help-49

[radiant helm]

perhaps

an easier approach to this

i always like simplifying things like tan, but in this case it just gets too much

[prime hornet]

I was asked to come here??

what’s going on @radiant helm

[radiant helm]

im trying to solve an equation

but

[prime hornet]

what’s the equation

[radiant helm]

im kinda confused with what would be the right thing to do here, whether to distribute it to cos^2x or not, so this person tried helping me by asking me for my work, and i sent it

[prime hornet]

Where is the bottom expression coming from?

is it related to the other two expressions?

[radiant helm]

here, step 4

i just got rid of the denominator

[last slate]

But wasn't the original question 3tan^2x-1?

[radiant helm]

yea it is

did i do something wrong

[olive matrix]

this step doesn't make any sense to me but up until this point it was good.

something that can be really helpful here is to instead of writing sinø and cosø all the time, just write S and C

[radiant helm]

oh okay

wait

maybe i couldve factored it..

[prime hornet]

was about to say

I couldn’t figure out what was going on there

[radiant helm]

i just converted cos^2x to sin^2x since there's cos and sin 😭

[prime hornet]

ah I see

[olive matrix]

ohhhhhh ok

no yeah that's fine sorry i misinterpreted what you were trying to do

(yeah then at this point i'd start writing with S instead of sinø so that i don't have to write sin so many times lol)

but let me keep going on your work

[prime hornet]

looks like you get a quadratic @radiant helm

[radiant helm]

no worries thanks !

[olive matrix]

this step -- the sin^2 terms all cancel out and it looks like you transmogrified sin^4 into sin^2

[radiant helm]

yeaa so i couldve done x=sin, y=cos and did -3x^2+4xy+y^2?

[radiant helm]

OHH

wow

[olive matrix]

yeah - and then that's factorable if you wanted to do it that way

[radiant helm]

hmm okay

so technically it's -4sin^4x+1

[olive matrix]

yep! (theta not x but yes)

[radiant helm]

would it be hard to work with considering there's a fourth root

[olive matrix]

not really -- we're not considering imaginary solutions

fourth root is just a square root inside a square root

[radiant helm]

so id get sin^4x=1/4?

[radiant helm]

oh wow

technically just 1/sqrt2?

[olive matrix]

±

[radiant helm]

ohhhhhhhh

tysmmmm

[olive matrix]

(or you can like factor it with difference of perfect squares etc)

[radiant helm]

okay !

[midnight plank]

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[livid crystal]

Hello, is this correct? My teachers solution is different from mine ….

[livid crystal]

Will my method be bad for future math?

Oh btw this is POLYNOMIAL FACTORING

[tacit rose]

Your answer is not correct as it can be factored more

You should make those 4 be 2 * 2 since 4 = 2 * 2

Then you can see that all the terms have more in common

[stable dawn]

You can just find the hcf of 36,48,72 rather than writing all the factors btw

[livid crystal]

I don’t know how to do that..

[livid crystal]

Ohhh yes I see that

[stable dawn]

I mean to be honest it's the same thing you did by writing out all the factors but it's a lot more neat to find it first I guess.

[tacit rose]

What you're doing is basically hcf, you're just doing it the long way as that's the way your teacher taught you

[livid crystal]

Oh okay

I got the correct answer !!! I just needed to factor more like you said

Thank you

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[last slate]

Is the greatest common divisor of three numbers the same as the greatest common divisors of the first two numbers and the third number?

[last slate]

$\gcd(a,b,c) \approx \gcd(\gcd(a,b),c)$ ?

[grand pond]

We

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[pastel matrix]

halp

[pastel matrix]

how do i do this?

[dark tusk]

Could this help: 180-4x+4

[pastel matrix]

oo

ok ty

[dark tusk]

Then use that angle(which is x equals something) to solve the 180=angle1+angle2+angle3 in the triangle

[pastel matrix]

omg i did it

[dark tusk]

👏

[pastel matrix]

thank youuuuu

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[minor marten]

does that say limit as z approaches 1?

image is a bit blurry

[karmic cipher]

it is i.

