help-0

[jovial breach]

interesting analysis problem sir

[rich lava]

[crisp grove]

that's calc-0 probably

[jovial breach]

thats middle school

[crisp grove]

anyway 200 is right

[vale wigeon]

i think vikkstar123 is about to get b&

[lusty pewter]

what no

surely not

[crisp grove]

also to get height at midway put x=100

[vale ginkgo]

you can see by the above interaction theyre kind of a troll

[lusty pewter]

im not

i swear

i gave right answer

[sly mantle]

those pings were unneeded

[jovial breach]

they basically gave you how the rocket's path looks like , as well as giving you everything else the question asks for

[crisp grove]

[jovial breach]

just by describing it differently

use epsilon delta

strict proof for that

[crisp grove]

or calculus of variations

[vale ginkgo]

or gauge theory

[crisp grove]

or set theory

[magic geyser]

or topology

[crisp grove]

and rediscover R

[lusty pewter]

oh i speak english only sorry

[sly mantle]

let's not give troll suggestions

[vale ginkgo]

hi dad

[sly mantle]

hi dan

[lusty pewter]

dude surely u help u clearly have time on ur hands

for like 30mins

[jovial breach]

i suggest you use ergodic theory knowledge to solve that

[lusty pewter]

nah man im 14

[vale ginkgo]

30 mins

[rare temple]

[knotty jolt]

bruh

[crisp grove]

that dp doesn't look 14 tho

[lusty pewter]

whats dp

[urban inlet]

why the ping

[jovial breach]

they pinged analysis for a middle school problem

back to our daily lives

[lusty pewter]

lol 500 people just came here started spitting out stuff like Ergodic Theory to my middle school question and i still didnt get answer 😦

[urban inlet]

git gud

[vale ginkgo]

well. next time. dont ping those roles

[magic geyser]

man is 14 and has full beard and mustache

[urban lily]

is there a rule saying that each derivative has subtracted one power of the variable? if that makes sense

[lusty pewter]

my slowmode is an entire minute

[vale ginkgo]

thats called the power rule

[magic geyser]

wow

[urban lily]

bro nah thats the basic one I want something more general but i cant explain how i mean yk

[crisp grove]

2m fornFS

[vale ginkgo]

if you want that for polynomials, you can use the power rule and linearity

[tender harness]

@lusty pewter just put the height y = 0 when it lands after traveling, and x must be not equals to 0 since it has travelled some distance, now solve the quadratic equation 😅 don't ping analysis haha

[lusty pewter]

what sort of questions do people with the Analysis role assemble for??????

[magic geyser]

analysis problems

[tame falcon]

Problems concerning mathematical analysis, the kind you see in #advanced-analysis

Suffice it to say that pinging any role/user other than Helpers(again, in conformity with #❓how-to-get-help ) is not recommended

[crisp grove]

prove that 1+1=2

[magic geyser]

#chill

[sly mantle]

at this point vikk's question got buried, feel free to repost

everyone else move on

[lusty pewter]

lol even i know this, someone give me perms to chat in the analysis channel

[tame falcon]

Can we open the channel for questions now?

Casual chitchat can move to #chill

[sly mantle]

i set slowmode to 30s

[crisp grove]

wasn't talking about first grade maths, do it with succ function

[sly mantle]

you were warned to move on

[neon kraken]

bruh weres the ping from

[magic geyser]

#chill

[valid pier]

pls help

[magic geyser]

try to make a drawing

[valid pier]

i am not able to can You make the drawing i will be able to do the rest

[flat vale]

bruh just draw a triangle

[valid pier]

i am not able to get where to make d

[cloud valley]

https://tenor.com/view/angry-andre-sitolini-engetic-butthurt-gif-14985012

[tender star]

how do you solve questions like this?

[oak chasm]

@tender star What can you do to x/12 to change it into x?

[tender star]

idk

[oak chasm]

OK, do you know about cancelling with fractions?

[tender star]

no

sorry I suck at algebra

[golden nymph]

Why is slowmode enabled here

[tender star]

idk it's annoying

[alpine sable]

how to solve?

[oak chasm]

@alpine sable Sorry, channel is busy.

@tender star OK, you have 12 on the bottom. If you have 12 on the top, you can cancel the 12s.

[tender star]

yeah

[ocean seal]

Chai T. Rex

[oak chasm]

So, to get something on the top of a fraction, you multiply the fraction by what you want to put on the top.

[tender star]

yeah

[oak chasm]

So, you multiply x/12 by 12 to get x because then the 12s cancel. Now with equations (= sign in it), you do the same thing to both sides.

[tender star]

ok?

[oak chasm]

So, you multiply both sides by 12. On the left, you'll get x because the 12s cancel. On the right, you'll get 12 · 15:

x/12 = 15
12x/12 = 12 · 15
x = 12 · 15

See how I multiplied both sides by 12?

[tender star]

yeah

[oak chasm]

OK, now what's 12 · 15?

[tender star]

180

[oak chasm]

OK, so we got this:

x = 180

Now we can check our answer. Here's how. Fill in x in your original equation with (180) in parentheses.

x/12 = 15
(180)/12 = 15

Now, is (180)/12 equal to 15? Use a calculator or do it on paper to find out.

If it is equal to 15, 180 is the right answer.

[edgy mauve]

Can i get some help ?

if x = 3-√3^2 find valua of x^2 + 1/x^2

[tender star]

I don't get it😅

[oak chasm]

@edgy mauve Sorry, channel is busy.

[edgy mauve]

Oh ok 🙁

[oak chasm]

@tender star Where are you stuck?

[tender star]

uh I'm just confused which step is which

wait nvm I figured it out
It is 15, I'm right

[oak chasm]

OK, step 1 is to write the equation you were given.

x/12 = 15

Step 2 is to fill in all of the xs with our solution in parentheses. Our solution is x = 180, so we fill in (180) for all xs.

(180)/12 = 15

Then we do the math on both sides and see if the sides end up equal.

[tender star]

180 divided by 12 is 15

but then whats on top tho

[oak chasm]

Right! So, 180 is what x is.

[tender star]

so its 180

[oak chasm]

Yes. We solved it and checked that it's correct.

