And now I have to show that $\sum^\infty_{n=1} \frac{1}{(n-x)^2}$ is convergent but I can just use $\sum^\infty_{n=1} \frac{1}{(n-\frac{1}{2})^2}$ as the bound, right?
#help-19
paper cape
clever fjordBOT
Akkaman
fickle silo
yes
paper cape
Because if $x < \frac{1}{2}$ then it is less than it anyway.
clever fjordBOT
Akkaman
paper cape
Thank you so much again. ❤️
thorny kettle
HELPPP
latent scaffold
clever fjordBOT
kisnar
thorny kettle
i'm confused i don't get this stuff 
clever fjordBOT
kisnar
thorny kettle
mhm
clever fjordBOT
kisnar
thorny kettle
**kisnar**
i understand that yeah but like my answer choices don't match that like they made the 4 negative for both choices and i'm not sure why because it's not negative right here
mint mirage
i understand that yeah but like my answer choices don't match that like they mad...
It's to trick you
thorny kettle
in option B the 3 is positive shouldn't it be negative
mint mirage
What exactly are you asking?
thorny kettle
i don't get this 😭😭 sorry if i seem slow
mint mirage
I know
The goal is you use exponent rules to find the equivalent expression to $4^{-3}$
clever fjordBOT
CaptainNova22
mint mirage
**kisnar**
Use this
clever fjordBOT
kisnar
thorny kettle
thanks so when i evaluate 1/4^-3 in part B, how exactly should i do that like what's the rule for that
clever fjordBOT
kisnar
thorny kettle
it says don't put exponents
clever fjordBOT
kisnar
mint mirage
https://www.youtube.com/watch?v=TKj8kEofbAw
See if this video helps out
It's got plenty of examples with negative exponents
clever fjordBOT
kisnar
odd edgeBOT
odd edgeBOT
Available help channel!
hexed pulsar
Simplify
vernal yacht
odd edgeBOT
Simplify
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
rose shard
I was wondering what the proof is for max acceleration in shm being an^2 given an equation in form x=acos(nt+b)
(b is actually alpha or theta but idk how to put that here)
rose shard
(Not sure if this is the right type of channel for that I’ll move if it’s wrong)
upbeat drum
if you have x=acos(nt+b)
what's the equation for acceleration?
rose shard
a=-n^2x or -(n^2)acos(nt+b)
upbeat drum
and -1<=cos<=1 ?
rose shard
OH! Yea that finally clicked-
I found max speed by doing when acceleration =0 completely forgot my trig basics
Thank you so much
.close
odd edgeBOT
odd edgeBOT
Available help channel!
woven pier
In triangle ABC, the perimeter is 64
If AB+BC+(AB×BC)=98 and AC is greater than 30 the find the length of AC.
river brook
In triangle ABC, the perimeter is 64
If AB+BC+(AB×BC)=98 and AC is greater than ...
r u sure there are no typos
river brook
huh cause ac >30
And perim is 64, so the longest a side can be is 64/2
So 30<ac<32
mystic saffron
huh cause ac >30
yeah it should be less then ig
unborn folio
So 30<ac<32
so there literally ain't anything wrong with it?
woven pier
oh yeah]
unborn folio
<30 is possible
river brook
so there literally ain't anything wrong with it?
U right but u don’t rly need any of the info given
mystic saffron
bruh
odd edgeBOT
woven pier
.reopen
mystic saffron
bruh what
woven pier
The area of a triangle is 5. Two of its vertices are (2,1) and (3,2). If the third vertex lies on y = x+3, then the third vertex is/are
odd edgeBOT
✅
mystic saffron
The area of a triangle is 5. Two of its vertices are (2,1) and (3,2). If the thi...
just use the determinant one
woven pier
idk what's that
mystic saffron
let the variable point on the line be x,x+3
so you got all the points
right ?
and you have the area too
i think youre good to go now
mystic saffron
wdym
woven pier
it also implies that the lineas are parallel
mystic saffron
mystic saffron
it also implies that the lineas are parallel
wait lemme see
oh yes
wait its correct
should not matter
woven pier
wdym
mystic saffron
show yer work
woven pier
Aw
Ok
point on y = x+3 will be of the form (a,a+3)
area = a(1-2) + 2(-a-2) + 3(a+2)
disappointed?
wait
mystic saffron
well you have everything to solve the question, yer making some error ig
mystic saffron
mystic saffron
better image
mystic saffron
yeah so ?
