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shoould this be 0 or 1/7??
i did it by doing the lkimit on the tan first, it is 0, than anything times 0 is just 0, but photomath used L'sHopital rule and ended up with 1/7
i used photomath to be sure, but now idk what is right
You can't do the multiplication thing if one of the limits is not defined as a real number
cot7/x dne
i don't know the L'hopital rule, not yet lol, if someone can teatch me
thank you
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i dont understand why when x=2 dy/dx =0
so when y=7, dy/dx=?
uhh
@high lily do u have any advice
to generally
preparing for a math exam?
sorry for random question XD
but my exam is in 5 days
and im kinda
nervous

practice, do past papers under exam conditions
identify knowledge gaps
review content/questions on those
yes
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@tight oasis
sorry for the late reply
but heres the link
Answer (1 of 2): I assume you are looking for the definite integral of 1/(x^8 + 1) from 0 to infinity.
Since the integrand is even, the integral is doubled if we take the limits as from -infinity to +infinity. The latter is easy to evaluate using Cauchy Residue Theorem.
Consider the integral of...
@timid silo Why taking k=1,3,5,7 ?
its not
k= 0,1,2,3
or well it kinda is
if u solve it you will get e^ipi(1+2k)/8
oh yeah my bad
1/2 i pi (e^-i(pi/8) + e^-i3pi/8 + e^-i5pi/8 + e^-i7pi/8) was my result of the integral idk if its right or not
@timid silo Has your question been resolved?
<@&286206848099549185>
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Im relearning math for the GED and i guess I got confused and maybe over complicated it. Apologies if this seems incredibly simple and stupid of me.
So it wants me to find the equation that runs through the line (1,6) (-1,2) I already know the answer but i guess i got lost in the steps.
I know this ties in with y=mx+b
So I solved for M using m=rise over run which is 2
So youre left with y=2x+b and then you plug in either of the coords and the steps after have me confused I guess
which part of the last step is confusing
The test gave me the steps for the answer and I understood it up to this point.
Im not understanding how in the steps we went from
2=-2+b to 2+2=b like the equation got flipped or i missed something
Firstly, it's okay. It's not stupid if you tried your best already
Secondly, when a line passes through a point, it means the coordinates at that point (the x and y values) are shared by both the line and the point.
Btw... You did it correctly so far. The last step just wants you to write an equation using the values you found for b and m and express the whole equation, and say that that is your answer
<@&268886789983436800>
Yummmm beans
fuckin hate beaners like u
sorry im jus a lil buzzed
from the bar
should i sleep
On the right side, if you solve for b, you'll find that it's the same value as the left side.
The point of the question is so you can express y in terms of x without any other unknown variables in the equation
@flint glade
I believe i’ve understood it.
<@&268886789983436800>
<@&268886789983436800>
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I just had a question
guinearW
you are differentiating with respect to y
NO
what
You're unhelpful, @abstract snow
you didn't notate your expressions properly
dx/dy e^(2x) =0
you typed out
$$\dv{x}{y}e^{2x}$$
when you probably mean
$$\dv{x}e^{2x}$$
ℝam()n()v
or dy/dx where y=e^(2x)
yep that's that
this is my 2nd past paper and i'm getting tired sorry ToT
but thank you for the help
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✅
shouldn't it be 2x in the denominator
wait hold on
i don't understand how they got that once they simplified
nvm i stuffed up
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let's see...
b) incorrect: missing -4
c) incorrect: missing -1
i) incorrect: missing -4, -1
everything else is correct
im assuming this strange symbol is supposed to be a 1
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Closed due to the original message being deleted
Epsilon Delta Proofs?
not really an epsilon delta proof ig
when can i say a is non positive
I just presume epsilon is a widely used variable.
is it the epsilon delta definition of a limit?
im not trying to prove a limit here
Interesting so ur questioning why the proof works in a certain manner for a certain theorem?
ig im just confused about the order in which quantifiers are used and how to like use themtogether
Questioning why the proof works the way it does?
im not actually questioning epsilondelta proofs
im not speaking abt epsilon delta
he's questioning if those two statements are equivalent
im asking for whatever theorem ur doing rn.
😅
I love that.
dothese statements mean different things because i put brackets differently
and if i see something like $\forall\epsilon>0, a<\epsilon\implies a\leq0$, how shud i interpret it
SilverSoldier
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hey
hi
hey
Guys if i am solving absolute values inequalities, Should i always make an associated equation?
Or i can just evalute the inequality for x?
