compass Has your question been resolved?
grand void
Is ChatGPT 4 making this too complicated or is there something that is not easy to explain about applying chain rule to e^cos(x)?
vocal sleetBOT
Is ChatGPT 4 making this too complicated or is there something that is not easy ...
grand void
I am expecting there is just two values for g(x) and f(x), I'm not sure why it throws s(t) into the mix
scenic ravine
!nogpt
vocal sleetBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
grand void
!nogpt
Sure, do you know what is going to be f(x) and what is going to be g(x) for the derivative applying chain rule to e^cos(x)?
scenic ravine
it's $exp(cos(x))$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
scenic ravine
so what is f(x) according to you?
if f(x)=e^x
you are finding the derivative of $f(cos(x))$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
scenic ravine
were cos(x)=g(x)
brisk moss
I am expecting there is just two values for g(x) and f(x), I'm not sure why it t...
because chatgpt often says things that are silly or wrong when you ask it math
grand void
if f(x)=e^x
So it’s f(x) is going to equal e^x and then g(x) is whatever is in the exponential place of e?
vocal sleetBOT
Available help channel!
undone ravine
Yes
robust tide
cos(h)/h, where h tends to 0
vocal sleetBOT
cos(h)/h, where h tends to 0
robust tide
what will be the value of this?
peak matrix
that's undefined
yep
and not indeterminate
it's not 0 / 0, it's not infinity / infinity
so the limit DNE
(Can infinity / -infinity be result of the limit?)
robust tide
so the limit DNE
DNE?
peak matrix
doesnt exist
peak matrix
what happens when it is 0/0
you need to further manipulate it
robust tide
smth called l'hospitals or sth right
peak matrix
and examine if it's DNE, 1, 0, pi or smth else
peak matrix
smth called l'hospitals or sth right
thats one of the options
but its better to avoid it
robust tide
otherwise?
peak matrix
if you can
robust tide
can you explain?
peak matrix
otherwise?
whatever is convenient
e.g. if the limit was x / x, we can just cancel the x's and get 1
which is the result of the limit as x -> 0
robust tide
yeahh
peak matrix
yeah
robust tide
okay and if it is (x+1)/x
peak matrix
plug in
robust tide
then it is also 1?
peak matrix
wait x tends to infinity?
robust tide
yeah
peak matrix
and if x tends to 0(+), 1 + 1/x tends to infinity?
yep
peak matrix
if its from right side then it tends to + infinity
from left side itd tend to -infinity
peak matrix
cos(h)/h, where h tends to 0
and here, its the same btw
robust tide
yeah....
peak matrix
from right side its + infinity, left side - infinity
peak matrix
doesnt it become 1/0?
1/0 doesnt even have a definite answer
it can be -infinity, infinity, or it can be "both" meaning it doesnt exist
subtle summit
the limit is +infinity from the right and -infinity from the left, so it's not a single value and doesn't exist
peak matrix
This is 1/x, from right side it's + infinity, from left side it's -infinity
the limit cant have 2 values, so it doesnt exist
robust tide
i seeeee
peak matrix
But if its something like 1/x^2, then it's + infinity from both sides and so the general limit is just +infinity
vocal sleetBOT
vocal sleetBOT
Available help channel!
grim bluff
e^sin^2x
grim bluff
What is the value?
outer warren
of?
grim bluff
The differention of the thing above
jade anvil
You want the derivative?
jade anvil
What have you tried till now?
jade anvil
Can you send that working?
jade anvil
Try solving it and send your working
potent timber
This what you mean? If so I can help you with it
Differentiation of exponential function is quite easy once you know the trick
@grim bluff
potent timber
Okay well ln() is not really needed, it is just important that you understand that if i have a base raised to the power x. like in this pic:
Then the derivative is this function times the ln(2)
potent timber
Now here we have hidden a little extra trick which is that we did just use the chain rule. Because in the exponent is a function. Here we secretly multiplied by 1 because x->1
grim bluff
Oh ok
potent timber
If we first apply this logic to your function the start should look something like this:
But ln(e)=1 because it like saying, if i raise 2 to a power of, what, then my answer is 2. Of course then the power is 1.
So we leave that out. Now we multiply by the derivative of what is in the power itself because we are dealing with a function inside a function
potent timber
Well ln() is just an operator. So if i say ln(2) it will just spit out an ugly number
its not a function like ln(x) which is because of the x
potent timber
If we first apply this logic to your function the start should look something li...