woven pier
did you consider it when I calculated the area to be not equal to 5
mystic saffron
that doesnt even matter
there is a random point of red line such that area is 5
what you wanna prove saying that the slope is equal ?
woven pier
the thing is, the area is always 2 sq. units
given base by (2,1) and (3,2) and the third point on y = x+3
mystic saffron
lemme calculate for a sec :v
mystic saffron
point on y = x+3 will be of the form (a,a+3)
area = a(1-2) + 2(-a-2) + 3(a+2)
looks fine to me
so that means there would be no such triangle with area 5
woven pier
therefore the question must be wrong and also the answer given in my book makes up a triangle of area 2
mystic saffron
therefore the question must be wrong and also the answer given in my book makes ...
well, i wonder that how area is independent of what point we choose on our red line
it has to always 2
interesting
i think its cause of lines being parallel ?
not sure
alr bye
woven pier
well, i wonder that how area is independent of what point we choose on our red l...
i mean the perpendicular distance (which is the height here) is the same throughout the graph
the base should be constant
alr alr
bye
.close
odd edgeBOT
mystic saffron
i mean the perpendicular distance (which is the height here) is the same through...
even for a really stretch triangle it would be 2
woven pier
uh yes sir
odd edgeBOT
Available help channel!
winter breach
I’m working on a problem involving changing variables for a function and I’m stuck on some parts. The function is given by:
[
f(x, y) = 3x^2 + 4xy + 3y^2
]
I need to:
- Make a change of variables using ( u = x + y ) and ( v = x - y ), and rewrite the function in terms of ( u ) and ( v ).
- Sketch some of the level curves of the new function.
- Sketch the graph of the function ( f(x, y) ).
- Determine a parametrization of the curve that results from the intersection of the graph of ( f ) and the plane given by ( z = x + 3y ).
clever fjordBOT
dghf
winter breach
The question now is how I can express x and y in terms of u and v
wanton bison
The question now is how I can express x and y in terms of u and v
You can take one equation, like u=x+y and solve for example for y then plug that into the other equation
winter breach
I have x = u-y, and y = x-v
So solving for x using equation for y, I get:
x = u-(x-v) = u - x + v
So 2x = u + v
Then x = (u+v)/2
And for y we get:
y = (u+v)/2 - v
y = (u+v)/2 - 2v/2
= (u - v)/2
@wanton bison is this correct?
wanton bison
looks good
winter breach
So this was part a), right? @wanton bison
I have trouble knowing how the level curve would be sketched.
wanton bison
I have trouble knowing how the level curve would be sketched.
you would have z(u,v) = some constant and then you would solve for one varivle e.g. in the uv plane for v and draw that function then
odd edgeBOT
@winter breach Has your question been resolved?
worldly osprey
odd edgeBOT
tepid pelican
odd edgeBOT
odd edgeBOT
Available help channel!
tall flax
Is it possible to write something like this in latex?
tall flax
clever fjordBOT
thecrumbeler2
vagrant hazel
this works about the same
vagrant hazel
wait
lemme try something
mmmm
wow i am screwing up
alright nvm just use the other one lol
tall flax
Lmao
But yeah thanks, trying to write up a pset but got stuck on how to copy it from my tablet
brittle beacon
(there's also #latex-help here too, btw 
)
odd edgeBOT
@tall flax Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
hollow jewel
Can someone help me with this
odd edgeBOT
Can someone help me with this
pale atlas
Can someone help me with this
Denominator (x+1)² will always be ≥0 at x = -1 f(x) will be infinite
If you increase x value, f(x) value will decrease but will never reach 0
hollow jewel
But i don't know how to put it in my solution 😢
pale atlas
Well you can see f(x) goes from 0 till infinity, but not equal to 0
That's your range of f(x)
hollow jewel
I watch some YouTube videos but idk where I am going now
pale atlas
How to exactly solve it I am not sure , but theoretically you can understand what I said above to find the range of f(x) or y
hollow jewel
Yes, i get it now but idk if my teacher will accept that solution 😢
lunar marten
Hello, I don’t understand what the tantheta > 0 parts tell you about the quadrant. These are a friends notes from a day I missed
green sage
tan > 0 just means that tan is positive, which is only true in 2 quadrants
in the other 2 quadrants, tan is negative
lunar marten
Yeah but like how do you tell which 2 quadrants it is true in
And which of those 2 quadrants
lunar marten
tan > 0 just means that tan is positive, which is only true in 2 quadrants
So you just reverse the sign on the hypotenuse then?