[tender star]

yes

thx so much for the help

[oak chasm]

You're welcome.

[ember token]

I need help with conditional probability:
In connection with the roll of a single fair die.

a. State by extension the events

E: the roll is even
T: the roll is 2
O: the roll is 1

b. Determine
i. The probability that the roll is even.
ii. The probability that the roll is even, given that it is not a two.
iii. The probability that the roll is even, given that it is not a one.

The formula would be P(AnB)/P(B)=P(AIB)

The problem is that I don't know how to find P(AnB)

[oak chasm]

@ember token Given works like this. a given b means that b is the entire set of things you can consider.

Probability that the roll is even given that it is not a one means you can consider {2, 3, 4, 5, 6} as the possible die rolls.

So, how many of those are even? How many are there in total? Divide.

[ember token]

I already did the first part

[oak chasm]

If you want to use that formula, P(even roll n roll not a one), you get all the things that satisfy both even and not a one.

[ember token]

E= 2,4,6
T= 2
O= 1

[oak chasm]

Which rolls satisfy both conditions?

[ember token]

Wouldn't that be: P(EITc)

[oak chasm]

You did not ask how to do that. You asked how to do P(A n B).

How many outcomes satisfy both A and B?

[ember token]

Are we taking about the first question?

Of b

[oak chasm]

This question.

[ember token]

P(AnB) can be found if the event is independent or dependent. But it doesn't apply to conditional

[oak chasm]

I don't care.

To find P(A n B), you get the count of events that satisfy both A and B. Then you divide by the count of total events.

[ember token]

You count the events that are sharing with a and b?

If not they are mutually exclusive right?

[oak chasm]

No, you count the events that satisfy both A and B. For example, P(even n not 1) has {2, 4, 6} since 2 is both even and not 1, 4 is both even and not 1, 6 is both even and not 1.

I don't really care if they're mutually exclusive or not.

There are three events that satisfy both conditions. There are six events in total. 3/6 is 1/2, so P(even n not 1) = 1/2.

[ember token]

Yes

The thing is the second question of b

That's the one im having trouble with

[oak chasm]

What is P(even n not 2)?

[ember token]

{4,6}

[oak chasm]

How many events in total?

[ember token]

2

[oak chasm]

No, in total, not matching.

[ember token]

1?

[oak chasm]

When you roll a die, what events can you get?

[vale wigeon]

chai you may be confusing outcomes vs events

[ember token]

E{2,4,6}
T{2}
O{1}

[oak chasm]

So you can't possibly roll a 3?

[ember token]

Possible outcome: 1,2,3,4,5,6

[oak chasm]

Right, so there are 6 outcomes in total.

[ember token]

Yes

[oak chasm]

There are 2 that fit both conditions.
So, P(even n not 2) = 2/6

What's P(not 2)?

[ember token]

P(T complement)= 1/6

I think

[oak chasm]

No.

How many outcomes aren't 2?

[ember token]

Oh wait lol

I got confused

5/6

For some reason I only counted 2

[oak chasm]

OK, so P(even | not 2) = P(even n not 2)/P(not 2) = (2/6)/(5/6)

Does that make sense so far?

[ember token]

So

2/5?

[oak chasm]

Yes.

OK, a sometimes quicker way is to take the part after the | and make that the universe (all outcomes).

not 2: {1, 3, 4, 5, 6}

evens in that: {4, 6}

2/5

[ember token]

So when we say given that is not two we subtract the two from E?

That makes sense!

Although I have a problem

The answer our teacher gave us is 2/3

Not 2/5

[oak chasm]

That might be their answer for i, not ii.

No, it doesn't work there either.

You should ask them about it. They may have made an error.

[ember token]

i= 1/2
Ii= 2/3

iii= 3/5

[oak chasm]

iii is correct.

not a one: {2, 3, 4, 5, 6}
evens in that: {2, 4, 6}
3/5

P(even n not 1) = 3/6
P(not 1) = 5/6
P(even n not 1)/P(not 1) = (3/6)/(5/6) = 3/5
P(even | not 1) = 3/5

So either way you do it, it's 3/5.

[ember token]

So E without 2 is P(TcnE)?

[oak chasm]

Yes.

[ember token]

At the first time I thought you needed to multiply

E and Tc

[oak chasm]

No, that's only if you know they're independent.

If you don't know that, you count the outcomes that are in both E and T^c and divide by the total outcomes.

[ember token]

This question now makes a lot of sense now

My god

[ember token]

Wait, since we don't count the 2 here, wouldn't E be 2/5

[oak chasm]

That's what (2/6)/(5/6) is .

There are two ways of calculating it.

Reducing the total outcomes:

not 2: {1, 3, 4, 5, 6}
evens in that: {4, 6}
2/5

The other one is the formula:
P(even | not 2) = P(even n not 2)/P(not 2)
P(even | not 2) = (2/6)/(5/6) = 2/5

Do the two ways make sense?

[ember token]

Ah

Yes

I think reducing the total outcomes is easier

Less confusing

Now everything is clearer

[oak chasm]

You should know both ways. Sometimes the reducing total outcomes method can't be used.

[ember token]

It was that simple lol

[oak chasm]

Like some problems give you P(A n B) and P(B) and want you to give them P(A | B).

[ember token]

Find P(AIB)?

Didn't we do that?

[oak chasm]

Yes, but I mean that in future problems they may not give you enough information to know what outcomes there are.

[ember token]

Ohhh

[oak chasm]

They may only give you P(A n B) and P(B) and expect you to know how to get P(A | B).

[ember token]

Ok

Thx anyway

[oak chasm]

No problem.

[ember token]

[dim acorn]

pls help

[arctic steeple]

Im not even mad about the ping the following conversation was hilarious

[rigid smelt]

what have you tried?

[dim acorn]

nothing

it was in my sqp

[rigid smelt]

?

[dim acorn]

sample question paper

[rigid smelt]

ok lets try a shot in the dark

lets inspect the dneominator a bit

ok so how can we make 1+2log_{a^2 * b^2}(c) looks a bit less intimidating

hint: change of base

[dim acorn]

I have no clue

[rigid smelt]

do you know the change of base identity?