[minor marten]

okay I see

[karmic cipher]

Just put the limit into the variable z, so you should know that
i = root( -1 )
i^2 = -1
i^3 = - root(-1)
i^4 = 1
i^5 = i (again)

[olive matrix]

you'll get 0/0 if you try that

[minor marten]

L’Hospitals rule

[karmic cipher]

ya then we know it's a 0/0 form so we apply this

[olive matrix]

you could... i'd probably do polynomial long division before L'H here

[minor marten]

😭

[chrome hill]

iota

[chrome hill]

I have a doubt

z^6+z^4=z^10?

oh by direfct putting after doing l hoipital i got 10/6

5/3

[chrome hill]

yes

i^10+1/i^6+1=0/0

so after 10 i ^ 9/6I5

10/6=5/3

[honest kelp]

looks correct )

[chrome hill]

thanks angel

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[digital prairie]

honestly just curious.
2+5=7
5+2=7.
7-5=2.
5 ? 7 = 2.
What operator belongs in the last one?

[worthy wing]

None

You probably copied wrong or the original text has a typo

[runic hamlet]

you can write -5+7 if you specifically want the 5 and 7 in that order

[digital prairie]

I came up with it

hmm

[runic hamlet]

but there is no operation for 5 ? 7=2 (because it would be quite useless and basically only artifically increase the number of operations we have to deal with)

[digital prairie]

heh fair enough

well uh thanks anyway

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[midnight plank]

@ornate sonnet Has your question been resolved?

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[atomic lagoon]

I tried finding the stationary distribution, but couldn’t get anywhere without the transition matrix

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@atomic lagoon Has your question been resolved?

[atomic lagoon]

<@&286206848099549185>

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@atomic lagoon Has your question been resolved?

[atomic lagoon]

Could you reason like this?

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[last slate]

wow

if you dont mind which exam are you preparing for ?

[atomic lagoon]

Markov processes

[warped gate]

From any state, there are 52 states we can reach, including the current state

each with probability 1/52

So you 'd have a transition matrix of size 52! x 52! , but extremely sparse with only 52 nonzero entries per row of value 1/52

@atomic lagoon if that helps maybe

(So in total the matrix has $52! *52$ nonzero entries)

[grand pond]

TRAMPELTIER

[dark tusk]

Oh sick! What year are you? Im currently a 1st year might take it sometime in sophomore

@atomic lagoon

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[last slate]

I need help with this

[astral garnet]

i think the key word is OR

[last slate]

Okay

Or

Sometimes I have the answer short

And sometimes the answer is long

I understand how to do the math

I want to know what I did wrong

[astral garnet]

well u got the right numbers

x>-3/2

x<1

keyword was OR here

it could be either one

[last slate]

Can you explain by either one

What would be one

@astral garnet

[astral garnet]

well it doesnt say AND

meaning it doesnt have to fit both those rules

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[last slate]

Are my answers correct?
a) 1
b) 2
c) DNE
d) DNE
e) 1

[rose trout]

Why is there no limit as x->2?

[last slate]

Would it be 2

Which ones are wrong?

@rose trout

[rose trout]

I mean you said that the limit at 2 doesn't exist but I don't see any holes or anything

The rest seems fine.

[last slate]

So would it be DNE or 2?

[rose trout]

Neither?

To me f(x) doesn't seem like it approaches 2.

[last slate]

The only other possibility is 1

But it doesn’t seem that way either. What could it be if it’s not DNE, one or two?

[rose trout]

We're talking d) right now, yeah?

[last slate]

Yes

[rose trout]

The function does seem to be approaching 1 to me.

[last slate]

I can’t think of anything else. Isn’t L a possibility

[rose trout]

But why wouldn't it be 1 though?

[last slate]

Cause it doesn’t come close to the line

And it’s a solid dot

[rose trout]

Are you sure you're looking at x=2?

The line is solid there

Both sides get close to the same value, 1.

[last slate]

Yea

3?

