help-38

[real rose]

Okay.

So, what should be your final answer for domain and range?

[near flax]

Domain (-infinite,5]

range (5,9]

[real rose]

Why did you change your answer for the range?

^

[near flax]

oh wait i forgot negitive

:,o

[real rose]

👍

[near flax]

ok for quetion #2 f(-4) x=-4 right?

[real rose]

Yes.

[near flax]

(-4,-5)

for a)

(3,5) for b)

[real rose]

Good.

[near flax]

F(X)= is another word for y

[real rose]

Yes.

[near flax]

y=2 and x=1.5,2.5 and -1.5 ! idk if it correct but its close enough? kinda gotta guess the numbers

for c)

[real rose]

Yeah, about.

[near flax]

y=-5 x=-3,-4,-5,-6,-7 question d)

[real rose]

On the graph (you can just say that $x\le -3$).

[solid kiln]

mathisfun

[near flax]

oh yea thats way quicker

UHHHH as for question #3 what does it mean for value increasing and decreasing?

i know turning points are for when it changes from-to + or + to -

[real rose]

The y-values are larger than each other as the x-values increase for an increasing interval.

[near flax]

uhhh i kinda dont get it :,0 is it when its at it s highest and lowest?

idk what to do for a),b) but im pretty shure c is (-3,-5) and( 2,0) im not shure of the line up top has anything to do with turning points?

ima probs do #3 later

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[frank horizon]

Why is A2 a negative integral

but here the total area is just being added?

[split chasm]

integrating gives signed area,
would give a - value since the A_2 region is below the x-axis. - is applied to get the actual area

considering what's happening geometrically, lengths were used, so sign adjustment isn't needed

[frank horizon]

so this is applied to all regions

regardless of what ur calculating for

total area, signed area

etc

[dapper swift]

mmmmm the total area requires you to discard the negative sign

so how this would be asked is: "find the area bounded between the line/curve and the x-axis"

you would not count A2 as negative in that situation

[frank horizon]

can u solve it

and tell me what u get

[dapper swift]

it's already here bud

you don't need integrals to find the area of (right) triangles

[frank horizon]

thats different

[dapper swift]

how so?

oh right same setup different numbers

[frank horizon]

this is like the explanation

this is the question

[dapper swift]

total area = 1/2 * 3 * 3 + 1/2 * 1 * 1
signed area = -1/2 * 3 * 3 + 1/2 * 1 * 1

for the signed area count A2 as negative and A1 as positive

[frank horizon]

truee

right so for triangles

i just dont need to do integration to find exact area

just do that

oh this one doesnt really tell us the height

so we have to integrate

[dapper swift]

okay now you need the integrals

[frank horizon]

this is asking for total area

right?

[dapper swift]

yep

[frank horizon]

also also

the area of a shaded region under the x-axis will ALWAYS be negative

is that correct to say?

[dapper swift]

yes

[frank horizon]

ok

i understand it now

[dapper swift]

well make sure they're not doing any weird tricks on you like

$\int_5^2 f(x) \ dx = - \int_2^5 f(x) \ dx$

[solid kiln]

south

[frank horizon]

oh yeah ik that rule

[dapper swift]

cool

[frank horizon]

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[real herald]

Does my logic for allowing the values to commute make sense in this proof?

[real herald]

Prop to prove its a subgroup

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@real herald Has your question been resolved?

[real herald]

why are there so many people named help lmao

oh nvm i didnt see the reaction

tysm @whole coral

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[west sleet]

I tried using this approach to solve the problem, but it gives a negative diagonal

We also tried expressing all the variables in terms of L or b but the expressions are very complicated and I'm pretty sure how to obtain them is not in our syallabus

[thick zephyr]

2x-2d not -2x+2d

Oh nvm

[west sleet]

Apparently we were only supposed to explain the process with words😭

Still my curious why this doesn't work

You can find b in terms of L and all but that's a bit out of syllabus for us

[thick zephyr]

That’s the way I thought of first but I’m trying to figure out why yours doesn’t work

It might just be the maximum possible for d given x gives the largest area

[west sleet]

Maybe I'd have to take the end points?

But that'd be like

d=0

And that also doesn't make sense

I was thinking that if I found d

Then I could find all the pairs of L and b that give the max area

<@&286206848099549185>

[thick zephyr]

If you have d I think there is only one pair of L and b that equal x

[austere cedar]

There's another endpoint

d can't be arbitratily large without forcing x to be too big

[thick zephyr]

Oh yea that’s it

[austere cedar]

That's really neat actually, that if you want to maximize this area, you also want to maximize the diagonal

x = 2L + 2b + d
So in order to give the most to d, L + b has to be as small as possible

[west sleet]

Makes sense but

If L+b decreases

d decreases too

Ah nvm I see

[austere cedar]

Sorry I forgot to explicitly say what I was thinking, that d = sqrt(L^2 + b^2) so they're all locked

[west sleet]

Yea this textbook sucks man

In the explanation they gave in the answer

They didn't even talk about testing end points

[austere cedar]

What's the answer?

[west sleet]

You know how the question said explain

Yea they basically only wanted us to find the 3 equations relating d L and b

[austere cedar]

Tbh testing endpoints rarely actually matters, this is just one of the cases where it happens to

[west sleet]

And explain in words how we would do it

The explanation in words being 'find b in terms of L, then find derivative...'