ancient patrol
so sin and cos are the same posi/negativity
late pine
odd edgeBOT
late pine
Literally I don't know where to start
I tried to factorise to (1+x)^-1/2 but GPT doesn't do it
the result has to be 2
I don't understand it
can anyone give me a hand?
idle heart
u can split the fraction first with something like 2(1+x)^(1/2) / (x+1) - x(1+x)^(-1/2) / (x+1)
then consider the denominator as power of 1, just do ur casual exponent division into subtraction
so i think should be 2(x+1)^(-1/2) - x(x+1)^(-3/2)
late pine
Im cooking, but every solution is different:
Symbolab gives me one, GPT other and the book other
idle heart
wait is this question want u to simplify or what?
idle heart
also i dont recommand asking chat GPT without knowing the correct ans, that thing sometime very weird
fervent hawk
also i dont recommand asking chat GPT without knowing the correct ans, that thin...
agreed
late pine
also i dont recommand asking chat GPT without knowing the correct ans, that thin...
I think it confuses more than help, but I don't know where to look when I'm so stuck
well, I come here xd
idle heart
i usually use chat GPT to give me some idea when i am stucking on some que, but i never use it to fully help me
odd edgeBOT
I think it confuses more than help, but I don't know where to look when I'm so s...
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).
fervent hawk
XD
idle heart
the result has to be 2
just 2?
fervent hawk
anyways, @idle heart 's guide is useful for this question
late pine
just 2?
oh lol
i was seeing other section result 😭
this is the result
if thats the solution I got it right
fervent hawk
yea, it's correct
late pine
But I don't know when to do factorisation or start by doing the power rule
how should I know that?
fervent hawk
But I don't know when to do factorisation or start by doing the power rule
you mean when you integrate it?
late pine
I mean: I see that it has the common factor of (x+1)^-1/2
late pine
give me a sec
ill try a thing
yeah, i was seeing
I am not able to factor them at first
or atleast I don't know how
i see that the factor in common is (1+x)^-1/2
but once there, what exponents should I use?
for getting the 1/2 and -1/2 in the right place?
fervent hawk
Let's look at a easier but similar example:
$$a^{\frac{1}{2}}-a^{-\frac{1}{2}}$$
clever fjordBOT
Biscuity
late pine
i don't see how to get to -x(1+x)^-1/2
Right now im on:
$$ ( 1+x)^{\frac{-1}{2}}\left[ 2^{\frac{3}{2}} -x\right] $$
clever fjordBOT
S0S4
idle heart
wdym by exponential use in -x?
late pine
**S0S4**
Im trying to resolve by first factorising, and I'm stuck in here
I dont know what to ^ on -x for getting: -x(1+x)^-1/2
Am I explaining?
idle heart
oh
fervent hawk
hihi
I'm back from typing things.
Let's look at a easier but similar example:
$$a^{\frac{1}{2}}-a^{-\frac{1}{2}}$$
Since you've already known that $a^{-\frac{1}{2}}$ is a factor in common. We can try to see factoring it as:
\begin{align*}&a^{\frac{1}{2}}-a^{-\frac{1}{2}}\=&\left(a^{\frac{1}{2}}-a^{-\frac{1}{2}}\right)\cdot\frac{a^{-\frac{1}{2}}}{a^{-\frac{1}{2}}}\=&a^{-\frac{1}{2}}\left(\frac{a^{\frac{1}{2}}-a^{-\frac{1}{2}}}{a^{-\frac{1}{2}}}\right)\=&a^{-\frac{1}{2}}\left(\frac{a^{\frac{1}{2}}}{a^{-\frac{1}{2}}}-\frac{a^{-\frac{1}{2}}}{a^{-\frac{1}{2}}}\right)\=&a^{-\frac{1}{2}}\left(a^{\frac{1}{2}-\left(-\frac{1}{2}\right)}-1\right)\=&a^{-\frac{1}{2}}\left(a^1-1\right)
\end{align*}
clever fjordBOT
Biscuity
idle heart
actually u dont need to check, cuz when u factoorise, u r like dividing both term with (1+x)^(-1/2), while u can check by subtracting the power, the base has to be same to subtract power
here 2 and x is just a "coefficient" or a mutiple of (1+x)^(whatever)
so they just stay there
2(1+x)^(1/2) - x(1+x)^(-1/2)
so if u divide both term by (1+x)^(-1/2) or u can say factorise (1+x)^(-1/2) from both term, the 2(1+x)^(1/2) actually become 2(1+x), cuz when u divide, the power become subtract, so u r like doing 1/2-(-1/2)=1
2(1+x)^(1/2) - x(1+x)^(-1/2)
=(1+x)^(-1/2) [2(1+x)-x]
= (1+x)^(-1/2) [2+2x-x]
=(1+x)^(-1/2) [2+x]
= (x+2) / (1+x)^(1/2)
hope i explain well lol
late pine
I'm analyzing everything
idle heart
Let's look at a easier but similar example:
$$a^{\frac{1}{2}}-a^{-\frac{1}{2}}$$...