For these.
idk what you mean by "evaluate the inequality for x"
find the solution set?
is that not synonymous with "solving the inequality"?
yes
thats true but i meant evaluating with an equal sign in an associate equation, is that necessary?
i have... no idea what you're saying
well i can see an alternative route here yes
i guess it doesn't
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“Check answers for Q2 and 3 “
question 2:
a) correct
b) correct
c) correct
d) incorrect: asked for first FIVE square numbers, saw only four
e) correct
f) incorrect: 4/5 and 9/10 are greater than 3/4.
Q3 is all correct
.
Yeeeeeeeeeee
31/100 is too small.
i'd like to add in 1c, 1d and 1i that you should probably be more careful with where you put the decimal point. It looks like a dot product
poor handwriting makes for easy-to-miss mistakes later on
Wat pic
Oh yea
Saved me fr
any of them. The purple is yours, right?
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please someone help me with this:
I broke down the components of force N and F
its physics
🤯
the magnitude of vertical component for N + magnitude of vertical component for F = 10 right?
F is 10g
10 is just mass
what is your doubt?
You just need to break it down, no?
did you try to balance forces in horizontal direction?
|N|sin(55)+|F|sin(35)=10 right
for vertical
how am i meant to find |N| and |F| from that
Ncos btw
and this
i dont understand
See
From fig N=x right?
and F=Z
i only need to find N
then X=mgcos35
whats mg
why is it assumed as a right angle triangle
and G is gravitational force
why does 10 become hypotenuse
its drawn perpendicular to it
10 aint hypo
i just resolved the forces
i resolved the mg force in direction of N and F
didnt get it?
yeaa vector addition
ohh the 10g is the resultant vector right?
and since F and N are perpendicular
its trig right?
OHHHHHHHHHHH
THANMK YOU
omg ive been struggling for like 30 minutes on this stupid question
thank you
no worries
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Kinda wondering where I'm going wrong here
I'm doing alright in life right now actually, math too. I'm just snagged on this one problem hahaha
i didnt understod what u did in this steps
Oh I just wanted to make the denominators the same
the little 5/5 and 3/3 are meaningless I was just using them to help me remember what I was doing. (In this case multiplying the top and bottom of both fractions by 3 then 5 for the second one)
ahhh fine it confused me
,calc 81*15
Result:
1215
not 135
Sorry which line are you referring to?
5th
its under root
Is this not correct?
it is
So where is the 81 coming from?
but 9sqrt(15) is not sqrt(135)
the 9 isn't getting squared anywhere unless I've missed something
ah sorry it's not the 9th root of root15 its 9 * root15
Oh i see where I've made a mistake
I took a 9 out of the root 135 and didn't put it under a root symbol lol
so it should be root9root15 over 1
or 3 * root15 over 1
correct
Ah cheers for the help everyone, It's greatly appreciated as always
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the opposite hypotenuse and adjacent are all in correct spots right?
simple question but i think im losing my mind
They are
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Hi
I think it’s probably easiest to just draw each of these separately and then if you’re pedantic join them up
thats the problem
idk how to combine them
i graphed it...
is this how
os this
can you show the actual problem?
"sketch the graph of an exmaple of a fucntion that satisfies all the given conditions"
that sounds like they want one graph per condition
all the given conditions
mb
but yeah they want all the graphs
if you want one graph that satisfies everything at the same time, you can just draw the parts close to the points given, and then join them (or not) however you like. They never say that the function needs to be continuous where you're not given a condition
did i do it right
i'd bitch about how badly you drew the branches that go to inf and -inf at 0 and 2, but it looks like the conditions are satisfied
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Letter B number 9 and 10
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okey so
lets say i i have to make a function
or better to say i got given info
i know that P1(x y) P2(x y) and i know the vertex which is also where the y interecept is
is there anyway that i can calculate this with the calculator
If you know 3 points on a parabola, you can find its equation. Is that what you're asking?
I am gonna be honest, you don't need a calculator to do all your work. A calculator is a tool to help check your work. You shouldn't utilize a calculator to do everything
yeah but i have an exam which if i fail i have to move to a whole different city and basically lose everything so im trying not to make that happen...
so if u could please tell me how lol (my b for the trauma dump)
As I mentioned, a calculator is a tool, not something you should use to rely on
But post an image of the problem you are doing
Tennis players often train with a ball machine. The one described here is in one half of a 24m long tennis court and shoots tennis balls from a height of 1m into the other half of the field in such a way that the balls cross the net at a height of 1.3m.