Which is just bullshit man😭

[austere cedar]

I suspect that the solution is a perfect square

But actually getting that would take solving some intense algebra

[west sleet]

I know but yea here we are

Farmer sobbing man, all bro wanted to do was build a fence😭

[austere cedar]

Well, actually I guess we can do it from here:
x = 2L + 2b + d
d = √[L² + b²]

Find L and b that maximizes d, given x

The paperwork you did proves that this also maximizes A

[west sleet]

Alright well

[west sleet]

I graphed it or attempted to

Seems like there exists only a min pt

x=L,d=y

k is the amt of fencing

[trim jolt]

@west sleet Has your question been resolved?

[thick zephyr]

You can try solving it as a system of equations

But since there is 3 variables and 2 equations I don’t think there is 1 answer

[trim jolt]

@west sleet Has your question been resolved?

[boreal harbor]

note that youre given x, not k. youre fixing the wrong variable

[west sleet]

I think the intention is that our dimensions should be in terms of x

[boreal harbor]

x is the total length of fence right

[west sleet]

And that we take x as a constant

[west sleet]

Ye

[boreal harbor]

right but in your graph youre letting x vary

[west sleet]

Oh that's just because I have to name it x

Because desmos

[boreal harbor]

if you let x vary then the graph wont tell you anything useful

[west sleet]

Here I specify the graph variables

I'm writing X to mean L

y to mean d

[boreal harbor]

since for infinite fence length you can get infinite area, you wont really see a maximum

[west sleet]

Yea that's the issue then

[west sleet]

k is the amt of fencing x

[boreal harbor]

oh

[west sleet]

It's just I have to name the varying variables X and y

So desmos plots them

If not I can't really plot the graph

[boreal harbor]

okay i see and y is d

[west sleet]

Ye

[boreal harbor]

i dont believe maximizing the diagonal is the same as maximizing the area, rather the opposite--minimizing the diagonal maximizes the area. without loss of generality, we can just consider the perimeter of a right triangle. then the diagonal attains a maximum at d = L = half the total length of fence, but the area is 0.

this is a limiting case of course

ah disregard that i was wrong

max d <=> max A

[silver glade]

i believe the area is maximized when the length and width are equal and the fence length is x
but this took too much algebra to justify

[boreal harbor]

yeah

[boreal harbor]

im not sure how to explain this graph tbh like. y should be bounded below by k/3 for some fixed k and above by the optimal diagonal length.

[boreal harbor]

okay yeah i guess it makes sense because you dont have anything to enforce that 2L + 2b + d = k. so graphing like this just wasnt the way to do it

anyway the way id normally do this is with lagrange multipliers

$f(x,y) = xy\g(x,y) = 2x+2y+\sqrt{x^2+y^2}-L= 0$ where $x,y$ are base and height and $L$ is the total length of fence

[solid kiln]

esca

[boreal harbor]

then $\nabla f(x_0,y_0)=\lambda\nabla g(x_0,y_0)$

[solid kiln]

esca

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[west sleet]

Think that's it then

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[echo jetty]

where did I go wrong here? my working out was I=PRN, 200,000=120,000x18%xn, 200,000=21600n, divide both sides, 9 years

[split chasm]

you're calculating the time needed to earn 200000 of interest

where you're starting with 120000

you want the time needed to earn 200000 - 120000
of interest

[echo jetty]

wait so what would be the working out

[split chasm]

state that you want

you want the time needed to earn 200000 - 120000
of interest

[echo jetty]

why do we do 200,000-120,000?

is that to find the interest

[split chasm]

yes

[echo jetty]

so the interest isnt stated in the question pretty much, and we are trying to find n

so without the interest equation cant be completed

so we do that

so would it be like

80,000=120,000x18%xn

would it be like that?

[split chasm]

yes

[echo jetty]

okay tysm

i appreciate it greatly

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[wraith wedge]

I don't understand why they are doing the 162 part. I understand how they got the number (196 - 35 + 1), however, I don't understand why they are doing that. Wouldn't the sum of the natural numbers who are not divisible by 7 be = 0? It's a sequence of multiples of 7 so how can they magically get numbers from elsewhere?

[trim lichen]

162 is the count of all numbers from 35 to 196 inclusive

it's the number of terms in the AP 35+36+...+196

[wraith wedge]

AP?

[trim lichen]

arithmetic progression

[wraith wedge]

Ah

[trim lichen]

Wouldn't the sum of the natural numbers who are not divisible by 7 be = 0?
no, it would not. they arent talking about terms of the sequence not divisible by 7

they are just talking about the numbers themselves not divisible by 7

the arithmetic progression given in the question is the stuff you subtract away to remove all the multiples of 7 from the sum (bc you arent counting those)

[wraith wedge]

The subtraction makes sense, but I'm still a little confused on the natural numbers part I think...
What do you mean by the count of all the numbers?

[trim lichen]

it's how many natural numbers exist between 35 and 196

including 35 and 196 themselves

i don't want to say "number of numbers" bc that sounds both confusing and stupid

[wraith wedge]

OhhHHH

I was thinking terms of the sequence still. 35; 42; ...; 196. But you mean 35; 36; 37; ... ; 196?

Ahh I see I think now. The question actually helps you by giving the multiples of 7 in that range?

And the question is not actually about the given sequence but the natural numbers in the range. Or so I think

Thank you!

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[nimble bolt]

Hi

[nimble bolt]

What did i do wrong?

[zinc ginkgo]

where even is the question

[nimble bolt]

The top part..find values of x and y

[trim lichen]

you assumed x isn't 0 silently

x(y-3) = 0 means y=3 or x=0, and your work has shown the first of these two cases ends in a contradiction

[trim lichen]

taking y=3 gives x^2 = -8, which is impossible when x is real.

so y isn't 3, and instead x must be 0.

find y.