So what we have here is the first step by multiplying the whole equation by the base inside the ln() which in this case is 1 because ln(e)=1
The second step is to take the derivative of what is in the exponent, sin^2(x). You know how to solve this?
potent timber
Power are really just based on this one rule here:
grim bluff
Wait I need to check something
potent timber
Alright
grim bluff
Wait I'm sorry I have to leave can you send the rest of the answer to I can check it later
Please and thank you
Bye!
vocal sleetBOT
@grim bluff Has your question been resolved?
vocal sleetBOT
full grotto
hi could someone help me solve this
vocal sleetBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
frozen bobcat
he got a common denominator and combined fractions
$\frac{-c}{a} + \frac{b^2}{4a^2} = \frac{-c(4a)}{a(4a)}+\frac{b^2}{4a^2}$\
$=\frac{-4ac}{4a^2}+\frac{b^2}{4a^2} = \frac{b^2-4ac}{4a^2}$
twin meteorBOT
Zybikron
frozen bobcat
nope, he's not multiplying the whole right side by something. Just the one fraction to get a common denominator
he's multiplied a fraction by 4a/4a = 1
jade anvil
which part are you not clear about specifically, if you could reiterate your question?
he did not divide by 2a
frozen bobcat
$\sqrt{4a^2} = 2a$, so he simplified the bottom of the radical, then combined fractions
twin meteorBOT
Zybikron
vocal sleetBOT
honest violet
I was doing a problem on khan academy where the perfect square polynomial, "(x+3)^2+14(x+3)+49" simplified to "(x+3+7)^2". When I checked if (x+10)^2 was equal to the original equation it was equal to "x^2+20x+100" instead of "x^2+14x+100". Why is this so and why is the answer correct?
vocal sleetBOT
I was doing a problem on khan academy where the perfect square polynomial, "(x+3...
honest violet
huh? lemme see. (x+10)^2 = x^2+(2)(10)x+10^2 = x^2+20x+100 thats the same thing?
graceful surge
honest violet
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
somber salmon
Why is the constant of integration negative
vocal sleetBOT
Why is the constant of integration negative
inner osprey
typo probably
- C and - C are technically both correct but by convention it's typically written as + C
vocal sleetBOT
@somber salmon Has your question been resolved?
somber salmon
+ C and - C are technically both correct but by convention it's typically writte...
thank you
lavish geyser
Hi
twin horizon
what is the derrivate of x^2
2x¹
twin horizon
can you elaborate how?
Power rule
twin horizon
🫤
twin horizon
Now .close please
twin horizon
derivative of x^n is nx^(n-1), n is 2
You type fast though
lavish geyser
wait
mellow oyster
do you genuinely not understand why the derivative of x^2 is 2x and not 2?
lavish geyser
'
mellow oyster
x^2 does not have constant slope, if you got that the derivative of x^2 was 2 then you'd expect the rate of change of x^2 to be the same everywhere which isn't true
..
mellow oyster
once you bring the 2 down and subtract 1, it's not still being operated on by d/dx
you also can't treat that operator like multiplication or a fraction 😭
lavish geyser
alr
twin horizon
you also can't treat that operator like multiplication or a fraction 😭
Emotional math fr
lavish geyser
you also can't treat that operator like multiplication or a fraction 😭
love you too ❤️
hahah
!close
mellow oyster
.close
lethal mesa
how can I show that $\displaystyle \lim\limits_{n \rightarrow +\infty} \frac{\left\lfloor (n+1)^a \right\rfloor - \left\lfloor n^a \right\rfloor }{(n+1)^a - n^a} = 1$ where $a > 1$ ?
vocal sleetBOT
how can I show that $\displaystyle \lim\limits_{n \rightarrow +\infty} \frac{\le...
twin meteorBOT
Groudon
twin horizon
Oh ok
rough patrol
so we first need to bound the difference in floors with the original difference
rough patrol
Simplify then divide top and bottom
well more clearly the numerator is greater than or equal to (n+1)^a-n^a-1
twin horizon
so we first need to bound the difference in floors with the original difference
Lol. Nice bio
rough patrol
and we reduce this to showing that (n+1)^a-n^a goes to infinity
rough patrol
Lol. Nice bio
lol
twin horizon
Wait i just saw floor
rough patrol
and then (n+1)^a-n^a is greater than n^(a-1)
and as n goes to infinity n^(a-1) must also go to infinity
since a>1, a-1>0
so n^(a-1) will go to infinity
twin horizon
so n^(a-1) will go to infinity
What then is floor of ∞
rough patrol
What then is floor of ∞
well more specifically, the limit as x goes to infinity of (x-1)/x is 1
and we define x as (n+1)^a-n^a
so first we show as n goes to infinity so does x
twin horizon
Ooh
rough patrol
and then we show that floor((n+1)^a)-floor(n^a)>=x-1
vocal sleetBOT
@lethal mesa Has your question been resolved?