at this point it is just easier to write in paper and take a photo
lmao
fervent hawk
at this point it is just easier to write in paper and take a photo
I'm in a toilet, so ..... 
late pine
2(1+x)^(1/2) - x(1+x)^(-1/2)
so if u divide both term by (1+x)^(-1/2) or u can s...
I don't understand this
let me do it on paper
and I send you photo of my thinking
idle heart
alright
late pine
When I try to "defactorise" if I do the (1+x)^-1/2 * 2(1+x)^2 , it's the same base, but the exponential value I get is 0?
idle heart
well ur thinking is just reverse of what i say, but u got something wrong, when u defactorise, it become power of 0 , so ur goal is to defactorise to make back original stuff, so it would make sense to put (1+x)^(-1/2) [2(1+x)-x]
like that, if u defactorise, it would become -1/2+1=1/2
which is original
clever fjordBOT
S0S4
idle heart
this is correct
late pine
okay
give me one sec
lets see if I can solve it now
I got the result but with different sign on the denominator
like this but ^-3/2
idle heart
cuz u miss the (x+1) in denominator as the start
late pine
I reached: $$ \frac{( 1+x)^{\frac{-1}{2}}[ x+2]}{x+1} $$
clever fjordBOT
S0S4
late pine
but if I operate here, I have same base in nominator and denominator
but different exponential
so I do: -1/2 - 1
and I get -3/2
late pine
but
idle heart
and negative exponent can become denominator with positive exponent
late pine
.
idle heart
(x+1)^(-b) = 1/ (x+1)^b
its the defination of negative exponent
it is just denominator
late pine
ouh yeah
I got it now
but wtf
it remains the same
I mean
how can (x+1)^-3/2 be the same as (x+1)^3/2
idle heart
how can (x+1)^-3/2 be the same as (x+1)^3/2
(x+1)^-3/2 = 1/ (x+1)^3/2
it is just reciprocal
flip it upside down
late pine
Okay damn
I got it now
and understood it
thank you so much for time and patience
almost a hour teaching me 😅
I really appreciate it
❤️
idle heart
late pine
.close
odd edgeBOT
odd edgeBOT
Available help channel!
mint sluice
Hello, i am curious if we can solve for b and c in the equation. I've tried to use silmutaneous equation in the calculator, but it doesn't work.
tacit haven
maybe use wolfram alpha?
mint sluice
.close
odd edgeBOT
odd edgeBOT
Available help channel!
kind compass
odd edgeBOT
fervent hawk
0.134134134..….
odd edgeBOT
fervent hawk
there is no bar above 3
different convention
uneven osprey
there is no bar above 3
and also Lord Biscuity don't need bars, bro is the reason they exists
(sorry for cringe joke)
odd edgeBOT
Available help channel!
serene axle
odd edgeBOT
serene axle
Don't really understand question 3
serene axle
Yea
serene axle
No of permutations is 4! I can get that
serene axle
every digit from 1 to 4?
Yes
serene axle
No of permutations is 4! I can get that
What do I need to do after this?
proper solstice
so the sum of digits will always be = 1+2+3 +4 = 10 for a given permutation
sum = 10*24 = 240
serene axle
Hmmm yea I guess
proper solstice
so answer is 6
tacit haven
so the sum of digits will always be = 1+2+3 +4 = 10 for a given permutation
sum...
n isnt the sum of the digits, no?
serene axle
Oh so I need to find the sum of the digits of this
rose radish
no
proper solstice
n isnt the sum of the digits, no?
it is
rose radish
First u need to find how many permutations are possible
tacit haven
n is the sum of the possible permutations,
rose radish
which if uk is 4! = 120
serene axle
First u need to find how many permutations are possible
4!