[nimble bolt]

I did smth like this…(loading)

[trim lichen]

why are you doing x^2 + 3*3 = 1 a second time?

[nimble bolt]

I thought the ans might change..

:c

[trim lichen]

you thought that doing the same manipulations a second time could lead to something different?

[nimble bolt]

No miss..sorry bout that

x=0 ?

[nimble bolt]

?
final would be x=0 and y=1/3 ?

[trim lichen]

yes

[nimble bolt]

Ok thanku

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[storm walrus]

hi I was wondering how I got this wrong

[zinc ginkgo]

did you do this

[storm walrus]

no 😭

i got the same integral by taking the derivative idk what I could’ve done wrong

or maybe I took the derivative wrong

<@&286206848099549185>

[spring current]

can you show your steps while taking the derivative

[storm walrus]

sure

my apologies for the messyness

did i make a mistake?

[spring current]

,w integral (x+14)/(x^2 + 22x + 125)

[solid kiln]

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Requested by m3nny

[storm walrus]

so i should put log instead of ln?

[spring current]

Ok then the mistake is with the coeffecient for arctan

[spring current]

no thats just a matter of notation ln is okay

[storm walrus]

oh so 3 arctan instead of 3/2

didn’t realize I typed 3/2 in my answer when it was 3 on my paper idk how that happened 😭

[spring current]

Yeah i got kinda confused when 3arctan was on your paper and then yoy seitched it to 3/2 while derivating
regardles so yeah youre all good now

[storm walrus]

thanks!

[spring current]

anytime

[storm walrus]

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[nova pumice]

What's the difference here..?

i dont see it

mayb different nth term

idk

[spring warren]

Is there any more context to this because usually i and j are dummy variables and there isn't a difference between them

[nova pumice]

theres no more context

theres this

thats it

[woven python]

first one has no difference and the second one will be

(a1+a2+a3.+..+an)

vs

n * aj

[nova pumice]

ah okay

thank you

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[unique cobalt]

Where do i even start

[brisk oar]

are there any angles that are known within the diagram?

maybe not any angles individually, but the sum of angles

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[tribal juniper]

Yo

[tribal juniper]

Solution says D is over A I thought the common notation would be that C is over A, the task didnt specify anything further, is there a correct notation or would both be correct, if the task didnt specify anything ?

[mellow tendon]

When you say over do you mean above it?

[tribal juniper]

yes

[mellow tendon]

So what does the task want ?

[tribal juniper]

you have point A. B, C ant it wants you to calculate D

it also says its a parallelogram

[mellow tendon]

Ok so what are you stuck on

[tribal juniper]

Read my original question

[mellow tendon]

Ok, I think I understand.
I think that the question specified that that you have an ABCD parallelogram
If that's so, then the order of the letters matter in the parallelogram. A should be connected to B then B followed by C then C followed by D then D connected to A

[tribal juniper]

No it didnt specify?

It say the points A(...) B, C are given determine the point D so its a parallelogram

Thtas the exact question in english but how do u read that D is over A ?

[mellow tendon]

Then you can't really determine if the parallelogram will be ABDC or ABCD
So either solutions should be correct
But as a common notation the ABCD is much more used than other weird notations
So I would recommend using it.

[tribal juniper]

ABCD is that c is above A ?

[mellow tendon]

No, C will not be connected to A
As I said the order matters

A connected to B then B to C then C to D then D to A

[tribal juniper]

Ive way more commonly seen that C is above A tbh

anyway thx

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[mellow tendon]

As it appears here parallelograms Usually use this notation

[tribal juniper]

aye

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[ancient nest]

can i get help i dont know how to get started

[ancient nest]

i know than b/2a = 1

so im assuming finding k and a would be ideal first

to then solve for b

[trim lichen]

no, not in the problem's notations you don't

[ancient nest]

how do i get started??

[trim lichen]

you know that in terms of x coordinates, the turning point is halfway between the two x intercepts

yes?

[ancient nest]

yes’

for the most part

[trim lichen]

there is no "for the most part"

either you know and understand what i said, or you do not

one of the x ints is -3 and the turning point is at 1

1 is halfway between -3 and what?

[ancient nest]

yes i understand

[ancient nest]

4??

[trim lichen]

hmmm... what's halfway between -3 and 4?

not 1, i would think

[ancient nest]

1

wait

[trim lichen]

(-3+4)/2 isn't 1

[ancient nest]

5

[trim lichen]

right

so your x ints are -3 and 5

[ancient nest]

mhm

[trim lichen]

you can fill in the values for two of the three letters they ask you

do so now

[ancient nest]

sorry how though??

i understand tp is between the 2 x intercepts

and than -3 and 5 are the x intercepts

and 1 is the line of symmetry

[trim lichen]

yes

look at your formula

y = k(x-a)(x-b)

[ancient nest]

-a and -b are x intercepts??

[trim lichen]

a and b themselves

not their negatives

[ancient nest]

hmm

wdym

[trim lichen]

the x ints are a and b themselves and not -a and -b

[ancient nest]

so b = 5

a = 3?

[trim lichen]

-3

a is -3

[ancient nest]

oh alright

[trim lichen]

the first x int was -3, yes?

no black magic

[ancient nest]

yes

[trim lichen]

right.

[trim lichen]

plug those values for a and b in here

[ancient nest]

alr

what next ??