Where should the ball machine be located so that the tennis balls hit the ground 0.5m in front of the baseline in the other half of the field when the ball is at the apex of the parabolic trajectory when crossing the net?
At what height does a tennis player have to hit the ball when he is 2m in front of the net?
Solution
i dont rlly need the solution just the way how to put it into the calc
like
You can do that all without a calculator. But if you want to keep being persistent and wanting to use a calculator to do every single math problem, so be it. Good luck with your future classes, because some classes don't allow a calculator
well thats why im trying to use it cuz i can i know how to solve but that just takes time our teacher allows us to do the vertex zeros everything with the calc so i just wanted to know if something like this were to come up how would i need to solve it
You still haven't posted the question, but seriously a calculator doesn't help you here. It's just not the right tool.
If you know how to solve it without a calculator, then do it without the calculator, and send your work
@sharp ivy
then will you tell me how to do it on the calc? hhahaaha
a= -26/2654
Omg, sorry, I saw the start of this and I thought you were OP was ranting about tennis players using machines to train as a metaphor for using a calculator to train. Sorry!
hahhahahahaaa
Lmao 
Yeah, so a calculator doesn't really help, does it? You just start with the form of the equation, then plug in the point where the ball lands. I guess you can use a calculator here to solve for one of the coefficients.
a=-1.3/11.5^2
It seems like you understand that though.
so theres no way to just write this formula into the calc in get the a 😦
nvm got it i just put it in wrong the first i tried
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Sorry for skill issue just wanna know how to do this
exponent laws
What I did is I multiplied 7/4 by 3/2
and extra care when doing shit w/ fractions
multiplica em cima e em baixo por n^(2/3)?
eu multiplico oq ta dentro e fora do parentesis?
n entendi ent
a minha resposta final foi 89/24
AH
entendi oq eu fiz de errado
n pera
n entendi n
kkkkk
multiplica o numerador e denominador por n^(2/3)
dps do q tu fez
é a msm coisa que multiplicar por 1
mas teoricamente n era pra eu fazer a parte de cima menos a parte de baixo?
@timid silo
dá certo tambem sepa
caraalho eu tava mto perto
eu botei 89/24 errei a conta de mais e esqueci de mandar pra baixo pra ficar positivo
mas vlw pela ajuda men
tmj
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I know for a fact that’s not the right answer
Where did I mess up
I have last try on the hw :/
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ive currently tried to do ∫2 over 0 pi(sqrt(x))^2
but its saying the answer is 64pi/15 so i have no idea how to get there but i understand the basics
you're rotating about the y-axis, so you should be integrating whatever x is equal to (so an integral of y^2 or 2y)
it's also the region bounded between the two curves
so you should be subtracting something here (figure out which is "further" from the y-axis)
your bounds 0 to 2 look fine
oh for real? i thought if i rotate over the y-axis i would do it with respect to y so id try to find what is = to y
"about the line x=0"
they both touch the y axis so i thought i could just plug it in without subtracting
this is what the graph looks like
if you just integrate one, you get area between that line and the y-axis rotated
so here you want the area between
ohhh okay okay
so do the volume of rotation for the 2y line, then y^2 line, and find the difference
can i ask why would i subtract the 2y line from the y^2 line
other way around
ohh okay
the integral with 2y gives a cone thing
with base radius 4 and height 2
so you can remove the smaller funnel you get from the y^2 rotation to get the desired volume
looks good
ohh
yeah
thats the answer LOL
mb i thought i did something wrong
would u mind if i ask some logistical questions abt these types of problems
okay
so for these types of questions
i got this one right so i dont really need help on it
do i not have to subtract anything from it to find the solid because it gets cut off from the bounds
like for example
the area i shaded in; if i wanted to find the solid from the x-axis i wouldnt have to subtract anything from it id just do bounds of 5 to 1 pi(x-1)
bc like the rest of the equation gets cut out
after the bounds
you subtract whenever you have a concavity basically
for both of those, it's just a solid thing up to the axis
it's not like a coffee cup or something which has a void between the volume and the axis of rotation
whereas the original question is a cone with a funnel in the middle removed, which is concave
ohhhh okay okay
well now i have another one idk how to do lol
if anyone can help me with this one
im pretty sure the bounds are 4 and 0
so i tried doing ∫4 over 0 pi(x/2)^2 - ∫4 over 0 pi(sqrt(x))^2
yeah so this time its over the x-axis right
consider the order of your integrals
you subtract the thing that's closer to the axis of rotation
wdym by closer?