rose radish
and since all the numbers are like
proper solstice
oh
serene axle
which if uk is 4! = 120
Its 24 not 120 ;-;
rose radish
their sum of digits is constant
proper solstice
mb
rose radish
mn
proper solstice
sorry i was wrong
serene axle
their sum of digits is constant
Yea
serene axle
Ye
pale atlas
They are asking
1234+4321+4213+... = abcd
So a+b+c+d
rose radish
got it ?
serene axle
They are asking
1234+4321+4213+... = abcd
So a+b+c+d
Oh
mystic saffron
The question is worded a bit weirdly but it's what Thunder is saying
serene axle
Bro he got it
So it's 6?
serene axle
What
serene axle
Yea ;-;
rose radish
my bad bruh
serene axle
It alr dw
pale atlas
sum of all permutations
Get the number by adding all permutations, then add all digit of that number
serene axle
So each number appears 6 times?
proper solstice
In ABCD
for A = 1
1234
1243
1324
1342
1423
1432
..
...
...
...
...
number of times 4 has occured = 2*3 = 6 = 24/4 = 6
number of times 3 has occured = 6
so adding like a column,
we get 6(10) = 6(0)
6 is carried above
again the same case repeats
so
60+6 = 6(6)
6 is carried forward
again 6(6), and 6 is carried forward
again 66
so 66660
rose radish
yea so that
proper solstice
is it correct?
serene axle
.close
odd edgeBOT
mystic saffron
In ABCD
for A = 1
1234
1243
1324
1342
1423
1432
..
...
...
...
...
number of tim...
(don't just give out the answer next time by the way, encourage with hints)
odd edgeBOT
Available help channel!
bleak idol
odd edgeBOT
mystic saffron
All the steps after the second step are wrong
marsh hawk
yes
marsh hawk
cos(pi/2) = 0
bleak idol
cos(pi/2) = 0
Oh hm..
bleak idol
cos(pi/2) = 0
So just subsitute ?
marsh hawk
yes
mystic saffron
If you get 0/0 after substitution of the limit variable, you have an indeterminate form
(Also, sorry for ambiguity, we said to sub cos(π/2)=0 and sin(π/2)=1)
marsh hawk
sin(π/2) = 1 and you have -sin(y) left
bleak idol
sin(π/2) = 1 and you have -sin(y) left
Oh..
So i dont need to subtitute -siny
Woww dang
Thankyou
bleak idol
do you remember standard limits
Like this?
bleak idol
t tends to zero
Oh, yea
bleak idol
Ohh thankyou very much
marsh hawk
make sure to bring -4 outside of limit
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
Hey how can i find cos(x) = 0.3242
odd edgeBOT
Hey how can i find cos(x) = 0.3242
mystic saffron
All the possibilities*
devout dove
Is there any restrictions?
steady tide
there are infinite solutions
fickle silo
think about the periodicity of cos
steady tide
like peteozzy said, you need some restriction
boreal stag
like peteozzy said, you need some restriction
OH SHIT THIS PERSON IS LEGENDARY
fickle silo
and cos being an even function
boreal stag
hoW ARE YOU HELPING TWO PEOPLE AT ONCE
steady tide
something like $0\le x\le 2\pi$
clever fjordBOT
mystic saffron
Ahh ok the other solution is negative ?
devout dove
No, it's just an example
sweet cloak
quick Q: they gave me the integral and I solved it, what do they mean by convert back to x in part e how do I do that?
devout dove
If there was no restriction provided then it's countless solutions
fickle silo
Ahh ok the other solution is negative ?
first of all, whats the period of cos?
uneven osprey
quick Q: they gave me the integral and I solved it, what do they mean by convert...
!occupied
odd edgeBOT
quick Q: they gave me the integral and I solved it, what do they mean by convert...
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).
devout dove
quick Q: they gave me the integral and I solved it, what do they mean by convert...
Please go to another channel
mystic saffron
first of all, whats the period of cos?