[trim lichen]

your parabola goes thru the point (0, 30)

plug that in too, and find k

same way you did it on a recent question a few hours ago...

[ancient nest]

y = 30??

[trim lichen]

plug in x=0 and y=30. you will have an equation in k only

[ancient nest]

k=2??

how do i start this one??

if it has 1 real root then it equals 0 right??

[trim lichen]

you are using the word "it" for 2 different things rn i think

[ancient nest]

?

[trim lichen]

if it (what?) has one real root, then it (what?) equals zero

[ancient nest]

1 real root = 0

[trim lichen]

...

ok congratulations you have reduced the amount of sense you're making rn to zero

[ancient nest]

idk what you’re trying to ask

[trim lichen]

i was trying to ask you to formulate your question properly

[ancient nest]

if the discriminant has 1 real root then it equals 0

is that what you are asking??

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[gritty notch]

given that A is a point on fx and B is a point on the line y, find the minimal value of AB if AB is vertical to the line y

[gritty notch]

hi, still couldnt solve it

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@gritty notch Has your question been resolved?

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@gritty notch Has your question been resolved?

[trim jolt]

Channel closed

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Use .reopen if this was a mistake.

[trim jolt]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spark breach]

I am in the last year of high school and I am watching the explanation of the professor, but I do not know to apply and the curriculum for my country wants certain ways

[spark breach]

I am learning the ends

[bright quarry]

brother what

[spark breach]

Wait

It's called like that in Arabic

[hollow summit]

I’m inJapan highschool and today is test but no matter how much I study I just can’t understand this one problem and can someone help 😭

[lyric nymph]

where are you from

[spark breach]

∞

[spark breach]

Syria

[spark breach]

∞

[lyric nymph]

alright i am from lebanon we can talk in arabic if you want

[spark breach]

Endings

اي تمام

[lyric nymph]

i will try to help as much as i can but there are some words that i may not know because in lebanon math is not taught in arabic

[spark breach]

برو انا عم بدرس قسم النهايات عندي بالكتاب
انو مسيطر ع مسيطر وكذا مهارة بس عم بجي بحل نماذج ماعم بعرف

[spark breach]

I will explain everything

[lyric nymph]

fik tb3tli 2msli

[spark breach]

Ex?

One sec

[spark breach]

@lyric nymph u learn math in English?

[real rose]

!occupied

[trim jolt]

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).

[spark breach]

The guy that gonna help me got offline i think

[lyric nymph]

Yes

[spark breach]

Hmmm

Did u see the pics

[lyric nymph]

Sorry but I gtg rn to eat I will be right back

Hl2 3ndi ftar

[spark breach]

Ok bro

Ramadan Mubarak

[lyric nymph]

3lyna w 3lykm nshallah

Ba3d lftar brj3lk

[trim jolt]

@spark breach Has your question been resolved?

[spark breach]

He's eating

[real rose]

What does it say

[spark breach]

No

[real rose]

?

[spark breach]

My question did not been solved

[real rose]

I'm trying to help

What does it say

[spark breach]

Aha sorry

The pics?

[real rose]

Yes

Number 9

[spark breach]

Let us have a follower f On the field (written in the picture), according to the follower, it is written when studying an end f when ∞+ We find it equal

@real rose

I hope u understand

[real rose]

Hmm

[spark breach]

Follower means f and f(x)

[spark breach]

Is it easy to solve this problem for you?

[real rose]

So they want $\lim_{x\to\infty}x-\sqrt{x}+\frac{1}{x}$?

[solid kiln]

mathisfun

[spark breach]

One sec

[spark breach]

Yes

My teacher teach me that i have to Hit the facilities and divide it@real rose

The facilities I mean by Kalashi after the root

[real rose]

Indeed you do

What do you get?

[spark breach]

I have problem with how to Hit a x on one

1/x

[real rose]

What do you mean

[lyric nymph]

rj3tlk @spark breach

[spark breach]

He's back @lyric nymph

كيبوردك عربي؟

[lyric nymph]

la2

[spark breach]

So let's go into the problem

[lyric nymph]

3m tfhm 3lyi mni7 bs 2ktb hek?

[spark breach]

I mean yeah

There's some numbers i don't what they mean

7= ح

5= خ

٢ ك

٣ عين

[lyric nymph]

2 أ

[spark breach]

انا حليت تمارين مشابهة لهاد بيطلع النهاية 0

[lyric nymph]

ma fi mshkli fini ehki blehn eza bdk

hek 2hsn?

[spark breach]

Bro talk like u want

That's more than enough

[lyric nymph]

alright

[spark breach]

U are helping me

[lyric nymph]

hon 2za jrbt t3wd

bytl3 m3k ∞-∞

[spark breach]

يب

حالة عدم تعيين

بدي اصلح

Fix it

[lyric nymph]

fa hl2 5od x

common factor

[spark breach]

That's why لازم اضرب بالمرافق وقسم عليه

هيك علمني الاستاذ

[spark breach]

One sec

اذا اخدت عامل مشترك من 1/x شو بضل@lyric nymph

ربع؟

[lyric nymph]

5od x 3aml mshtrk mn kl shi

la t3rf sho bisir b 1/x

sho lshi li 2za drbto b x by3tik 1/x?

ma 2nti lma te5d x 3aml mshtrk btkon 3m t2sm 3la x

[spark breach]

..n

Finally

[lyric nymph]

??

[spark breach]

Discord frozen me

Now I'm back

[lyric nymph]

ah no problem

[spark breach]

يعني بدو يصير ١/x على x

بصير بدي اضرب بمقلوب الكسر

[lyric nymph]

y3ni 2desh ?