[dim acorn]

no

its higher level maths for me

i havent done logarithms

[rigid smelt]

then i think you should look over it

because this question require some knowledge of logarithms

[silk umbra]

If I am intruding please forgive me -- I am just not sure. where I went wrong here and would like some help if possible 🙂

[ocean seal]

waler

[silk umbra]

Ohhhhhhh

LOL I missed that thank you

Makes it a lot easier

[alpine sable]

hi! may i ask how i would go about this question? i completely forgot how to solve this

[frigid stream]

@alpine sable Hint: What are f(0), g(0) and h(0)?

[alpine sable]

okayokay, so i got 6, 7766, and - 1/7766. i assume you just plug in x?

so itd be answer 2?

[frigid stream]

🙂

[karmic dew]

anyone use magic hexagon or find it useful?

[alpine sable]

no

[frigid stream]

https://tenor.com/view/cat-gif-22200253

[fiery berry]

I know the big circle is 3

what is the small one

[frigid stream]

The big circle is a 3? I didn't know a circle was the number 3

[alpine sable]

is the answer B?

[fiery berry]

meant value

[wary stream]

There's online derivative calculators that you can use to check your answers

[alpine sable]

they dont give the ans in the options

[wary stream]

Then you just simplify

[fiery berry]

<@&286206848099549185>

[whole herald]

My drawing is terrible

But I hope you get it

Looking to the AEO triangle we know that:

$3^2 + 4^2 = (h-3)^2$

[ocean seal]

kvictor

[whole herald]

as it is a 3, 4, 5 triangle we know that h-3 = 5

so h = 8

And now you can apply some similar triangles to ADO' and AEO

they're similar

so we have:

$\frac{3}{r} = \frac{h-3}{h-6-r}$

[ocean seal]

kvictor

[whole herald]

And then you can find r

@fiery berry if you have any doubt I'll help you with that

[alpine sable]

guys how to solve this

can someone help me solve this

[drowsy root]

Please Help me with this hard to answer

[reef urchin]

have u learnt this before or what have u tried? can go to #help-8

[alpine sable]

The picture isn't clear for me

No nitro:(

[reef urchin]

use a diff channel

use a diff channel to ask ur q

[cursive phoenix]

is there a changing the subject channel?

[vale wigeon]

what?

[cursive phoenix]

stuff like this but a little more advanced

[vale wigeon]

are you referring to exercises that instruct you to "make <variable> the subject"

if so, that sounds like algebra to me

[cursive phoenix]

sry i didnt send the full pic

ik how to do this but idk the more advanced stuff

[vale wigeon]

are you referring to exercises that instruct you to "make <variable> the subject"

so that's a yes

[cursive phoenix]

ye

[vale wigeon]

then i've already answered your question

[cursive phoenix]

k

umm

let me type the one im stuck on

y=x/x-5

[vale wigeon]

$y = \frac{x}{x-5}$

[ocean seal]

Ann

[vale wigeon]

did you mean this?

[cursive phoenix]

ye

[vale wigeon]

that's more properly written in plaintext as y = x/(x-5).

parentheses are important.

[cursive phoenix]

right

ill remember for next time

[vale wigeon]

so how much progress have you made on this

[cursive phoenix]

one sec

lemme send it

im not sure if im on the right track

[vale wigeon]

you've gone in circles a little

like, nothing you've done here is illegal (except for writing y5 instead of 5y, which is just a little weird)

you seem to have lost sight of your goal somewhat

[cursive phoenix]

oh i forgot number then letter

[vale wigeon]

your goal seems to be to make x the subject

[cursive phoenix]

mhm

yes

[vale wigeon]

so why not shuffle some terms around to arrive at yx - x = 5y

now all the x's are on one side

[cursive phoenix]

k

lemme find a way to do that so it aint cheating

got it

up to that point

[scenic wind]

x = -4 or x = 6

[vale wigeon]

@scenic wind do not give out answers.

[cursive phoenix]

thats not the point of learning

[scenic wind]

Sorry

[cursive phoenix]

good intentions wrong way

[vale wigeon]

it even says that in our rules

rule 7 to be more specific

[lone heart]

From

#❓how-to-get-help

Rule 7

When asking for help, do not insist on getting just the answer; we are here to help you learn, not cheat. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.

[cursive phoenix]

is there anything else to do or would that give me the answer to easily

[vale wigeon]

there are some steps left to do, yes.

[cursive phoenix]

k

[vale wigeon]

i mean, i've seen proof of work from your end, so it's much less of a concern if i were to disclose the answer

[cursive phoenix]

no

pls dont

[vale wigeon]

i'm not going to.

[cursive phoenix]

i shouldnt sheat

cheat

ty for ur help

[vale wigeon]

if only more people had the same attitude as you.

[scenic wind]

Same idea for second one

[gaunt mulch]

what did you guys use to get good at math?

[cursive phoenix]

practice

practice gets u good at anything if u put in enough effort

[gaunt mulch]

ok

[vale wigeon]

miss coder, giving out full solutions is just as bad as giving away answers...

[gaunt mulch]

thanks!

[cursive phoenix]

np

[scenic wind]

Sorry am an iddiot

[cursive phoenix]

well dont say that if u can solve stuff

[vale wigeon]

you're not an idiot you just didn't listen to me the first time i said it

whether accidentally or on purpose i cannot say, but listen to me you did not

[scenic wind]

Sorry i miss read

[vague canopy]

hi

[fast steppe]

Question on 27. Am I doing it right

[alpine sable]

Yes But what do you mean by odd.

[scenic wind]

Like this

[fast steppe]

Odd degree

Oh did I interput the q

[vale wigeon]

urgh

please do not make me repeat myself

[scenic wind]

what's urgh

?

english is not my first language sorry

[gray isle]

urgh is the sound of cringe

[scenic wind]

what cringe?

you mean orange?

[alpine sable]

Which is creepy in sense.

[scenic wind]

creepy

like scary

like ghost

[alpine sable]

Nah, weird (strange)

[scenic wind]

oh

i see

wait

am not strange 😭

am only 14

[vale wigeon]

i'm frustrated

that's what my "urgh" meant

[scenic wind]

sorry don't be sad

[vale wigeon]

sad ≠ frustrated.

what is your native language?