2 pi
fickle silo
right, btw is 71.08 in degrees?
fickle silo
so you work in degrees rather than radians?
mystic saffron
Yep
fickle silo
right then period would be 360 degrees
mystic saffron
Ah yeee
fickle silo
so if you know that cos(x) = 0.3242, then you also know that cos(x + 360°) = 0.3242
mystic saffron
Yes
fickle silo
can you generalize this to obtain infinitely many solutions?
mystic saffron
71.08° + x * 360
fickle silo
and what exactly can x be here?
fickle silo
right, its important that x here is a whole number, so I would write it as 71.08° + n * 360° instead
mystic saffron
Okkaayy
fickle silo
also 71.08° - 360° would be another valid solution
so not only all the natural work here
mystic saffron
Ah yes
fickle silo
so we can say that $n \in \mathbb{Z}$
clever fjordBOT
rbit
fickle silo
lastly cos is also even, so if x is a solution, then -x is also a solution
mystic saffron
Z is negative and positive numbers
fickle silo
right
mystic saffron
lastly cos is also even, so if x is a solution, then -x is also a solution
Ohh ok
And if it was a sin
fickle silo
with sin it's a bit more difficult, but it holds that sin(x) = sin(180° - x)
fickle silo
tan hits every y position only once per period, so this doesn't work here
we have tan(x) = tan(x + 180n)
fickle silo
then -54.46° + n*180° are already all the solutions
mystic saffron
Oh ok ty
fickle silo
so to recap, for the cos case we have 71.08° + n*360° and -71.08° + n*360° which are all rhe solutions
mystic saffron
Yesss tysm
foggy tendon
odd edgeBOT
foggy tendon
uhhh what? It satisfies 0,0 yet when graphed it's not passing through?
foggy tendon
even tho its a continuous differentiable function at every point, and well for some reason it's derivative does not exist at 0,0
it jus gives a 0/0 result when x=y=0 is put in f'(x)
foggy tendon
can you maybe guess why?
yeah, witchcraft
white brook
it jus gives a 0/0 result when x=y=0 is put in f'(x)
youre doing it wrong
now that that method fails, youve got to try another one, it shuld work
its continuous at the point
foggy tendon
f(x+h) definition? or solving it as a limit?
timber gyro
Please help.
nimble blaze
not a function
white brook
f(x+h) definition? or solving it as a limit?
both of them are valid techiques, but there are different methods to solve using them
try to figure it out, brb
foggy tendon
not a function
oh right...but i can still take it as an equation?
and it's satisfying (0,0) as an equation-
nimble blaze
desmos doesn't show individual points like that
foggy tendon
i don't really get what you're trying to imply, could you please enunciate your point
nimble blaze
many graphing programs don't show points that are separate from the continuous parts of the graph
foggy tendon
so ur saying that 0,0 does satisfy it and everything but desmos is not showing that?
.close
odd edgeBOT
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merry lily
how to prove n|sum(a=1..n, 2^gcd(a,n)) for n>=2? popped up in my cyclic code research. i have no starting leads other than this is equal to n|sum(d s.t. d|n, totient(d)*2^(n/d)) - dirichlet convolution of totient and 2^n, but that doesn't make it easier
merry lily
according to "Tomaz̆ Pisanski, Doris Schattschneider and Brigitte Servatius. (2006). Applying Burnside's Lemma to a One-Dimensional Escher Problem. Mathematics Magazine, 79(3), 167–180." this may have some connection to Burnside's lemma.
odd edgeBOT
@merry lily Has your question been resolved?
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@merry lily Has your question been resolved?
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@merry lily Has your question been resolved?
hollow topaz
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desert marlin
even the questions are piece-wise
Do you know what a right hand or left hand limit is
desert marlin
yes
hollow topaz
okay good good i know something!
desert marlin
So for (a)
to compute the right hand limit as x-> -1
what values is f(x) taking on when x>-1 , aproaching it from the right
desert marlin
Why
desert marlin
it doesn't have to do with the first piece
hollow topaz
okay let me think again
desert marlin
what values is f(x) taking on when x>-1 , aproaching it from the right
think about this
hollow topaz
it has to be 1 because it technically hits the last piece first
coming from the right
desert marlin
it doesn't have to do with the last piece
When you're approaching -1 from the right
you're in the interval -1 < x < 0
so what is f(x) in that interval?
-x
So what is the right hand limit of -x approaching -1?
hollow topaz
i dont understand the question
i understood ur explanation but not the recent question
desert marlin
So what is the right hand limit of -x approaching -1?