[spark breach]

بصير x² right?

Discord is stupid why i have to turn vpn to send pics

هلق فكرت

اذا انا بدي اسحب عامل مشترك بروح ال x وبرجع ال x لمحلوا

لان بدي ارجع قسم عليه

[lyric nymph]

1/x^2

[spark breach]

لانو لازم اضرب بالمقلوب

[lyric nymph]

(1/x)/x=1/x^2

wl x sho btsir ?

[spark breach]

طيب رح ورجيك طريقة الاستاذ

[spark breach]

1

[lyric nymph]

w sqrt(x)?

[spark breach]

فيني هلق عوض اللانهاية

[spark breach]

There's -

Negative

[spark breach]

هي طريقتو

اضرب بالمرافق

بتصير مطابقة

مربع اشارة مربع

[spark breach]

@lyric nymph is ur way better?

Or this one

[lyric nymph]

bisir lsh8l 2twl

[spark breach]

8 = ?

[lyric nymph]

??

[spark breach]

ايا حرف

التمانة

[lyric nymph]

غ

[spark breach]

I don't understand the last word

أتول؟

تقول

؟

[lyric nymph]

2atwal

wait

[spark breach]

😂

Mani mt3od

[lyric nymph]

hay ltri2a ma btfidak

[lyric nymph]

basita 😂

[spark breach]

ليش

[lyric nymph]

l2no b3d ma todrob bdk trja3 te5od 3amil moshtarak

[spark breach]

بوصلني لعند عدد ع لانهاية صفر

[spark breach]

Loop

Or just extra work

[lyric nymph]

l'hospital rule ??

[spark breach]

طريقتك

انو دغري سحبت عامل مشترك

[lyric nymph]

2e

d8ri s7ab 3aml moshtrak

[spark breach]

هلق الاستاذ عامل لكل حالة عدم تعيين طريقة

[spark breach]

ايوا

[lyric nymph]

$x-\sqrt x+\frac 1x= x(1-\frac{\sqrt x}x+\frac 1{x^2})$

[spark breach]

Let me show u

[lyric nymph]

hl2 3wd ∞

[lyric nymph]

alright

[spark breach]

+infinite

لانو 0+0-1)+inf

+لانهاية اقوى شي

والباقي يهمل

[lyric nymph]

100%

[spark breach]

Aha

الاستاذ مقيدني بطرق معينة

[lyric nymph]

shift hay ltri2a 2sra3

[lyric nymph]

2ni 3rft 2sdk bhidik ltri2a

[spark breach]

اي كتير بحتاج هيك طرق لانو اتمتة هي السنة انا

[lyric nymph]

bs hwi jebrak tst3mla ?

[spark breach]

Can i talk to u in dm ?

[lyric nymph]

sure

[spark breach]

Ok I'm gonna message u there

[spark breach]

Somtimes

[lyric nymph]

well i would prefer if you ask here

because if i am not around

[spark breach]

Ok

[lyric nymph]

then someone else can help too

[spark breach]

Yeah u are right

I said it cuz u understand Arabic

Bro u made it easy

[lyric nymph]

yea i get your point, no problem you can message me whenever you want

[lyric nymph]

but also post your questions here at the same time for this reason

[spark breach]

علمني هو وقت شوف كوساين او ساين

[spark breach]

Yeah i will

يعني تطوعي المساعدة هون؟

[lyric nymph]

2e

[spark breach]

Nice

Wallah

[lyric nymph]

2e ktir mni7 hek klo bystfid

[spark breach]

اذا استفدت برد الاستفادة لما صير جامعة

[lyric nymph]

hon sho lmshkli ?

wen m3ali2

[spark breach]

Atani aktar mn tarika bs 3m dal insa kef hla

O m g discord

[bright quarry]

,rotate

[bright quarry]

i got you bro

[spark breach]

استعمل هي الطريقة

[spark breach]

Appreciate bro

[lyric nymph]

yoo tysm knief

[spark breach]

هية متل قواعد مثلثية صح ؟@lyric nymph

[lyric nymph]

tyb lek sho

[spark breach]

I'm all ears

[lyric nymph]

sho bt3rf 3n sin(x)?

kif fik t7sra ben r2men ?

[spark breach]

He's between -1 and 1

احاطة

[lyric nymph]

y3ni 0=<sin^2(x) =<?

[spark breach]

الاستاذ قال احاطة

بس هون ما بعرف اذا احاطة ولا لاء

[spark breach]

-1 < Sin x² < 1

Like that?

Or 0?

[lyric nymph]

tzakar 2no sin^2(x)=(sin(x))^2>=0

[spark breach]

0 and 1

[spark breach]

الحصر؟

[lyric nymph]

tyb hl2 $\lim_{x\to\infty}\sin^2x$ msh mwjod l2no $\sin^2(x)$ btdal tro7 w trja3 3la nfs l2r2am

[lyric nymph]

s7i7?

[spark breach]

I think

بالدائرة قصدك ؟

[lyric nymph]

lek hayda lbayen tba3 sin^2(x)

[spark breach]

Ok

[lyric nymph]

ma 3m yro7 3la ra2m m3yn

3am ydl yl3ab ben ktir 2r2am

[spark breach]

1

And 0

Like a loop

[lyric nymph]

bs fina n3rf 3no sh8li

2no 3m ydl =< 1

[spark breach]

Show hya

Yeah

[lyric nymph]

y3ni $\lim_{x\to\infty}\sin^2 x\leq 1$ sho ma kent $x\in\mathbb{R}$

[spark breach]

Aya kema?