[scenic wind]

arbic

[alpine sable]

Whatever Guys answer to @fast steppe

[scenic wind]

&arabic&

my english is so bad

😦

[vale wigeon]

https://en.wiktionary.org/wiki/إحباط#Arabic

this is the word for "frustration"

er

إحباط

[scenic wind]

sorry

i just try help

people because people help me all the time so i want to return favour

[fast steppe]

I shouldn't be involved in this but i think this can be carried to the general

[scenic wind]

good point

[fast steppe]

Thanks i moved my question to #help-6

[alpine sable]

can you simplify $\frac{2n^2}{n^3+3}$ ?

[ocean seal]

sanjay

[fringe robin]

nope

[alpine sable]

fk

[fringe robin]

what do you mean simplify ...?

[alpine sable]

I need to solve $\left|\frac{2n^2}{n^3+3}-0\right| < \epsilon$ for n

[ocean seal]

sanjay

[vale wigeon]

is this for the purposes of showing 2n^2/(n^3+3) -> 0 as n -> +∞

[alpine sable]

yeah..

[vale wigeon]

then no you don't need to solve it for n

[alpine sable]

well I think abbott asks to?

They want find that N

Right?

yeah

[vale wigeon]

you don't need the perfect N

just one that's good enough

[alpine sable]

I find that, then let N > (what I find)

and n >= N

[vale wigeon]

and here you can observe that $\frac{2n^2}{n^3 + 3} \leq \frac{2n^2}{n^3} = \frac{2}{n}$

[ocean seal]

Ann

[alpine sable]

So(( 2n^2)/(n^3+3))<2n^2/n^3

Who pinged

[vale wigeon]

so you can just let N = 2/epsilon, rounded up if you wish for it to be an integer,

and your epsilon-N proof will work

[alpine sable]

oh

So I could let N be any natural number such that N > 2/n?

but why?

[vale wigeon]

?? no thats not what i said...

[alpine sable]

uh, so this is the template he has in the book

I want to prove that

[vale wigeon]

yeah, and i'm telling you an easy way to choose N

in the derivation of the inequality, you will have the following:

take $N = \frac{2}{\ep}$, then for all $n \geq N$ we have $$\absv{\frac{2n^2}{n^3+3} - 0} = \frac{2n^2}{n^3+3} \leq \frac{2}{n} \leq \frac{2}{2/\ep} = \ep$$

if you want strict inequalities you can take N = 2/ε + 1 or something

[ocean seal]

Ann

[vale wigeon]

or to put it another way, the choice of N = 2/ε is motivated by wanting to make the inequality 2/n < ε work, which itself is motivated by being the missing link between the inequality chain i showed above (2n^2/(n^3 + 3) ≤ 2n^2/n^3 = 2/n) and epsilon

[alpine sable]

humm

and in fact 2/(2/epsilon+1) < 2/(2/epsilon)

oh no

it isn0t

but I see the point

its weird, from the theory I didn't get that

[sly mantle]

we can get a strict ineq by using archimedean property to guarantee the existence of N where N>2/ep

[vale wigeon]

ceil(2/ep)+1

tbh

[alpine sable]

Also, isn't $\frac{2n^2}{n^3+3} < \frac{2n^2}{n^3}$ ?

[ocean seal]

sanjay

[quaint trout]

Ann said so right here

[alpine sable]

indeed

[sly mantle]

yes but not much care was taken to establish a strict ineq

[alpine sable]

I am sorry, wdym?

[quaint trout]

Are you asking why Ann said <= instead of <?

[sly mantle]

a=<b if a<b or a=b, so it's ok to write the above strict ineq as a nonstrict

@tacit epoch use an unoccupied channel

[tacit epoch]

Isn't this unoccupied?

0 questions

[alpine sable]

Noo!!

[vale wigeon]

ha ha ha. very funny.

[sly mantle]

no that's the name of the channel

[tacit epoch]

Then how can I know if the channel

[vale wigeon]

it is strict but i find myself not caring enough to check all my ≤'s for strictness in contexts where it doesn't matter.

[tacit epoch]

Is occupied or no

[sly mantle]

usually by seeing if there's an ongoing convo

[alpine sable]

Also

[vale wigeon]

from experience if you need a strict ineq it's probably for a very obvious reason, such as not wanting something you divide by to be zero

but if you don't need a strict ineq and just need to bound something it's fine to write ≤ no matter if equality can actually happen or not

[alpine sable]

I just noticed something Ann, maybe it was what you were saying

that when I go from 2n^2/(n^3+3) to 2n^2/n^3

[vale wigeon]

parentheses

2n^2/(n^3+3)

but yes, continue?

[alpine sable]

that 2n^2/n^3 isn't bigger than epsilon?

why isn't epsilon there?

[sly mantle]

it's not immediately clear the preceding expression is <ep

[alpine sable]

but it is a possibility?

[sly mantle]

not just a possibility but an established fact

[vale wigeon]

@nocturne sorrel channel busy please move

[sly mantle]

how long a string of ineqs you need to show |x_n-x|<ep doesn't matter

what DOES matter is that each ineq clearly leads to the next

[alpine sable]

but does 2/n < epsilon follows clearly?

[sly mantle]

recall the conditions on N & n

[alpine sable]

Hum

[sly mantle]

if we pick any $N$ st $N>\frac2\ep$ then let $n\ge N$

[ocean seal]

Dreadful Encore of Twisted Karma

[alpine sable]

I see

[sly mantle]

then 2/n<ep

[vale wigeon]

the choice of N = 2/ε is motivated by wanting to make the inequality 2/n < ε work

[alpine sable]

exatly! you said it

Is that something I should state in the proof?

[sly mantle]

very much so

otherwise that step in the chain of ineqs isn't guaranteed true

[alpine sable]

Indeed

Let me write it up

[vale wigeon]

what, the motivation thing?

no, that doesn't belong in the proof.

[alpine sable]

oh

[ocean seal]

sanjay
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[sly mantle]

the 'motivation' is scratchwork done on the side

[alpine sable]

so

[sly mantle]

very bad form

you wrote the ineq before N,n are introduced

[alpine sable]

I believe the string of inequalities can be left out?