You don't understand this?
desert marlin
yes
desert marlin
1 is correct just earlier I didn't think you had the right reason
desert marlin
Not sure why you wrote that
No
the function is f(x)=-x
as you approach -1 from the right
its like
-0.5
-0.7
-0.9
-0.99
-0.99999
hollow topaz
yes
desert marlin
approaching -1
but then in f(x)
all of these become
f(-0.5)=0.5
f(-0.7)=0.7
f(-0.9)=0.9
f(-0.99)=.99
and so on
desert marlin
why?
hollow topaz
it has to do with the 2nd piece
desert marlin
think again
desert marlin
approaching -1 from the left means x <= -1
hollow topaz
etc
desert marlin
approaching -1 from the left means x <= -1
So its actually the first piece
hollow topaz
okay
i think
i understand
i just
cant visualize it in my head i n eed to draw it out
desert marlin
Good idea
hollow topaz
can you show me how you did that in desmo
like
what did you input
to create each line
desert marlin
hollow topaz
thanks
desert marlin
So approaching -1 from the left, we're in this yellow shaded region
and if we follow along our function there, the red line, what does it approach as we go to -1
desert marlin
Yes
hollow topaz
okay
desert marlin
The way you should do this without plotting is
Okay, approaching -1 from the left so
-1.5, -1.2, -1.1, -1.01, -1.0001
plug this into f(x)
f(-1.5)=1
f(-1.2)=1
f(-1.1)=1
f(-1.01)=1
f(-1.0001)=1
So the left hand limit is 1
Does that make sense?
hollow topaz
okay so
the red line
when it comes to -1
the y value is
1
wait hold on idek what im saying
desert marlin
Okay, approaching -1 from the left so
Read this part
if you have questions about it ask
desert marlin
We're taking a limit of f(x), so yes
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wise zodiac
Just question 3.
Howcome mathway doesn't say the answer is y=1/4x+1/2? It says the answer is y=1/4x-3/2
wise zodiac
upbeat drum
,rotate
clever fjordBOT
wise zodiac
But if I say solve (2,1) 1/4, it gives me the answer I think it is
upbeat drum
$-1=\frac12+b \implies -1-\frac12=b$
clever fjordBOT
chlamydia
wise zodiac
**chlamydia**
Does this mean b=-1.5
odd edgeBOT
@wise zodiac Has your question been resolved?
boreal jewel
Yo this stuff got me confused how do I do this stuff
odd edgeBOT
boreal jewel
.reopen
odd edgeBOT
✅
fervent oxide
What is the question
boreal jewel
What is the question
Find the x y intercepts
fervent oxide
For x intercepts, make y = 0 and y intercepts, make x =0
fervent oxide
The square root is redundant in finding the x intercept
x multipled with the square root x+6
You have to find x such that multiplying one another will result in 0
think of it as x(x+6) = 0
boreal jewel
So x²+6x?
fervent oxide
think of it as x(x+6) = 0
How would you solve for x in this situation
boreal jewel
Idk how to with x²+6x
boreal jewel
Domain?
boreal jewel
Divide
fervent oxide
An another way of thinking is anything multipled by 0 is always 0 right?
So 6 x 0 = 0
boreal jewel
Ye
fervent oxide
A same way of thinking can be applied in your question
It is literally “x” times “sqrt(x+6)” = 0
If either variable is 0, the answer would be 0
Meaning if x is 0, then 0 times sqrt(x+6) would be 0. Alternatively, if sqrt(x+6) was 0, that times x would be 0
boreal jewel
Ye
fervent oxide
So there’s two possible solutions: either x is 0 or sqrt(x+6) is 0
So what would x be
boreal jewel
6?
fervent oxide
How did you get that
boreal jewel
Idk im confused on that part
fervent oxide
So x could be 0 meaning x=0 or sqrt(x+6) could be 0 meaning sqrt(x+6)=0
boreal jewel
So it's also 0?
fervent oxide
Wdym
fervent oxide
Ok then what about when sqrt(x+6) is 0
odd edgeBOT
@boreal jewel Has your question been resolved?
desert dome
odd edgeBOT
desert dome
how do u do thjs
quasi sparrow
,tex .shift trig
clever fjordBOT
riemann
quasi sparrow
either use the cos(pi + x) = -cos(x) twice or use cos(x) = cos(x - 2pi)
odd edgeBOT
@desert dome Has your question been resolved?
desert dome
.close
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vivid kelp
pls help
vivid kelp
Consider the quadratic equation ax^2+bx+c = 0 ,a , b and c belongs to natural numbers which has two two real roots beloging to the interval (1,2)
Q1) The least value of a is
a) 4 b)6 c)7 d) 5
Q2) The least value of b is
a) 10 b)11 c)13 d) 15
Q3) The least value of c is
a) 4 b)6 c)7 d) 5
Thanks in advance please give me the solution as well thnx
odd edgeBOT
@vivid kelp Has your question been resolved?
heavy oak
can someone tell me how they would answer this
odd edgeBOT
can someone tell me how they would answer this
brave gale
fog(1) means f(g(1))
granite ferry
can someone tell me how they would answer this
Have you read about compositions?
heavy oak
no i was put in the wrong math class and i have no idea how to do anything
brave gale
o stands for of
heavy oak
its not multiplication
brave gale
so fog(x) stands for f ( g ( x))
brave gale
yea
heavy oak
uh which is that
heavy oak
so just -7?
mint mirage
Yes
mint mirage
Can you show what you did?
mint mirage
Where are those equations and values coming from?