lethal mesa
and then we show that floor((n+1)^a)-floor(n^a)>=x-1
To show that the original limit goes to 1 shouldn't you bound it above by something that goes to 1 as well ?
rough patrol
To show that the original limit goes to 1 shouldn't you bound it above by someth...
oh yes
rough patrol
oh wait nvm
lethal mesa
I believe
rough patrol
you can bound above by floor((n+1)^a)-floor(n^a)+1
yes
candid grove
Determine the curves represented by the following complex functions of a real variable
latex not cooperating
I dont need anyone to do all of this
Just nudge me in the ritght direction,
Idk where to start
vocal sleetBOT
Determine the curves represented by the following complex functions of a real va...
candid grove
.close
vocal sleetBOT
candid grove
.reopen
vocal sleetBOT
✅
candid grove
rough patrol
um which one do you want to start with
candid grove
Let's start with point a
rough patrol
ok
so think of this in the complex plane
our imaginary part is the y-axis
and our real part is the x=axis
so for example, part (a) will be z_1(t)=(t,cos(t))
so this is just a cosine wave
from 0 to 3pi
the next one, would be z_2(t)=(1/t,t)
rough patrol
why is it just cos and no sin(t) - e^xedfgsfg or some other thing
?
we are just taking the imaginary component which just happens to be cosine
nothing related to e on this page
candid grove
that was just a dumb exaggeration, sorry
ok but I think im getting there
we are lineary getting thou x
the horizontal axis
and i alternates between i and -i
as a cos sign
so if i can create a scenario when
(t, f(t))
my anwser will be just f right?
rough patrol
yep
candid grove
ok let me try the second one
rough patrol
although
be careful on the domain of t
usually when we answer "f", we are assuming the domain is -infinity to inifnity
however, this is not always the Case
try drawing it out at points if you need
rough patrol
(1/t, t) will be the second one
yes but specify the domain
rough patrol
can I do like u = 1/t and substitute?
um yes.
you get (u,1/u)
i would write this as xy=1 instead but same thing.
however, the domain isn't over everything. we have that t goes between 1/2 and 3.
rough patrol
and the anwser would be 1/x?
thats only part of the answer
you need to specify the domain
candid grove
ok ok
rough patrol
we are given that 1/2<t<3 in the problem
so since x=1/t, we have that 1/3<x<2 in this case.
therefore, our answer would be, the graph of 1/x, when 1/3<=x<=2
rough patrol
You substituted t with 1/x and fliped the whole thing right?
yes
candid grove
ok, I think im getting there
Is the more to it? Any edge cases or some hard example in those that I provided?
rough patrol
Is the more to it? Any edge cases or some hard example in those that I provided?
no thats really it. for parts a through d
candid grove
Ok
Thanks so much king ❤️
And btw, Your "about me" made me chukke xd
Thanks again, closeing this now
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
HALP
vocal sleetBOT
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
bright patrol
??
vast shale
im stuck on figuring out how to do this
like should i multiply 37x2
since its doubled
bright patrol
no
bright patrol
no like look at the numbers for both
bright patrol
yea
vast shale
bright patrol
so what would the answer be??
vast shale
37
bright patrol
yes
vast shale
bright patrol
correct
bright patrol
yw😭
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
i cant see the triangle degreees cuz too pixilated
vocal sleetBOT
@vast shale Has your question been resolved?
bright patrol
@vast shale close the channel
spiral turtle
Why?
livid helm
how do you determine domain for this quesiton?
vocal sleetBOT
how do you determine domain for this quesiton?
vast shale
You mean the domain of x?