the parabola describes a larger volume
because it's higher up than the line
it's further from the x-axis over [0,4]
like further as in it contains more area?
sure
or just
draw vertical lines from the x-axis to the lines; you meet the line before the parabola
oh yeah its further from the axis from 0 to 4
yeah that makes more sense tyty
so i set up the equations right i just subtracted in the wrong order?
yes
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yooo
i need help with this question
whats the question?
thats okay dw
have you done any working so far?
yeah but this is online and it keeps saying im wrong
okay what working have you done?
okay thats the SA of the outer edge
huh
the surface area of the outer edge
o yeah
yeah but idk if its write or not
whats the a? sorry if im missing something
im not sure what you mean sorry
but i would use the area of a circle to work out the area of the top and bottom
ok
thats for a cube not a cylinder
its alright
what is it for the cylinder then?
the formula for this if SA=2pirh+2pir^2
pi as in 3.14.... , r is radius and h is height
yeah
oooo
ok
ima write this down
what does the arrow pointing to the top mean
like squared
yes
okay so this is alot of smaller equations
yes
@earnest frost Has your question been resolved?
yes
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beta is the angle with the -x axis, not the +x axis.
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Herels
also you can't factor out x like that
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curious if i did this right as i dont have a way to check
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It looks like you cropped out a good chunk of your question
@broken hare Has your question been resolved?
Sorry my dude but no
Actually wait
OK yeah nvm it's got things wrong
want me to try to draw out the answer or do you wanna give it another shot or go step by step on the mistakes or what :p
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If you want to draw it out that would be helpful
Or if u just want to explain which parts are wrong
Nothing is cropped out
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question?
Scroll up just a bit
Q
A
<@&286206848099549185>
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No one knows how to solve this?
Where is the problem
This message is what is pinned by the bot as the problem
You won't find help like that my friend
What?
Here’s the problem
Ok this is wrong and not really precise
Can you elaborate
For instance at x=1.5 your function f(x) should be positive
I didn’t do x=1.5
So my line is not precise
But the points I did do, are those wrong?
That’s what I need to know to know if I’m understanding conceptually
It doesn't matter, between 1 and 2 it should be positive not null
At x=2 it's ok, at x=3 also ok and at x=4 it's wrong
And between x=1 and x=2 the function should be positive
x=4 should be -4?
Do you know what the integral computes?
No actually it should be -3.5
Explain how that’s wrong
I just did the math again
Do you?
I will explain once you told me what does the integral actually compute?
I just want to be sure you are doing the exercise properly 🙂
WAIT I read your graph wrongly sorry
You should graduate your axis bro 😭
Yes but you are not answering my question
You just want the answer
I'm not giving free answer and I'm not spending my time to solve your exercise right?
The answer I wanted was:
The integral computes the area between 1 and x
You have to add the area that is above the x axis and substract the area that is under the x axis.
Which is what I did lol
So as long as you know how to compute an area you should be ok
So answer the damn question if you want the damn answer bruv
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can someone help with this
Do you know the formula for this
use power of a point
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yo
how do i do this
what?
im getting any other answer
how do i do the problem i sent before
so uh ED =x then (2+x)/3 * (4+(2+x)/3) =2*(2+x) or something
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is this correct

i dont really get the whole compress dicompress stuff yet
nevermind i graphed it and its fine without that
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How i can prove is it total ?
n belong to total
What do you mean by total? Like natural numbers?
ye i now, i wana designate for whats n it is integral
oh okoko
Well the first n multiple doesn't change much about whether or not the result is an integer
So you should be looking at n's such that $$\frac{\sqrt{(n+1)}}{\sqrt{2}}$$ is an integer
Azyrashacorki
Now you can rewrite this as $$\sqrt{\frac{n+1}{2}}$$
Azyrashacorki
ye i know but can it be prove
What do you want to prove? It's pretty clear that your expression is an integer if and only if (n+1)/2 is a perfect square.
Just from that it's pretty clear that n must be odd.
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OK, you want to isolate a.
wait so whats the difference between one step and two step
So, if you knew a and you were calculating the right side, what would you do first and second?
Like let's say a = 10.
so do we subtract 2 from both sides
Well, let's learn how to do it in general.
If a = 10, how do you figure out 5a + 2? What do you do first?