Those are different from the screenshot
heavy oak
yea
mint mirage
And what do you get when you do that?
clever fjordBOT
CaptainNova22
heavy oak
yes
mint mirage
So when you plug in 4, it should be $\sqrt{\frac{9 \cdot 4}{4}}$
clever fjordBOT
CaptainNova22
mint mirage
Yes
mint mirage
ok it said it was wrong
That's when you do g(4)
heavy oak
huh
mint mirage
for this would it not be 2 + rad 3
This was it but you needed to follow this part of the question
You needed to calculate the value of that
heavy oak
idk that
mint mirage
Alright go head and try this
heavy oak
2.31
mint mirage
Looks correct
heavy oak
what the heck would the domain be
mint mirage
Do you know what domain means?
heavy oak
i got x e r, x not equal to 0
mint mirage
And how did you get that?
heavy oak
is that not it
heavy oak
yeah that x can be any real number
mint mirage
Alright, I just didn't think a question like that would have asked for that kind of notation
heavy oak
its wrong tho would the answer be (-infinity,infinity)
mint mirage
Well, like you said, x can't be equal to 0
heavy oak
so what do i put
mint mirage
I'm not sure how the site wants the answer
heavy oak
okay whats an option
mint mirage
Does it show you the answer if you get it wrong?
heavy oak
no it just gives me a strike
mint mirage
Yeah
heavy oak
yay got it
thank u
ok i literally cian with domain
i got x e r, x not equal -5
how would u put it in the other form
mint mirage
Same idea as what I did, the ) ( is notation that, that value isn't included and the U is used to join together multiple sets of the ()
So instead of 0, you have -5
heavy oak
mint mirage
Yep
brave gale
see x^2 is always +ve u agree?
heavy oak
uhh what
mint mirage
So this is asking for end behavior
heavy oak
yes
mint mirage
You want to identify the dominant term
So you need to figure out what the leading term is for each set of brackets
mint mirage
What's the leading term for each bracket? The leading leading term is the term with the highest exponent, so in (x + 5), what's the leading term?
mint mirage
Identify the roots first
odd edgeBOT
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errant timber
odd edgeBOT
errant timber
.close
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primal solstice
how would i go about this? i have no idea where to start with deriving it bc of the g(x)
true nest
derive it as normal, when you get the g(x), apply the chain rule
inland rover
do you know the quotient rule ?
primal solstice
yes
inland rover
so then apply that to $\frac{4x^2}{g(x)}$
clever fjordBOT
convergence
odd edgeBOT
@primal solstice Has your question been resolved?
primal solstice
so then apply that to $\frac{4x^2}{g(x)}$
does this look right
wait fuck
i forgot the other term 💀
-9 not -8
inland rover
also how did you get 144?
bleak idol
odd edgeBOT
forest sky
to start, what is $\cos^2(x) -1$?
clever fjordBOT
cloud
desert marlin
Find the roots (there are two graphs that will match) and then find the sign on the x^3 term to determine if it should be going to -infinity or +infinity as x->infinity, and you'll have the matching graph
bleak idol
to start, what is $\cos^2(x) -1$?
Oh, is it sin²x?
forest sky
Oh, is it sin²x?
close, but not quite
bleak idol
close, but not quite
2sin²x?
bleak idol
Do you know pythagorean identity
I forgot
forest sky
Oh, is it sin²x?
recall the connection between $\cos^2x$, $\sin^2x$ and $1$
clever fjordBOT
cloud
bleak idol
recall the connection between $\cos^2x$, $\sin^2x$ and $1$
-sin²x
Ohh
i hate my memory
Hm
bleak idol
recall the connection between $\cos^2x$, $\sin^2x$ and $1$
Hm, hello?
odd edgeBOT
@bleak idol Has your question been resolved?
bleak idol
<@&286206848099549185>
inland rover
its wrong..