[sly mantle]

entirely?

that'd leave |x_n-x|<ep insufficiently shown and wastes the last 30min of help

[bold mantle]

I need someone who can speak Spanish

Pls

Fluently

Pls

And English of course

Pls

[vale wigeon]

@bold mantle this channel is occupied, please move.

[sly mantle]

'observe' should be put before the ineq

[bold mantle]

Ok

[sly mantle]

also technically you didn't justify such N exists (recall archimedean property or ann's choice of N)

[alpine sable]

Well yeah for any real number x there's some n in N with x < n

[sly mantle]

mhm

[alpine sable]

Take $\epsilon>0$. Since $\frac{2}{\epsilon} \in \R$, according to the \textit{Archimedean Property} there's some $N \in \N$ with $N > \frac{2}{\epsilon}$. Assume $n \geq N$. Observe that $n > \frac{2}{\epsilon}$ implies that $\frac{2}{n} < \epsilon$. Note $$\left|\frac{2n^2}{n^3+3}-0\right| = \frac{2n^2}{n^3+3} < \frac{2n^2}{n^3} = \frac{2}{n} < \epsilon.$$Thus $\left|\frac{2n^2}{n^3+3}-0\right| < \epsilon$.

[ocean seal]

sanjay
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[sly mantle]

it'd be nice to conclude lim ..=0

[alpine sable]

Therefore by definition of convergence of a sequence, we deduce that lim(2n^2/(n^3+3)) = 0.

[sly mantle]

yes

[alpine sable]

this was instructive, thank you very much guys

get ready for some stupid questions i should know

Ø (⊂ or ∈) to {0}

former

[ocean seal]

sanjay

[wispy olive]

Why do we do this? Especially why do we do the underlined part? Can someone explain?

[alpine sable]

If: A and b are two sets, then this set {(x,y): x ∈ B, y∈ A}

former

[hollow merlin]

how to do part b

[tight locust]

(16+2p+2q)/(9+p) = 3
16 + 2p + 2q = 27+3p
16 + 2q = 27 + p
2q = 11 + p
p = 2q - 11

now you are given p<3

[fringe spindle]

honestly, i'm not entirely sure how they've done their explanation, i just remember you can parametrise pythagorean triples in the form a² - b², 2ab and a² + b², because (a² - b²)² + (2ab)² = (a² + b²)², so since you're given the hypotenuse, if i had to solve that problem, i would just try expressing 97 as a sum of 2 squares, seen as their aren't that many squares less than it, it makes the problem relatively easy (or at least easier than half the problems i've encountered before put it that way), just by trial and error i eventually found 97 = 9² + 4², so that's our values of a and b, a = 9, b = 4, a² - b² = 9² - 4² = 65 and 2ab = 72, exactly the same as given in the solution, just a different way of solving it.

[strong furnace]

(its called euclid's formula btw)

[hollow merlin]

oh so q < 7

wait and p also gotta be more than 0

q > 5.5

q = 6

eyyy

and if q = 6 p is ofc 1

damn thx

[alpine sable]

How many possible 4 character combinations are there? (using 0 - 9 and a -z)
i couldnt figure out whether it would be:

  26 * 26 * 26 * 26 + 10
  26 * 26 * 26 * 26 * 10
  26 * 4 + 10
  26 * 4 * 10
  4 * 4 * 4 * 4 + 10
  4 * 4 * 4 * 4 * 10

Im really starting to doubt my own maths here

[crisp grove]

36⁴ assuming repetition is allowed

[alpine sable]

wdym by repetition?

[crisp grove]

'aaaa'

[alpine sable]

yes, tysm! 🙂

[crisp grove]

👍

[fervent anchor]

Someone ping me?

[dark granite]

Yea someone pinged the Analysis role a while back

It was about 8 hours ago

[wanton beacon]

Hi, question, so if I have say a function, like g(2) + 5[f(1)], how would I go about solving it?

[fervent anchor]

Oh ok

[alpine sable]

so what that basically means is that u plug in the number 2 for the function g(x) and plug in the number 1 for f(x)

u multiply the number u get from f(1) by 5 AND THEN add that to g(2)

if u can show us the functions i can help u a bit more in depth

[wanton beacon]

So

f(x)=-2x+7

And

g(x)=x^2

[alpine sable]

mk so plug in 1 into f(x) and 2 into g(x)

so for f(1)=-2(1)+7=5

[wanton beacon]

So f(x)=5

[alpine sable]

g(2)=2^2=4

mhm

and remember, its 5(f(1)), so its 5 times 5 or 25

[wanton beacon]

And g(x)=1

[alpine sable]

25+4=29

nope, because g(2)=2^2

so thats 4

[wanton beacon]

I meant 4 yeah

Ohh ok

I understand

[alpine sable]

yeah

so the answer is 29

[wanton beacon]

Right, yeah

Do you by any chance have time for maybe 1 more?

It reads 3[g(x)] + f(x)

But it uses the prior functions

@alpine sable

[alpine sable]

sure

so basically 3g(x)=3x^2, correct?

and f(x)=-2x+7

so u just add those 2 up

and get 3x^2-2x+7

lmk if its confusing

[wanton beacon]

So, did you multiply here? 3 * g * x?

[alpine sable]

yup

because it says 3(g(x))

so 3x^2

[wanton beacon]

Ohhh

I see

That makes a lot of sense

Thank you so much!

For your time & help

[alpine sable]

np

yo

trying to solve this problem

but this answer keeps getting marked as wrong

[magic geyser]

replace x with x+h

[alpine sable]

how i went about doing it was

i plugged it in

and i end up with this

and i simplify it

and i get this answer

of 5h+10x-3

am i missing something

[magic geyser]

let's see

[fervent anchor]

5x^2+5h^2+10hx-3x-3h+3

[magic geyser]

yes

[fervent anchor]

@alpine sable

[magic geyser]

it says only for f(x+h) not other parts

[magic geyser]

this is f(x+h)

[alpine sable]

yea no i ended up with that for f(x+h)

i understand that

[magic geyser]

how did u end up with that5

[fervent anchor]

yea thats what the ques is asking

[magic geyser]

yes

[fervent anchor]

For that blank

[alpine sable]

h

oh

i hate reading

my bad!