I mean every side has to have a positive length so we know x>0, 100-2x>0, 40-2x>0
Which gives 50>x>0
@livid helm
vast shale
Because you also have to consider the 100-2x>0
vocal sleetBOT
@livid helm Has your question been resolved?
arctic thorn
.close
vocal sleetBOT
Available help channel!
vast shale
how do i solve this?
vocal sleetBOT
how do i solve this?
vast shale
why is it 1?
cause a square means bounce
for a to be positive the bounce has to be on the positive side of x?
inner osprey
for a to be positive the bounce has to be on the positive side of x?
if a is positive, that means there's a root at -a, so the negative side of x
(because in (x + a)^2 when to get 0 you plug in x = -a)
vast shale
wait so if the graph is (x-2)^2(x+2)
on the x axis is it bounce at 2 and regular at -2?
vast shale
(because in (x + a)^2 when to get 0 you plug in x = -a)
if theres (x+a) in an equation without the square then is it -a or a thats on the intersect?
inner osprey
which one do you plug in to get 0?
vocal sleetBOT
@vast shale Has your question been resolved?
waxen hawk
waxen hawk
Shut up bot
waxen hawk
Why the period is 7pi
I’m the attorney who claims that the 7pi, the accused, is innocent. it has nothing to do with the period.
You guys are the opposition
Now send your argument!
lucid bane
why would it not be?
waxen hawk
why would it not be?
By the only information that the maximum points occur in (7pi/4, 5), the period cannot be determined.
lucid bane
no
you are also given where the function intersects its own midline
these points
but only one of them
which is all you need
waxen hawk
Consider that, from the span of x=0 to 7pi/4, the length could include (n+0.25) of period, where n is a natural number
Your statement is flawed, because you have unconsciously assumed n=1, which is not necessarily the case.
Can someone plays the judge
waxen hawk
Is there anything you want to add, Mr. Deer
lucid bane
you are correct in that there are multiple sine functions that satisfy these conditions
but the one with the biggest period, is this one
waxen hawk
but the one with the biggest period, is this one
“The biggest period” is not mentioned in the question.
lucid bane
it isnot
waxen hawk
That means the period cannot be determined by the information provided in the question
Do you agree, Mr. Deer
lucid bane
the period of the function they were trying to find was 7pi
the question itself was not asking about period
it was simply asking for a sin function that has the required properties
which there are multiple
waxen hawk
Your words just contradicted to the statement you had just made that there are multitudes of sine function satisfy these conditions.
lucid bane
one of which has period 7pi
???
no
there are sometimes multiple right answers
they simply chose to go with showing one of the possible (most simple) answers
waxen hawk
there are sometimes multiple right answers
But there’s only one written on the answer column.
waxen hawk
they simply chose to go with showing one of the possible (most simple) answers
How do you define the “most simple” and how do you know it is the most simple one that should be put into the answer sheet
lucid bane
the period for this answer need not be 7pi
waxen hawk
the period for this answer need not be 7pi
I agree.
waxen hawk
the period for this answer need not be 7pi
Then, do you agree that the period cannot be determined
lucid bane
How do you define the “most simple” and how do you know it is the most simple on...
a good given is that when you plug in for the maximum, sin is at is maximum value within an interval of (0,2pi) given no phase shift
i.e. for this b=2/7 and 2/7(7pi/4)=pi/2 and sin(pi/2)=1 which is its maximum value
for another period that works, say 1.4pi
b=10/7
waxen hawk
a good given is that when you plug in for the maximum, sin is at is maximum valu...
“Given no phase shift,” Mr.deer, Are you making some assumptions out of thin air?
lucid bane
10/7(7pi/4)=5pi/2
lucid bane
“Given no phase shift,” Mr.deer, Are you making some assumptions out of thin air...
even with phase shift this is a good rule of thumb
waxen hawk
“Given no phase shift,” Mr.deer, Are you making some assumptions out of thin air...
That should not be deemed as a definitive evidence.
lucid bane
you can probably look at the comments and find some similar questions. or post a comment on this particular problem and ask about it, email. :3
vocal sleetBOT
@waxen hawk Has your question been resolved?
frail dew
How??
frail dew
I do not understand how they got those new bounds of integration
vocal sleetBOT
@frail dew Has your question been resolved?
gaunt sparrow
The original bounds of integration are $0 \le y \le \sqrt{16-x^2}$, and $0 \le x \le 4$.
What does this look like?
twin meteorBOT
Azyrashacorki
gaunt sparrow
Yeah so it's definitely circular. y is from 0 though, so we're restricted to the upper half of the disk
And moreover, x is from 0, so we're restricted to the first quarter of the disk
Does that make sense?
frail dew
yes
gaunt sparrow
So the first quarter is delimited by angles 0 and pi/2
frail dew
that makes a lot of sense
i never really considered integration bounds as actual bounds for some reason :/ thank you
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
sacred turret
My question was, if Pi is an irrational number with an infinite number of decimal places which are not recurring. Then how can it be represented as the quotient on dividing the the length of the circumference by the length of the diameter (which in the form of a rational number; p/q : p=/= 0)?