This isn't about finding a.
oh
This is about how you do arithmetic.
define that please
Arithmetic is like having numbers and doing addition, subtraction, multiplication, division, exponents, roots.
alright
So, if I tell you a = 10, what number is 5a + 2?
so what answer are we trying to find from 2 step equations
No, don't worry about your problem right now.
sorry
Forget about two-step equations for right now.
If a = 10, how do you figure out what 5a + 2 is?
Then what?
OK, so you multiply a by 5, then you add 2, right?
yep
OK, now we're going to do the opposite backwards.
what?
What's the opposite of adding 2?
dividing
Right, dividing by 5.
So, I did the opposite for each step, and the steps are done in reverse.
Right, subtract 2 from both sides of 5a + 2 = 7.
OK, so 5a = 5, right?
OK, so our backwards opposite thing was subtracting 2, then dividing by 5, right?
OK, so here's the first step:
5a + 2 = 7
5a + 2 - 2 = 7 - 2
Do you see how I subtracted 2 from both sides?
ye
wheres the 5
The 5?
from the 7 we deducted out of
Well, I went back a step because you didn't understand how I got 5a = 5.
So, I'm showing more clearly what I'm doing.
ah
alr
wait now i think ik where the 5 came from
since 2-2 is 0
that cancels that out
So, we have:
5a + 2 = 7
5a + 2 - 2 = 7 - 2
Where are you getting the 10 from?
you said a = 10
Oh, that was an example.
oh
It might be 10, it might not, but to get the backwards opposite thing, we need to get the forwards regular way thing.
so 5 / 5
So, I was getting you to do it the normal way, then doing it backwards and opposite.
thats the only numbers we know in here
Right, so what's 5a/5?
1
Almost.
a = 1?
1
So, we have:
5a = 5
5a**/5** = 5**/5**
a = 1
Do you see how to get the forwards regular way, how to do that backwards and opposite, and then you isolate the variable that way?
To calculate 5a + 2, you multiply a by 5 and then add 2, right?
so thats 1 step?
so the opposite is onestep
So, do you see why you multiply a by 5 and then add 2 to calculate 5a + 2?
probably
5 * 5
wait
nvm
5a + 2
Regular way:
1. Multiply by 5
2. Add 2
Backwards and opposite:
1. Subtract 2 from both sides
2. Divide both sides by 5
The backwards and opposite steps are the two steps.
nvm im only focusing on 2 step
Oh, OK.
OK.
Can anyone dm
= a
Me
a = 1
It's unclear what steps you're doing.
Generally, you want to write it like this:
5a + 2 = 7
5a + 2 - 2 = 7 - 2
5a = 5
5a/5 = 5/5
a = 1
Can you dm me
That way, you can see exactly what's going on.
why
Sorry, we don't really encourage people to DM. Do you need help with a math problem?
wasnt gonna
Well like it’s a whole test coming up
Are you practicing for it or taking it now?
Practicing
I just wanted to somome to dm cause I forgot what they were covering and I needed somome to send me practice problems cause o need to study out of school
You can look up your course on https://www.khanacademy.org/, then pick a topic, and then it'll have video lessons and practice quizzes.
isnt there help channels?
Sorry, we don't really help over DMs, you just ask in the MATH HELP (AVAILABLE) channels. People have problems with all kinds of math, so we're not going to shame you or whatever.
#❓how-to-get-help has more instructions.
Positive and negative integers but it’s not just adding and subtracting them it’s like simpfying fractions to see if there integers
Is there a channel for those
And absoulte vaule
That's fine. Just ask a question in one of the MATH HELP (AVAILABLE) channels.
If you have a textbook, you can show a problem from the book you're stuck on.
OK, then try https://www.khanacademy.org. They do fractions and absolute values in it.
@topaz tartan Do you see how you can see what I do each step here ^
It has 5th grade math, yes.
Still there?
OK.
OK.
@scarlet gale is this like a + 2 = 7? Stuff
Yes.
,rccw
also pardon my handwriting
OK, that's good, except do both sides.
i did
High school?
I mean you have 5 on the third line there, but you don't have 5a on the third line.
And do you guys have positive and negative Intgers in channels?
wait so question
It's generally for middle school when they learn this kind of thing.
does 5a come first when dividing]
I’m in middle school
Yes, they can help with positive and negative numbers if you're stuck on that.
Please send it
Oh, you can do either side first.
I don’t see anything with intgers on this sever
well what if theyre different numbers
5a + 2 = 7
-2 -2
==========
5a 5
/5 /5
==========
a 1
wait
See the MATH HELP (AVAILABLE) section of the channels?