[harsh belfry]

Was asked to find the the limit if x->0

I think my goal here should be to get rid of the x in the numerator right?

I'm not sure really where to go with this question initially

What should I start doling?

[wispy sorrel]

simplify the numerator first and then get rid of the complex fraction

[harsh belfry]

Alright

I'm gonna try that out

Im just looking up how to eliminate the complex fraction right now.
I'm a bit rusty.

[fervent anchor]

Yup good luck👍

[amber marsh]

could someone show me working out for the arc lentgh

[fervent anchor]

-1/(25+5x)

[amber marsh]

i think im going wrong there

[harsh belfry]

Im having a hard time understanding how you got there

I'm assuming you multiplied the denominator by 5? @fervent anchor

[fervent anchor]

yh its actually-1/((5)*(5+x))
=-1/(25+5x) (ans)

[harsh belfry]

I feel real stupid tight now. By multiplying the denominator by 5 what does that do?

I'm so sorry that I don't understand

I'm still staring at my given function and not knowing how to include what you're saying

When looking at this in order to get rid of the fraction on the left

can you explain what you did?

@fervent anchor

[deft tiger]

Could i get some help in this?

How exactly do we find x = -2 as y = 10?

[fervent anchor]

just take lcm in the numerator
so
(5-(5+x))/(5*(5+x)) / x
= (5-5-x)/(25+5x) /x
= -x/ 25+5x *1/x
= -1/(25+5x)
This is the answer:) hope it helps.

@harsh belfry

[limpid snow]

how would i get the slope intercept form of a line with a sloope of -5 and the line passes throught (1,-3)

[alpine sable]

What do the triangles mean

Here’s the full equation

[limpid snow]

i belive thats called delta

[alpine sable]

What does it do

[limpid snow]

Uppercase delta (Δ) at most times means “change” or “the change” in maths. Consider an example, in which a variable x stands for the movement of an object. So, “Δx” means “the change in movement.” Scientists make use of this mathematical meaning of delta in various branches of science.

[alpine sable]

O

[limpid snow]

so in this case it means (the change) in y

[alpine sable]

Ohh

Okay

That kind of makes sense

[limpid snow]

explaining also why y2-y1/x2-x1=(the change in) in y / (the change in) x

8-4 is the change so its the Δ

[alpine sable]

Oh okay ty (:

[limpid snow]

yup np

[alpine sable]

I’m reviewing all of my math in a year for my exam in like a day or 2

I’m scared

And I still don’t know some units

[limpid snow]

bro i dont even know the simplist sh** dont worry youll be good

[alpine sable]

Lolllll

Wait in linear equations

Rise means go up and run means go right?

[limpid snow]

yea

rise over run

[alpine sable]

So if for example the y intercept was -2, and m was 5/1, you would rise (go up on the graph) 5 times and go to the right 1 time?

[alpine sable]

: D

[limpid snow]

yup but you would start doing that at -2

[alpine sable]

YEE

Lol why did that go into all caps

[limpid snow]

idk

[alpine sable]

When I think of rise I imagine jesus flying up along the graph

[limpid snow]

i image more of a hot air balloon...

but if it works it works

[alpine sable]

XD

wait a negitave rise means go down

And a negitave run means go left?

[limpid snow]

yup and yup

[alpine sable]

Okiiieieieieie Tysm

[limpid snow]

@alpine sable

[wary stream]

You should use parentheses when dealing with fractions like this because \verb|y2-y1/x2-x1| is read as $y_2 - \frac{y_1}{x_2} - x_1$ due to order of operations

[ocean seal]

dldh06

[limpid snow]

yeah sorry im not really a teacher more a student that was actually the first time i explained on here rather then asked

and the only reason i had knowledge on the subject was because i had to learn delta for engineering

[wary stream]

Still be cautious with typing fractions, because it can be interpreted in a way that you did not intend it to be

[limpid snow]

noted will do!

@wary stream as for writing a slope-intercept form of a line with a slope of -5 and passes through (1,-3) do you have any input for that? im still stuck there

[wary stream]

Point slope equation

[limpid snow]

yes but wouldnt i need 2 points?

[wary stream]

$y - y_1 = m(x - x_1)$

[ocean seal]

dldh06

[wary stream]

Nope, just the slope and a point

[limpid snow]

ahhhh i think im seeing it now

ive bein using the modified version and forgot it orginally sloved for y-y_1

[wary stream]

Or you could use the slope intercept form, $y = mx + b$ plug in the know values, and find b

[ocean seal]

dldh06

[limpid snow]

judging by what weve been we learning this is propbably how she (my teacher) wants it done

[wary stream]

Both equations work, point slope, you just plug everything in and set it equal to y. Slope intercept, you plug everything in, then find b, then just plug in m and b into that equation

[limpid snow]

ah i see now much appreciated

I need to transfer a line that passes through (0,-4) and (-2,-4) into slope intercept form how would i do this

pointslope formula gave me 0/-2 as the slope

[wary stream]

Then the slope is 0

[limpid snow]

which is a syntax error when multiplied by -2

so how would i slove for the y intercept

[wary stream]

Channel busy

[wanton beacon]

Ok sorry

[wary stream]

You can still use $$y - y_1 = m(x - x_1)$$

[ocean seal]

dldh06

[wary stream]

Everything on the RHS will just be zero

And you'll have just $y - y_1 = 0$

[ocean seal]

dldh06

[hoary quiver]

Does e^(lnx) = x?

[glass lichen]

yes

[wary stream]

Yes

[glass lichen]

that's the definition of ln

[hoary quiver]

And that only works with e?

[limpid snow]

@wary stream okay so -4--4/-2-0=0/-2 as the slope?

[glass lichen]

yes, cause ln is log_e

[hoary quiver]

ohh so log_e x = ln x?

[wary stream]

That gets simplified to 0

[limpid snow]

okay and where do i go from there?