Would you add them 😂

I’m so lost

[last slate]

Same distance from both dots

[rose trout]

From the right, the line approaches 1

From the left, the line approaches 1

So the limit is 1

[last slate]

Oh ok

Wait

Oh I see it now

Tysm

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[last slate]

damm what class is this

calc 2?

nope

we 17-18 y/o are supposed to solve it before entering any university/college :)

[weak cairn]

I start solving than see the power 🥲

[last slate]

also its not single correct
might have more than one correct

[weak cairn]

I think a theorem can help

[last slate]

i see

which book is this ?

but here

[weak cairn]

Sorry converse of that theorem not true

[last slate]

hmm okay

[weak cairn]

Sorry I think we can use it

Why we need Converse

Like you can take whole thing inside u_n and calculate lim u_(n+1)/u_(n)
Which is equal to lim (u_n)^1/n

[last slate]

yeah maybe i can use it

[prime hornet]

this is an infinity^0 situation...

but i really cant be bothered to deal with it lol

sorry

[last slate]

yup

[last slate]

yeah it would help
but the thing is...
i never knew this thing and i am supposed to solve it without knowing this thing
can that be done somehow ?

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[weak cairn]

I am not seeing any idea of getting rid of the power or you can use log to solve give it a try

[weak cairn]

I got a function solving by this method try it tell me if I am right

[last slate]

okay

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[twin tree]

if i make 10 k in 30 secs how much will i make in 10 mins

[twin tree]

i need to know how to find it out

im got confused on how to mutiply it

[terse lodge]

your question comes down to how many blocks of 30 seconds there are in 10 minutes

can you start by converting them to the same units

[twin tree]

no like im playing a game and i get 10 k every 30 secs cs thats how much money i get for winning a drag race

im trynna see how much i can get in 10 mins

[terse lodge]

what is 10 minutes in seconds

[twin tree]

600

[terse lodge]

cool, so what's the computation to find how many 30 second chunks there are in 600 seconds

[twin tree]

oo okk ty

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[unreal notch]

can i ask why c ii) the length is 0.21?🥲

ooo I know alrd

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[humble swan]

Do the things in red effect anything

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[simple spire]

if a and b are integers, show that ab(a^+b^2)(a^2-b^2) is divisible by 30

[midnight plank]

Please don't occupy multiple help channels.

[simple spire]

to anyone wondering why i occupied multiple channels

i dont think anyone's gonna answer my first question

[worthy wing]

Then close the first question

[simple spire]

but i want to keep it there in case soemone can answer it

[worthy wing]

You can’t, rules are to be followed not if you wish but to follow period,

[simple spire]

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[tender cliff]

my lecturer gave me this as a brain teaser

by "Half" he means half the distance

now intuitively i'd assume 40mph

[uncut ore]

wrong

average speed=totaldistance/total time

[tender cliff]

yeah , seemed a bit too easy lol

[uncut ore]

calculate the time of first half and second half individually then use this formula

[tender cliff]

thank you

this is what i did

lets call $D$ total distance , then $\frac{0.5D}{30}$ is the time for the first half and $\frac{0.5D}{50}$ is the time for the 2nd half

[grand pond]

ikraam

[tender cliff]

using your formula

[uncut ore]

yes

[tender cliff]

$\frac{D}{\frac{0.5D}{30} + \frac{0.5D}{50}}$

[grand pond]

ikraam

[tender cliff]

the D cancels out nicely

leaves us with

75/2

37.5 mph

for the next part i just need to figure out what number to replace 50 with to get the avg speed as 60mph?

[uncut ore]

yes

[tender cliff]

thank you

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[warm island]

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.reopen

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[chrome hill]

Angle PAD 70
Angle DAC 40
Angel BAC 40
Angle ADC = ?

[twilit field]

is AC the diameter of the circle by any chance?

[twilit jetty]

its not since PAC ≠ 90

[chrome hill]

Not given

[twilit field]

ah yeah, sorry

[chrome hill]

Helful role nice👌

[waxen willow]

Is PQ tangent?

[twilit field]

Have you tried using the fact that it's cyclic ?

[waxen willow]

Im guessing no it would be too easy if it is

[ivory ibex]

@waxen willow yes

Tangent

It is

[twilit field]

and yeah PQ being a tangent would help a lot too

[waxen willow]

But if its tangent then CAP = ABC

That is too trivial

[chrome hill]

Yes

[waxen willow]

What is BAC there for then?