Wouldn't that make Pi rational??
vocal sleetBOT
My question was, if Pi is an irrational number with an infinite number of decima...
half imp
p/q is only defined as rational if p and q are integers
viral copper
Recall that the definition of a rational number requires that BOTH p and q be integers
half imp
the circumference and the diameter can't both be integers
true grail
My question was, if Pi is an irrational number with an infinite number of decima...
no, because the radius being an integer precludes the circumference being one, and vice-versa
heady musk
`Im new to math and i tried to do an equation of adding fractions with different denominators and i got a weird result.
Its 4/6+1/2=14/12
And i calculated it by multiplying the denominators: 62=12
and cross multiplying the numerators with the denominators: 42=8 and 1*6=6, and then added them together. 8+6=14
Is this a correct method to solve the equation? 14/12 seems incorrect.
If it is incorrect, please do tell me whats the correct method of adding fractions with different denominators.`
vocal sleetBOT
`Im new to math and i tried to do an equation of adding fractions with different...
glacial osprey
Welcome to the wonderful world of math
half imp
any time you put more than 1 * in a message discord will remove them and italicize your text instead
you can precede the star with a backslash like this: \* to get around that
heady musk
Ah i didnt notice..
half imp
`Im new to math and i tried to do an equation of adding fractions with different denominators and i got a weird result.
Its 4/6+1/2=14/12
And i calculated it by multiplying the denominators: 62=12
and cross multiplying the numerators with the denominators: 42=8 and 1*6=6, and then added them together. 8+6=14
Is this a correct method to solve the equation? 14/12 seems incorrect.
If it is incorrect, please do tell me whats the correct method of adding fractions with different denominators.`
or just use ` on each side of a message to put it in code mode like this, that'll work too
half imp
14/12 is correct but it can be simplified further
heady musk
`Im new to math and i tried to do an equation of adding fractions with different...
Thank you
half imp
np
glacial osprey
well 14/12 is correct but it could be simplified
heady musk
14/12 is correct but it can be simplified further
But i dont understand how its correct, 14 fractions out of 12?
half imp
But i dont understand how its correct, 14 fractions out of 12?
yeah 14 parts out of 12
it's like if there are 12 slices in a pizza and you have 14 slices
you have a whole pizza, plus an extra 2 slices
14/12 of a pizza
heady musk
OHH
Okay that makes sense, so its not ONE shape, its a shape divided into 12 + 2 more slices
heady musk
14/12 is 12/12 + 2/12 correct
Is this how you further simplify the answer?
glacial osprey
nope
but its a representation of what you said
you have 12/12 of a pizza, meaning 1 whole pizza
and 2/12 of a pizza, or 2 slices
heady musk
Okay, i understand now. Thank you both.
half imp
np
glacial osprey
now if you want to simplify it
what number divides both the numerator and denominator
without remainder
heady musk
what number divides both the numerator and denominator
Elaborate please. Im new to this.
heady musk
No.
glacial osprey
do you know what factors are
outer warren
the method is valid, but inefficient
instead of just taking the product of the denominators,
consider their lcm so that you don't need to make numbers larger than needed
heady musk
do you know what factors are
Yes, i do.
heady musk
7 by 2?
glacial osprey
yes
1 and 14 is also a factor technically
so its 1, 2, 7, and 14
now list the factors of 12
heady musk
2, 6, 3, 4
glacial osprey
1 and 12 are also factors
so its
1, 2, 3, 4, 6, and 12
now do you notice any numbers which are the same between the two numbers you factored
1 2 7 14
1 2 3 4 6 12
heady musk
1, 2
heady musk
2
glacial osprey
thats the GCF
of 14 and 12
greatest (largest) common (meaning both numbers have it as a factor) factor
now divide the numerator and denominator by the gcf you found
heady musk
So for numerators
4/2=2
1/2= 0.5
Denominators
6/2=3
2/2=1
glacial osprey
whar
heady musk
What 😭
heady musk
14
heady musk
So the fraction of that entire equation when simplified is 7/6? And unsimplified is 14/12?
glacial osprey
yes
you could actually arrive straight to that
if you simplified 4/6
in 4/6 + 1/2
is there any instructions in what form the fraction should be in?
heady musk
is there any instructions in what form the fraction should be in?