For sure

مارح تطلع فوق ١

ومارح تنزل تحت ٠

[lyric nymph]

tyb

hl2 $\lim_{x\to\infty}(2x+\sin^2 x)=\lim_{x\to\infty}2x+\lim_{x\to\infty}\sin^2 x$

[lyric nymph]

hl2 st3ml hay

[spark breach]

اخد كل نهاية لحال

؟

[lyric nymph]

bs 2abl

[lyric nymph]

sta3ml hay

w 2ili sho bisir

[spark breach]

رح احصرها

للساين

دقيقة

[lyric nymph]

7sra ben 0 w 1

mtl ma knt 3m t2li

[spark breach]

سويت الحصر

عوض هلق ؟

[lyric nymph]

sho tl3 m3k l7sr

[spark breach]

النهاية

It's gonna be like that

[lyric nymph]

hl2 zid 2x

[spark breach]

ايوا كنت حل تمارين هيك انا

[lyric nymph]

ma 2nti bdk l7ad la 2x+sin^2(x) 3l -∞

[spark breach]

انو وصل شكل الحصر بلش من sin²x لوصل لشكل التمرين الاول

اضرب واجمع

[lyric nymph]

fa mn hon kif bisir l7sr la 2x+sin^2(x)??

[spark breach]

Wait

[lyric nymph]

ok

[spark breach]

Aza altarafen

طلعوا نفس الشي

[lyric nymph]

jweb l7ad tl3 nfs lshi ?

[spark breach]

I'm sending pic

[lyric nymph]

alright

[spark breach]

I think it's right

[lyric nymph]

almost

i missed something

[lyric nymph]

ntbh

[lyric nymph]

bdk 3l -∞

msh 3l ∞

[spark breach]

Ik

1+2x

[lyric nymph]

fa hon fi 8alat

[spark breach]

اشارة ال +2

(ما بتنضرب؟

[lyric nymph]

2e fa 3l -∞ sho bisir ?

2(-∞)=??

[spark breach]

-inf

No

+inf

Cuz if we × an positive number

The inf will change

Or what

[lyric nymph]

bs tdrob r2m > 0 w ra2m < 0 ljweb < 0

[spark breach]

Akeed

الرقم مالو قيمة

اذا هيك

[lyric nymph]

2>0 w -∞< 0

w ∞>0

[spark breach]

Nice

[lyric nymph]

2(-∞)=-∞ msh ∞

[spark breach]

Hmm

It's a big problem

[lyric nymph]

?

[spark breach]

لانو انا بحضر الاقسام بمنصة مشترك فيها و بحل ورا الاستاذ بس بعد فترة بطير كلشي

طريقة يلي انت عم تعلمني فيها افضل

[lyric nymph]

ahaa

[spark breach]

انا بحل كلشي تمارين بس ماعم بتعلم شي

[lyric nymph]

basita 3al tmrin bymshi l7al

[spark breach]

هاد غلطي

بجي ع نموذج بتفاجئ

لانو المبدأ انا مو فهمانوا

Do u have time to continue?

It's 2:07

[lyric nymph]

lezm traj3 lshar7 mni7

[lyric nymph]

2ni 3ndi ba3d bkir l2no 2ni msh b lbnen

[spark breach]

بدي بلش شرح الاشتقاق

[lyric nymph]

bs ba3d shway bdi ro7

[spark breach]

I thought ur in the middle east

[spark breach]

Okay then لحق شي تمرين

هون حصر مو

[lyric nymph]

2e 2ni mn lbnen bs hla2 btlt 3aysh honik

[spark breach]

عرفت مغترب

[lyric nymph]

tyb hon bdk mokarb meyl

[spark breach]

Yeah

[lyric nymph]

mokarb meyl hwi 5at 3ndo mo3adali y=ax+b

[spark breach]

Do. I have to use f(x)-y

[lyric nymph]

w hyda lmokarb hon bdk ye 3l +∞

fa bdk $\lim_{x\to\infty}(f(x)-y)=0$

[lyric nymph]

s7i7?

[spark breach]

اذا نهاية الطرف اليسار صفر

ف معاناتها هاد المقارب

رح جربهم

واحد واحد

[lyric nymph]

2e fik t3ml hek

[spark breach]

0 = 0

A 😊

[lyric nymph]

kif tol3 m3k A?

A 3m y2ol y=-x

[spark breach]

قصدي a smile

[vagrant imp]

wth how are u typing arabic using english alphabets and numbers

[spark breach]

هلق بلشت حل

😂

[lyric nymph]

y3ni hay btsir $\lim_{x\to\infty}(f(x)-(-x))=\lim_{x\to\infty}(f(x)+x)$

[spark breach]

Only Arabs

Can do that

[lyric nymph]

hahahahah

magic

jk

[spark breach]

Ik bro

قصدي a 😊
A smile

[lyric nymph]

well if i have to explain that, then i would say that many arabs use this way, they use some numbers to replace some letter that have nothing similar in english alphabet

and there are many letters which have the same pronounciation so you can type them using english letters

[vagrant imp]

ohh makes sense

[spark breach]

ضربت الناقص دغري بال -x

ووحدت المقامات

فيني اخد المسيطر ع المسيطر

[lyric nymph]

only some alphabets are left without numbers which are not dont have the same pronounciation to any english letter but these letters differ a little from some other letters in pronounciation so context show what letter is meant to be written