[chrome hill]

Name this tberoem?

[chrome hill]

It is given =40°

ACB=30°

ADC=70°

I got it

[waxen willow]

Search tangent criterion

Its called theorem of tangent and i forgot what do you call a side on the circle

[waxen willow]

Yes that

[chrome hill]

Angle b will be equal to other side angle?

[waxen willow]

Yes

[twilit jetty]

you can also use that since PAD = 70 and CAQ = 70, DC || PQ and so D = PAD

[chrome hill]

What??

DC and PQ?@twilit jetty

[twilit jetty]

the picture is lying

this is what it looks like

[chrome hill]

CAq=70 how?

[twilit jetty]

CAQ = 180 - 70 - 40

[chrome hill]

Yes

But how did you draw it?@twilit jetty

Yes now it looks parallel

[twilit jetty]

https://www.desmos.com/geometry

in other words I cheated

[chrome hill]

Ohh i have not learnt desmos geometry yet

CAQ=70° then again tangent criterion

[waxen willow]

I never used desmos for geometry. Is it better than geogebra?

[chrome hill]

ADC=70°

[waxen willow]

Yes

[chrome hill]

.close

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[twilit jetty]

it could be but youd have to try it, its a bit different than geogebra

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[chrome epoch]

Are there any other tools I can use at a freshman college level for grouping polynomials?

It feels like there has to be a better way than trial-and-error and eyeballing it to say "yeah, okay, that adds up to that, let's see if that works, we'll also try a negative sign here first." With larger problems, larger numbers, etc., there's no way I can eyeball it and say "is that the cube of some number?"

[chrome epoch]

I'm currently taking freshman college algebra (pre-calc).

[fast igloo]

grouping polynomials as in factorizing/getting roots of quadratic/cubic equations?

[chrome epoch]

Exactly, yes.

[fast igloo]

for quadratic you have the basic formula

[ivory ibex]

Go to flipped math

[chrome epoch]

Quadratics are easy due to the equation, but I'm mostly concerned with the polynomials

[fast igloo]

polynomials of what degree

[waxen willow]

Do you know rational root theorem?

[chrome epoch]

3rd degree primarily, I guess. And I do not know the rational root theorem

[fast igloo]

well you got to try to hit and trial one root, divide the equation by x-a where a is the root you found and then factorize the quadratic

[chrome epoch]

That seems substantially nicer.

Okay, I'll give that a go.

[fast igloo]

👍

[chrome epoch]

I don't expect math to be fast, but the occasional problem is way too long just trying to factor a polynomial when it isn't even the point of the exercise.

Seems a bit silly to brute force all the time.

[waxen willow]

Also look up synthetic division

[fast igloo]

in order to also make your list of "hit and trials" shorter, try putting in 2 values and see if the sign changes. this means that if I put a value of 1 and 3 in the cubic equation (in place of x) and I get a positive and negative value then it implies that one of my roots is in between 1 and 3 which helps you shorten your list

[chrome epoch]

Will do. Thanks for all the tips folks. I'll look into all of it.

[fast igloo]

no worries

[chrome epoch]

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[lucid nimbus]

Could I get a explanation for this problem?

[midnight plank]

@lucid nimbus Has your question been resolved?

[tribal tartan]

when a function is increasing its instantaneous slope in that interval would be positive

knowing that what could you do here

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[lucid nimbus]

.reopen

[midnight plank]

✅

[lucid nimbus]

could you explain what that means

[tribal tartan]

when a function is increasing

the slope of the function would be positive

yes?

these two terms increasing and positive slope are interchangeable

they mean the same thing

[lucid nimbus]

so it's DNE for decreasing and always increasing for increasing?

[tribal tartan]

well in this case the problem is actually saying that there isn’t an interval where the function is increasing or decreasing

that’s what DNE means

[lucid nimbus]

Am I looking for the point where it stops decreasing and starts increasing?

[tribal tartan]

you’re asked to find in which interval is the function increasing

and decreasing

so yeah kinda

also is this for calculus or some other math class

[lucid nimbus]

pre calc

[tribal tartan]

did you learn derivatives or

[lucid nimbus]

I don't think so

[tribal tartan]

so i would suggest you to graph the function

and look at when the function is increasing and decreasing

basically when the graph is going up or down

[lucid nimbus]

(-inf,-3) for decreasing and (-3,inf) for increasing?