There arent any instructions in the video im watching except for how to calculate it, which is the method i showed above.
glacial osprey
well ok
you can leave it as 7/6
or you can transform it into mixed number / whatever people call it
vocal sleetBOT
inner osprey
as you can infer from that diagram the answer is no
a cylinder is an extended circle, and a parabolic cylinder is an extended parabola
you can't make a circle using two parabolas so the same applies here
manic lance
if i know that i have a collection linear equations that have 3 variables, and the following two solution are true for the system:
(0, 1, 2)
(2, 0, 1)
then how do i know if the solution (1, 1, 1) could be true for that system to?
as in, is there such system?
vocal sleetBOT
if i know that i have a collection linear equations that have 3 variables, and t...
vocal sleetBOT
vocal sleetBOT
Available help channel!
foggy pebble
Hello, first time asking for help here!
I'm a bit confused by higher order differences, as derived by Wikipedia at least, I was looking at various documents but this one is particularly confusing for me (This is the relevant section, second-order central approximation of f''(x)).
Particularly, shouldn't we use h/2 instead of just h as shown by the central difference formula?
vocal sleetBOT
Hello, first time asking for help here!
I'm a bit confused by higher order diffe...
tidal dock
Hello, first time asking for help here!
I'm a bit confused by higher order diffe...
are you talking about this formula?
foggy pebble
I should've clarified my bad, I mean this one:
half imp
are you talking about this formula?
here they get the n/2 part right
foggy pebble
Alright, so the correct second order approximation of the second derivative is just $\frac{f(x+h)-2f(x)+f(x-h)}{h^2}$ right?
twin meteorBOT
Alex.-
twin meteorBOT
thewizardofOU
half imp
are you talking about this formula?
ah here they do
ok yeah
everything is the way it should be then
vocal sleetBOT
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Available help channel!
limpid summit
vocal sleetBOT
limpid summit
im a bit confused on part d
wouldnt there be an infinite number of integer pairs that satisfy that equation in r and s?
it looks like its just asking what x and y pairs satisfy f(x) but theres an infinite number of them
tranquil trellis
wouldnt there be an infinite number of integer pairs that satisfy that equation ...
No
shadow raft
its only asking for integers
tranquil trellis
key is integer
limpid summit
yeah
if you draw the y = k and let k vary theres gonna be so many intesections
oh wait
im dumb
tranquil trellis
if you draw the y = k and let k vary theres gonna be so many intesections
Yeah but not that many will have both x and y be integers
limpid summit
some of those intersections are gonna have decimals in the coordinates
alright i see why i was wrong there
so how would i go about solving the question
tranquil trellis
try polynomial dividing
limpid summit
yep done that
vocal sleetBOT
@limpid summit Has your question been resolved?
bitter pilot
Find the convergence radius of $\sum_{n=0}^{\infty} x^{2^n}$
vocal sleetBOT
Find the convergence radius of $\sum_{n=0}^{\infty} x^{2^n}$
twin meteorBOT
𝔸dωn𝓲²s
tidal dock
**𝔸dωn𝓲²s**
would you be able to solve this if this was x^2n instead?
bitter pilot
geometric series, yes
but it isn't
I tried a substitution
,,\sum_{n=0}^\infty x^{2^n} =\sum_{n=1}^\infty x^{2^n} + x = \sum_{\log_2(u)=1}^\infty x^{u} + x
tidal dock
but it isn't
it's the same logic though
also that is wrong, the first equals sign speicifcally
bitter pilot
also that is wrong, the first equals sign speicifcally
how the sum has infinite terms
wouldnt affect the radius
tidal dock
i mean that's true but the sums are not the same
twin meteorBOT
𝔸dωn𝓲²s
tidal dock
it's the same logic though
for x>1, x^(very big even power) explodes in value
bitter pilot
yea
tidal dock
same thing for x < -1
tidal dock
i know that it is most likely |x| < 1
that's the answer
tidal dock
but how do i show it
hmm
past thicket
does the sequence going to 0 imply the series converges? i thought it was a necessary but insufficient condition
tidal dock
does the sequence going to 0 imply the series converges? i thought it was a nece...