[lyric nymph]

ok

[vagrant imp]

damn, I actually know enough arabic to read, but seeing it in english confused th out of me

[lyric nymph]

wait no you cant just do this

this works here for a reason

[spark breach]

الساين

Ik

[lyric nymph]

bs hon 3ndak sin(x)

[spark breach]

Ik

Kef bde a3mlha

احاطة؟

[lyric nymph]

ohh nice, well no problem if you are confused because it is a wierd way to type ngl

[spark breach]

I have to re learn the whole thing

[lyric nymph]

la2 msh drori

[spark breach]

Do u see it

[spark breach]

How

Is there a tutorial that explains how to solve like these problems

ولمين الاولوية

[lyric nymph]

lek sho

[spark breach]

Ayoa

[lyric nymph]

jrb 5od x^2 3aml moshtrk mn fo2

[spark breach]

K

[lyric nymph]

sin(x)/x^2→0 lma x→∞

w r7 ytl3 m3k jweb l7ad hwi ∞ 2za 2a5dt y=-x mtl A

ya3ni y=-x msh mokarb meyl

bs tjrba btshof

2ni lezm ro7 hl2

r7 2lk sho ljweb bas t7awl w ma ymshi l7al shofo

[spark breach]

Ok bro I hope u get the help u did gave me in return

[lyric nymph]

w s2al 8yri 2za bdk

||y=x||

[spark breach]

I'm gonna sleep but ur way is beautiful

Of explaing

[austere sail]

Help fr pls

[spark breach]

انت عرفت بكم ثانية؟

[spark breach]

Go to help 31 and say ur problem

[hybrid field]

use a channel that isn't occupied

[spark breach]

I'm gonna go

[lyric nymph]

lma t5ls ktob .close

[trim jolt]

@spark breach Has your question been resolved?

[trim jolt]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[low cloud]

this is what i tried to put in and it said it was wrong

[whole coral]

They want the actual numerical value of the limit, not the expression for L

[low cloud]

oh so they want me to fully solve it first

okay am i at least on the right track? like does that look like what i should be doing?

[whole coral]

Yep, simplify what you have and keep going

[low cloud]

okay so the squarroot and the n exponent cancel and becasue of the absolute values the negative goes away right so im left with 3/arctan(n)

cool but i dont know how to get the limit of arctan🫣

[whole coral]

How dare you not know grrrr

Have you seen a graph of arctan?

[low cloud]

umm i know the regular tangent graph but i cant think of arctan without looking it up

[whole coral]

That's fair very naughty of you

I'll tell you that the limit of arctan(n) as n goes to infinity is pi/2, just this once I'll let you off

(it is worth remembering, or at least having to hand, some of these limits )

[low cloud]

okay i will put it in my important things to go over before exam notes!

okay its there! so the denominator is pi/2 and the numerator is 3 so the whole thing equals 6/pi?

[whole coral]

Yep, and that's your L well done

[low cloud]

and this is grater than 1 so its divergent right

[whole coral]

Yep to both

[low cloud]

okay sick i dont want to be too confident but i think im getting a hang of it

also i say this but i have more homework questions to do so who knows if i actually know what im doing

[whole coral]

You are getting the hang of it, it's always a matter of practice keep trying the rest and see how they go, you learn through doing

And you have here if you get stuck of course, we're happy to help you

[low cloud]

ya honestly this discord has saved my life!

[whole coral]

I'm happy it has, always great to have somewhere (and of course you'll see me lurking about with my cat reacts, especially the SCsnuggle one )

[low cloud]

oh no im already stuck

what do i do here since the (n+1) doesnt have an n exponent

[whole coral]

Quite a good one and while it doesn't have an n exponent by itself, you do get (n + 1)^{1/n}, and that has limit 1, similar to why n^{1/n} has limit 1

[low cloud]

okay sick this is also going in the exam notes haha

also for the denominator does the exponent just become 2?

[whole coral]

Yep it does

[low cloud]

great just wanted to make sure!

[low cloud]

okay how about here? what is the next step? (also i just realized hat i forgot the absolute value so i added them)

[whole coral]

You're gonna get something quite similar to the last one, in terms of working it out

[low cloud]

so like this?

so the denominator goes to 1 then right

but i have no idea what the 1/(2n) will do

[whole coral]

How about if I write it as $(n^{1/n})^{1/2}$, does that make it better?

[solid kiln]

@whole coral

[low cloud]

oh so then its just the square root of 1 which is just 1

so this test didnt tell us anything

[whole coral]

Correct, it doesn't

We don't know if it converges or not from that test

[low cloud]

oh no but thats not an allowed answer for this question

did i make a mistake?

[whole coral]

Could you show what it says, how it's set up?

[low cloud]

ya this is number 3

[whole coral]

Oh, should've shown that I was thinking we had to use root test or something

[low cloud]

but this is the root test section so i think we do

[whole coral]

I don't think so for one, root test can be inconclusive (as it is here), and converging immediately gives you absolute convergence by the design of the test

I'm guessing the idea is you use everything you know, usually if you have to use a certain test they say something along the lines of "even if you know it converges by some other method, still state N/A if you can't apply [the relevant test]"

[low cloud]

okay so i need to think of another test to do

[whole coral]

Yep (it won't be ratio test, because that would also be inconclusive)

Do you have any ideas?

[low cloud]

the alternating series test?

[whole coral]

A very good idea, but be a tiny bit careful I'll let you do the work first though

(can you guess why I'm saying to be careful? )

[low cloud]

because the limit needt so be 0?