[glass lichen]

yes, that's what I just said

[wary stream]

$$y - y_1 = m(x - x_1)$$

[ocean seal]

dldh06

[wary stream]

@limpid snow

[limpid snow]

so the answer is y=0x+-4

[wary stream]

Yes

[limpid snow]

ah okay i see now

[wary stream]

Because the it would be y - -4 = 0x

Then y = -4

[limpid snow]

ohhhhhhhhhhhhhh

thank you for the help

how do I get point slope from a line that passes through (-2,4) and has a slope of 1/2

[bitter yoke]

Hello, how do you prove that the function f is increasing on [1/2 ; +inf) only using inequalities and not derivatives such that f(x) = x² - x - 1

[glass lichen]

Might not be the best answer, but find the vertex then you can argue that it's inc on that interval by the shape all parabolas make

[bitter yoke]

well yeah using a graph is easy but need to prove it with inequalities, thanks for your help anyways

anyone here down to help/knows how to

[glass lichen]

didnt say with a graph, but ok

one side of the vertex is inc and one is dec, figure out which side you're on and then use concavity, QED

[bitter yoke]

oh then i am sorry i am not familiar with the term and i am looking for an algebraic approach

[jagged raptor]

f would be increasing if f(a) <= f(b) whenever a <=b
you can use that to show it with inequalities

[bitter yoke]

yea

but i faced a problem proving it

i know what i am supposed to show i just don't know how to do it

[jagged raptor]

so we want to show that if b >= a >= 1/2 then a^2 - a - 1 <= b^2 - b - 1
<=> a^2 - b^2 - a + b <= 0
factor that and then you can conclude if b >= a >= 1/2 then its true

[wispy sorrel]

How do you find the transformation from 1/x to (x-4)/(x-3)?

[bitter yoke]

thank you i'll try that

[jagged raptor]

(x-4)/(x-3) = (x-3-1)/(x-3) = 1 - 1/(x-3)
it should be more clear what the transformation is if you rewrite it like that

[hoary quiver]

If e^x = y
Then does x = ln y?

[bitter yoke]

if y>0 then yes

[jagged raptor]

and it always is

[harsh belfry]

Could use some guidance here. Currently working on this limit problem and I'm not exactly sure what I did wrong.

(note that the top expression is divided by h not x)

What should I have done differently?

[hot narwhal]

you missed 2xh

(x+h)2 = x2 +2xh+ h2

[harsh belfry]

Ahhh! Will correct that, Hopefully thats what I needed changed.

[jade birch]

(nvm didn't see the )

[harsh belfry]

currently working it out with the correction in mind

I'm a bit slow though

[knotty hedge]

👍 👍

[jade birch]

No one here is in a rush

[knotty hedge]

idk 8th grade math

[alpine sable]

I have a problem that says find the smallest possible value of x^2 - 3x + 2y^2 + 4y + 2. Since no endpoint were given I assumed the problem was talking about local minimum. Now this I can solve but here the problem this was in chapter 1 of spivak calculus, so the way I was going to solve it was out of the window. All that was left was to solve it for 2 cases when x is constant or y is constant, and using information about quadratic polynomial. I am asking how should one attempt this?

[knotty hedge]

no idea

[harsh belfry]

Thanks I think this should be the correct answer now

[hot narwhal]

no prblm

[knotty hedge]

ayo good job

idk if it's correct but good jobbbbb

😋 😋

[alpine sable]

@alpine sable partial derrivatives set equal to 0 and find the critical point

So $f_x(x,y) = 2x - 3$

[ocean seal]

Em

[alpine sable]

yeah that the way I was original going to solve it, but I can't since its chapter 1

Okay then complete the square

thx

Will that work?

yeah I just checked the solution answer to the book, I used complete the square already to get it. I was just verifying here

yeah it right

thx

You're welcome

[tight locust]

it's correct

good job!

1/2x = 1/14

wow

did you know?

that x-7 does not equal 7-x ?

(7-x) = -(x-7)

so the answer would then be -1/14

[jagged raptor]

suppose that we have x and y such that f(x) = f(y)
then consider the relationship between f(x) and f(y) if x < y or if x > y
from there you can conclude x = y

[tight locust]

there is no a,b such that f(a) = f(b) except for a = b

yeah pretty much @jagged raptor well put

you got to it before me

yes

[alpine sable]

supposing I have epsilon > 0. from the archimedean property can I assume that there's some n in N which 4/n + 1/3 < epsilon?

[tight locust]

no

[alpine sable]

why not?

[tight locust]

epsilon > 1/3 would work

not epsilon > 0

[alpine sable]

I see

[tight locust]

4/inf + 1/3 < epsilon
1/3 < epsilon

[alpine sable]

what if 4/n - 1/3 < epsilon ?

[tight locust]

then that would necessarily be true for all n greater than or equal to 12

[alpine sable]

I see 4 - 1/3 is much bigger than zero

[tight locust]

yeah

4/12 - 1/3 = 0

[tight locust]

the rationals are densely ordered

[alpine sable]

this?

[valid pivot]

what would be the equation of a tetrahedron

in terms of parametrics

so like x = , y =, and z=

i tried to look for it for so long but all i found was like the volume of tetrahedrons and stuff

[night geyser]

https://math.stackexchange.com/questions/1887532/parametrization-of-a-tetrahedron

[valid pivot]

i looked at that i dont think its working

it could just be something wrong in my code

oh wait

[alpine sable]

Help pls

What do I do

Like I literally don’t even know what to do

Like I’m doing linear relations using perpendicular and parallel lines

This question came up and idk what to do

[wary stream]

Do you know how a line can be perpendicular?

[alpine sable]

Idk

[wary stream]

The slope of a perpendicular line is the negative reciprocal of the line you are using

[alpine sable]

Sorry this is so confusing

[valid pivot]

just look at the current slope and make it negative. then do 1/(the value) and that's the new slope

[alpine sable]

Wait what’s the current slope

[jade birch]

reciprocal of the line?

[valid pivot]

the equation is currently in the format of y=mx+b where "m" and "b" are some values

m is the slope

[alpine sable]

So a slope is the line?