necessary but insufficient, right, but idk how that affects this problem
bitter pilot
yea true lol
rugged orchid
Can you say that x^(2^n) > x^n for every n and every x > 1
tidal dock
**𝔸dωn𝓲²s**
you can also show that \
$\lim_{n\to \infty} x^{2^n}$ has a convergence radius of [-1; 1]
twin meteorBOT
artemetra
tidal dock
and then eliminate -1 and 1 because in those cases the sum doesn't converge
which gives the answer (-1; 1)
brisk moss
the series diverges when x = 1. that implies the radius is at most 1. clearly the series converges if |x| < 1
bitter pilot
the n = 2^n doesnt make sense to me
brisk moss
there, done
bitter pilot
the series diverges when x = 1. that implies the radius is at most 1. clearly th...
that's a statement not a proof
cobalt crypt
this should read [ \limsup_{n \to \infty} \sqrt [n] {\abs {a_n}} ]
twin meteorBOT
tidal dock
the series diverges when x = 1. that implies the radius is at most 1. clearly th...
that "clearly" is working overtime
brisk moss
it’s clear to me
cobalt crypt
wtf
bitter pilot
i know
brisk moss
wtf
bitter pilot
that's why i am here lmao
cobalt crypt
,, a_n = \begin{dcases*} 1 & f"ur $n = 2^k$ \ 0 & sonst \end{dcases*}
hybrid flicker
I think they meant n = 2^k xd
twin meteorBOT
bitter pilot
it's anothet one
rugged orchid
n = n + 1
bitter pilot
I tried something like this
,,\sum_{n=0}^\infty x^{2^n} =\sum_{n=1}^\infty x^{2^n} + x = \sum_{\log_2(u)=1}^\infty x^{u} + x
twin meteorBOT
𝔸dωn𝓲²s
bitter pilot
Let $2^n = u \Rightarrow n = \log_2(u)$
twin meteorBOT
𝔸dωn𝓲²s
brisk moss
you what
cobalt crypt
wtf is happening here
bitter pilot
I just made a substitution
brisk moss
you what
cobalt crypt
holy
brisk moss
unholy
versed bane
h
cobalt crypt
discrete substitutions are unholy
bitter pilot
sorry for trying things, i guess
brisk moss
discrete substitutions into the continuous realm
brisk moss
sorry for trying things, i guess
it’s ok we are sorry for bullying you
rugged orchid
Speak for yourself!
cobalt crypt
i think layla's plan is the best ngl
obviously diverges for x=1
for $x > 0$, you have
[ \sum_{n = 0}^\infty x^{2^n} \le \sum_{n = 0}^\infty x^n ]
twin meteorBOT
cobalt crypt
which converges for x < 1
brisk moss
exactly what i was thinking
rugged orchid
Can you say that x^(2^n) > x^n for every n and every x > 1
Hey that’s nearly what I said
cobalt crypt
i wasnt thinking of that as the justification though
you're just adding in terms
positive ones at that
rugged orchid
Yeah you’re picking only specific ones of the x^n series
bitter pilot
brb need to pick groceries
rugged orchid
So if x^n converges…
placid osprey
the series diverges when x = 1. that implies the radius is at most 1. clearly th...
Is it not inconclusive when = 1?
bitter pilot
guess i can make that trivial argument
brisk moss
you should
bitter pilot
fuck you
brisk moss
my plan is the best according to both me and snow
brisk moss
what
vocal sleetBOT
bitter pilot
my professors solution makes sense now thanks again
bitter pilot
I think they meant n = 2^k xd
!! thanks
vocal sleetBOT
Available help channel!
brittle nebula
vocal sleetBOT
brittle nebula
i did the 2nd bit to get 47 but apparently im dumb
thats what i did
ignore the messy writing ahah
exotic beacon
brittle nebula
wdym?
half imp
I can't understand the reason for doing any of that
and also that is not the inverse tan of 1.076...
vocal sleetBOT
@brittle nebula Has your question been resolved?
brittle nebula
and also that is not the inverse tan of 1.076...
the number was longer
wait ok so
i did 46 squared plus 46 squared then square rooted it to get 46 root 2
twin meteorBOT
brittle nebula
umm
half imp
nvm
You should use a degree symbol though
Anyways you don't need angles here
you have a right triangle right
one leg is 46√2 and the other is 70
brittle nebula
You should use a degree symbol though
sorry i only use degree so normally i dont specify it 😭 mb
brittle nebula
one leg is 46√2 and the other is 70
yeah
half imp
np I was being dumb
half imp
The hypotenuse is the length of the stick that's inside the box right
brittle nebula
yeah
brittle nebula
yeah i did that bit but i cant do part b
brittle nebula
sorry i didnt specify 😭
brittle nebula
Did you try converting it to radians
i dont know waht that means
half imp
Radians are a different way of measuring angles
2π radians is equal to 360 degrees
So
brittle nebula
ooh okay
half imp
,w 47.097 * 2π/360
twin meteorBOT
half imp
^
this would be the answer in radians
The only other thing I can think is that you need more digits of precision
brittle nebula
this would be the answer in radians
it says its wrong
brittle nebula
The only other thing I can think is that you need more digits of precision
yeah no i did it as precise as i couldve
ill just blame the website 💀
half imp
,w 46sqrt(2)
twin meteorBOT
vocal sleetBOT
@brittle nebula Has your question been resolved?