[whole coral]

That isn't it that is a condition of the AST of course

Would you like to know now or later? (you'll still be using the AST regardless in this case )

[low cloud]

now, but im scared

[whole coral]

Don't be scared, you'll be alright

[smoky wadi]

what website is yhis

[whole coral]

The reason to be careful is that if you pass the conditons for the AST, that tells you that you converge at least conditionally, but you could actually end up converging absolutely and that's masked

[low cloud]

its called webwork

[whole coral]

e.g. if you had the series of (-1)^n/n^2, that actually meets the AST conditions, but converges absolutely of course

[low cloud]

wait so this one could still be absolutely convergent?

[smoky wadi]

are u guys on the first one

[whole coral]

It could be, you'd have to check whether it is or not (spoiler, here, ||it isn't||)

[low cloud]

and they way i would check would be the absolutly value test

[whole coral]

Yep, take absolute values and see the series you're working with

For now though, try the AST and see what happens

[low cloud]

ahh im stuck isnt the limit of sgrt(n) just infinity?

[whole coral]

It is, but be a bit careful!

[low cloud]

is the denominator 1?

[whole coral]

Well, more that the limit of the denominator as is is also infinity ♾️

(I have to head out for a while now )

[low cloud]

okay thank you!

[viscid flower]

which one are you on

[low cloud]

number 3 on this one

[low cloud]

but i actually just finished i did l'hospitals and then got 0 so its conditionally convergent

[smoky wadi]

sqrt n/n+5 is roughly equals to sart n/n

now that you know that try finding that limit considering that the top is n^1/2 and the bottom is n^1

[low cloud]

thanks i just finished thisquestion now im onto the next section

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[solid kiln]

w

[versed jasper]

are you sure it's convergent

well still

is the integral of sin(x) convergent or divergent

oh

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[fair wharf]

someone please help me with this. ive been given the answer yet i have no idea how they even got there

[low gazelle]

What have u tried

[fair wharf]

i though we would be finding f(x) then (fg(x)) but then the answer is apparently this

apparently they are seperate questions which makes me lost. i have no idea where they are even getting the y from

[low gazelle]

y is just a name for a variable. You can replace it with x if it looks better to you

There are 2 parts to this question, breaking down the function into a composition of simple functions, then finding the domain.

Let’s focus just on breaking down the function for the first part.

You can see two things, a cosine and a square root, so if you want to write it as a composition like f(g(x) you can try making f(x) = cosx or sqrtx then make g(x) the other one. You can test both to see which works

In general f(x) is going to be the “outer” operation and g(x) the “inner”in this case the cosine is inside the square root so it makes more sense for it to be g(x)

[fair wharf]

oh so they have already combined the functions and i needed to uncombine them to make 2

[low gazelle]

Yeah

[fair wharf]

and since you cant have a negative under a root and cos already has set values

[low gazelle]

Yeah for the domain part you need to find everywhere cosx isnt negative

[fair wharf]

yeah so for the other one i could use square root of x then 4-x^2 which means again any values that arent negative

[low gazelle]

Yeah

[fair wharf]

thanks heaps i get it now 😄

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[dapper oxide]

"find the volume of the solid bounded by z = 4-x^2-y^2 in the first octant", i get the level curve to be x^2 + y^2 = 4, does that mean the region is x^2 + y^2 <= 4? or can it be something else?

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[chilly crypt]

how do i get the null and alternate hypothesis of this? ive been trying for a while now but i still dont know how to...

[chilly crypt]

our teacher wants us to use symbolss

[sacred sapphire]

is this correlation/regression?

!xy

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@chilly crypt Has your question been resolved?

[chilly crypt]

hiii sorry!

waitt

its hypothesis testing we still havent gone to the correlation part

[sacred sapphire]

hypothesis testing on?

[chilly crypt]

wait holdd onnn

i will sendd

[chilly crypt]

Basically we were asked to do like a small survey research

a. Variable 1 (Independent): Amount of time spent studying
b. Variable 2 (Dependent): Grades of G11 students in General Mathematics

and theennn i collected 30 people and also did our final pt which was abt the normal curveee

so thennn now my teacher asked us to start hypothesis testing. ive already gotten my level of significance

but not my null and alternativeee

[chilly crypt]

these are the values from the survey

i actually have a null and alternatiev hypothesis but i asked my teacher if it was correct and she said not rlly bcs shes looking for symbolss (claim)

[sacred sapphire]

yeah the claim

which is the parameter you're trying to test

[chilly crypt]

Hₒ = There is no significant difference between the independent and dependent variable; there is no relationship between two parameters. The amount of time spent studying does not affect the grades of G11 students in General Mathematics.

Hₐ = There is significant difference / change / effect between the independent and dependent variable. There is a relationship between a parameter and specific value. The amount of time spent studying affects the grades of G11 students in General Mathematics.

this was what i had

[chilly crypt]

yesyes

but idk how to get the null and alternatiev hypo bcs theres 2 means T_T haha

[sacred sapphire]

i think you can only test their correlation really

[chilly crypt]

ohhh howw?

[sacred sapphire]

actually have you learnt about regression before?

[chilly crypt]

nooo we only started hypothesis testing so not a single person in our class knows what to do hasuahsh

i tried to find my teacher to ask her but she wasnt theree

[sacred sapphire]

hmm ok

[chilly crypt]

thankuu is my best approach looking for the colrrelationn?

[sacred sapphire]

its either regression or correlation

[chilly crypt]

okaiiii thankzzzzz ima tryyyy

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[empty tulip]

answer should be 4units^2