Proof of cos2a=cos^2a -sin^2a

[valid pivot]

slope is a characteristic of the line

the line is the entire thing and the slope is just how fast the y is increasing for the line

[alpine sable]

Okay Thalnks

[valid pivot]

np

[cold ginkgo]

Hi. I would like a bit of help with this question. What do I need to do to be able to solve this problem?

[lunar fjord]

let s=36.2.solve for r

[cyan fog]

can someone please help me with some accounting hw

if you click open original you can zoom in

[strong hamlet]

i need some help

[barren radish]

can someone help?

my math sucks

[astral dagger]

do you remember how to find the perimeter of a rectangle?

[strong hamlet]

add all sides together

[upper dagger]

I have a question

[tough hatch]

it has a typo, and you should be able to see that

[fresh relic]

Can anyone help me with this?

[tough hatch]

first term is 6 + 0×5
2nd term is 6 - 1×5
3rd term is 6 + 2×5
4th term is 6 - 3×5

the nth term, where n is odd, has the - sign

[barren radish]

how bout this

[wary stream]

Do you know how to factor?

[barren radish]

no

i dont understand a single thing inside this test xd

my math is really bad

[wary stream]

This is a test?

[barren radish]

not really

practice

next week is a test

[wary stream]

You can also FOIL each option to see which one gets that expression

[tough hatch]

just list all the terms in order with this pattern to see for yourself

[lone igloo]

aX^2 +bX + c you can factorise finding two numbers so that n1 * n2 = c and n1 + n2 = b => (x + n1) (x+n2)

where a = 1

so ask yourself what numbers multiplied give you 14 and summed give you 9

[tough hatch]

you know that the formula for the surface area of any sphere wirh radius r is S = 4πr^2, and the given surface area of some sphere is 36.2 cm^2.
then all you have to do is solve for r when S = 36.2 cm^2, i.e. 36.2 cm^2 = 4πr^2

[tough hatch]

are you familiar with one-sided limits?

[fresh relic]

to an extent

[tough hatch]

@fresh relic what value does f seem to stop at as x approaches 4 from the left? this value is exactly lim (x->4^-) f(x)

[fresh relic]

4?

[tough hatch]

as x approaches 4 from the left

not from the right of 4.

[fresh relic]

13?

[tough hatch]

13?

make sure to look carefully at the tick mark labels

[fresh relic]

7?

Ohhhh

1

Right?

[tough hatch]

don't guess

[fresh relic]

I am out of ideas

It’s the y value?

[tough hatch]

you are not looking at the right point

[fresh relic]

3?

[tough hatch]

so what is f(x) at the x-coordinate of that point?

yes

and what value does f seem to approach as x approaches 4 from the left?

[fresh relic]

3

[tough hatch]

yes

[fresh relic]

So

It’s 3 for the first 2 boxes?

[tough hatch]

the shaded circles are the points where f is defined at

sure

btw, what kind of activity is this?

im not asking about the topic.

[fresh relic]

It was a team activity but my team never made contact with me

So I was told to work alone

[tough hatch]

i see

np then

that's good

[fresh relic]

I’m screwed tho man

I’m majoring in computer science and I’m struggling with basic precalc concepts

[tough hatch]

Paul's Online Notes is a nice online resource:
https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

[fresh relic]

I’m still confused on these answers tho

[tough hatch]

what's confusing you?

[fresh relic]

what they are

[fresh relic]

Like I don’t know what to put in the boxes

[tough hatch]

you're going to put whatever values those have, if they exist

if they don't, then follow the instructions given for that case

[fresh relic]

What’s the instructions

[river brook]

PLS SOMEONE HELP I MATH TEST IN 40 MINS

[tough hatch]

in the parentheses

[river brook]

11TH GRADE

PLS SOMEONE

[fresh relic]

It just says x?

[glass lichen]

we dont help break academic integrity

[river brook]

PLS I WIL GET EXPELLED

[glass lichen]

sucks to suck

[tough hatch]

(write DNE (does not exist) if given limits do not exist)

[fresh relic]

But they’re all 4

Man I have such a big headache

[tough hatch]

they are not all equal to 4

[tough hatch]

didn't you just say this?

[fresh relic]

But how

I don’t understand

The first box makes sense

[tough hatch]

what is f(4)?

[fresh relic]

The other 3 don’t

[tough hatch]

ok good

[tough hatch]

do you see this?

[fresh relic]

I have no idea what it is supposed to mean

[tough hatch]

when x approaches 4

f(x) MIGHT approach a value

for example, in the constant function f(x) = x

f approaches 0 as x approaches 0

[wary stream]

We don't help people cheat

[tough hatch]

as you take values of x closer and closer to x=0, f "eventually" becomes equal to 0

[fresh relic]

So then the answer for the other 3 boxes is 4?

[tough hatch]

why would it be 4?

[fresh relic]

I’m not sure

[tough hatch]

if you know one-sided limits "to an extent", then you should know that they are sometimes not equal

[fresh relic]

So then put DNE for the other 3?

[tough hatch]

are these two points the same?

[fresh relic]

It’s an empty hole though

[tough hatch]

if they are, only then will your two-sided limit exist

no, i'm referring to the points (4,3) and (4,4)

[fresh relic]

There’s an empty hole at 4,4

[tough hatch]

yes, there is

but (4,4) is a point, nevertheless.

just answer the question

are they the same?

[fresh relic]

No

[tough hatch]

then that means your two-sided limit does not even exist.

[fresh relic]

I don’t get what that means

And I don’t get why either

[jade birch]

When you traverse from the left, you reach (4,3), but when you go from the right you get to (4,4). They do not approach the same y value so the limit doesn't exists

[tough hatch]

and you said earlier that f approaches 3 as x comes closer and closer to 4, from the left of 4

but f approaches 4 as x comes closer and closer to 4, from the RIGHT of 4

so the two-sided limit DNE

[fresh relic]

So for the one with the - and one with the + it’s DNE?

[tough hatch]

since 3 is not equal to 4

no

i just said what their values are

[fresh relic]

I’m ripping chunks of my hair out

[fresh relic]

Yes I get that but I thought we just established that it doesn’t exist

So why is the answer not DNE

[fresh relic]

So the last one is DNE?

[tough hatch]

yes, only that.

two-sided limit is the limit without either + or -

[fresh relic]

Ok