mortal hedge
Hint: the length standing out will be the 99 - the length of the longest diagonal of the cuboid. The angle will be arcsin(the length of the perpendicular from the upper end of the diagonal to the base (basically the edge present at one end or the other of the diagonal)÷length of longest diagonal )
half imp
No worries
mortal hedge
Hint: the length standing out will be the 99 - the length of the longest diagona...
If you didn't get it
half imp
Hint: the length standing out will be the 99 - the length of the longest diagona...
We did that one already
ah the angle
mortal hedge
What lol
half imp
actually maria didnit
did it
Before I got here
a
b neither of us can figure out what's wrong with our answer, she used arctan instead of arcsin but with the appropriate sides
brittle nebula
Hint: the length standing out will be the 99 - the length of the longest diagona...
yeah thats part A i was able to work it out but we dont get part b
mortal hedge
yeah thats part A i was able to work it out but we dont get part b
Hmm ig it should be easy
brittle nebula
b neither of us can figure out what's wrong with our answer, she used arctan ins...
^^
brittle nebula
Come on it's all about taking arctan(70/46√2)??
no its degree
and in degrees the answer is 47
but it says its wrong
brittle nebula
Maybe they want an integer answer, perhaps it should be 48
it rounds down though
let me check 48
says its wrong again
brittle nebula
Type the angle in radians then
says its wrong aswell lol
mortal hedge
My bad, the quiz is drunk, we need rehab right away
Gosh, I gotta sleep
Take care, sis
Oh yeah btw listen to John Legend's "All of Me" if you haven't listened to it
brittle nebula
...
mortal hedge
Because for us the assessments are usually online MCQs
mortal hedge
Because for us the assessments are usually online MCQs
And yeah even if we have numericals they'll try to ensure that all's well
Idk wth is wrong with this one
Or maybe type it all out like arctan(70/46√2)
Idk
mortal hedge
Nah, I didn't do anything with pen and paper so lol I didn't try literally
Leave it
vocal sleetBOT
vocal sleetBOT
Available help channel!
kindred rain
can you help me solve this
vocal sleetBOT
can you help me solve this
shadow raft
!15m
vocal sleetBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
kindred rain
oh okay sorry idk
vocal sleetBOT
@kindred rain Has your question been resolved?
kindred rain
<@&286206848099549185>
alpine vessel
?
kindred rain
hi
im still here
let me know if you know how to do the problem
<@&286206848099549185>
kindred rain
<@&286206848099549185>
viral plover
<@&286206848099549185>
cursive turret
start with a sketch.
vocal sleetBOT
@kindred rain Has your question been resolved?
olive trout
it's been a while since I've taken a math class, why are these the same/how do you get from the first to the second?
$$\ln{y}=2\ln{x}, y=x^2$$
vocal sleetBOT
it's been a while since I've taken a math class, why are these the same/how do y...
twin meteorBOT
PolloTundra | Aidan B
mellow oyster
there is a property that aln(b) is the same thing as ln(b^a)
you can bring powers down from the arguments of logarithms, and vice versa, you can bring coefficients up as powers
so 2lnx is the same as ln(x^2)
olive trout
oh, dang
mellow oyster
and if ln(y) = ln(x^2), you can easily get to the second equation
either by concluding that the arguments have to be the same
or by exponentiating both sides
to cancel the logs
olive trout
just like:
$$(\ln{y})^e = (\ln{x^2})^e$$
twin meteorBOT
PolloTundra | Aidan B
olive trout
or do you exponentiate some other way? it's been a while since I've done logs
flint idol
it’s more so
$$e^{\ln y}=e^{\ln x^2}$$
twin meteorBOT
y0shi
vocal sleetBOT
vocal sleetBOT
Available help channel!
umbral swift
Hello
umbral swift
Need help with limits
hybrid breach
show
umbral swift
yes
hybrid breach
well
umbral swift
i get stuck at derivations
hybrid breach
yep you forgot minus