[tribal tartan]

yep that’s correct

[lucid nimbus]

ok thanks :O

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[pulsar pasture]

hello

[pulsar pasture]

i'm trying to do a question in analysis

I've proven that when x is rational, f(x) is not continuous

and i'm trying to prove that when x is irrational, f(x) is continuous

[surreal moon]

What is f(0)?

why? 0 is rational

[pulsar pasture]

sorry i mean 1

[surreal moon]

How? is it 1?

oh derp

0/1

[pulsar pasture]

0=0/1, f(0/1)=1

[surreal moon]

(ignore me)

[pulsar pasture]

basically i am just shuffling the epsilon delta inequality and need to prove this
$\forall\epsilon>0\exists\delta>0:\forall y\in[0,1]:|y-x|<\delta\implies|f(y)-f(x)|=|f(y)|<\epsilon$ for x not in rationals

[grand pond]

george clooney real account

[pulsar pasture]

?

get ur own channel dawg

[runic hamlet]

so you know that f(y)=1/q. so you would want to choose delta small enough, such that all fractions near x have a bigger denominator than q

can you do that?

[pulsar pasture]

i'm not sure

i think delta = 1/q??

[runic hamlet]

well if x is for example near 1/2, then delta=1/2 is certainly a bad choice

cause then y=1/2 is included

[pulsar pasture]

i see the logic i think

but i'm not sure how to think of such a delta

especially in terms of epsilon + x

[runic hamlet]

well you dont need to be as explicit as you may think

also it may help to set eps as 1/n for some n

[pulsar pasture]

yeah im setting epsilon to 1/n for ease

wdym by not as explicit as i think?

[runic hamlet]

cause for every eps you can find n with 1/n < eps and if you can show it for 1/n then you have also shown it for eps

[pulsar pasture]

yeah by archimedean property

makes sense

[runic hamlet]

just guessing on what you might mean by this

[pulsar pasture]

i just mean $\delta(\epsilon,x)$

[grand pond]

george clooney real account

[pulsar pasture]

because delta cant be based on y (holds for all y)

[runic hamlet]

ok if x was for example 0.55961235... something

and eps was 1/2, how would you choose delta?

[pulsar pasture]

id pick like 0.05

because within 0.05 of our x we dont get any fractions with denominator 1/2

[runic hamlet]

ok because the closest fraction is 1/2 and thats further away

[pulsar pasture]

yeah

[runic hamlet]

what if eps for example 1/100

[pulsar pasture]

0.54

?

something that is more than 0.01 away from x

[runic hamlet]

do you mean delta = 0.54? or what do you mean

[pulsar pasture]

yeah delta = 0.54 sorry

wait i think im getting confused

[runic hamlet]

but for example then 0.57 would be included

[pulsar pasture]

why is 0.57 important?

[runic hamlet]

57/100

[pulsar pasture]

ah

gotchu

[runic hamlet]

so the numbers you would have to worry about are 0.5, 0.51, 0.52, 0.53 etc

[pulsar pasture]

ahhh okay

[runic hamlet]

(not all of these are reduced, but they all have denominator 100)

[pulsar pasture]

okay then i guess u can devise a kind of algorithm

find all the fractions w/ denominator 100

find the closest one

[runic hamlet]

why is there a closest one?

[pulsar pasture]

delta smaller than the distance between that and x?

[pulsar pasture]

i mean there kinda has to be

if not then there r two closest but thats okay too

[runic hamlet]

well there could be a sequence of them that converges to x

"no closest" in the sense that there is always a closer one

[pulsar pasture]

oh sorry i mean the closest fraction with denominator 100

like whichever of n/100 is closer

[runic hamlet]

well yes but why is there one

[pulsar pasture]

well because there r finitely many

[runic hamlet]

yes!

[pulsar pasture]

100 many in the interval [0,1]

[runic hamlet]

thats what I wanted to hear

I know it sounds trivial but its important

[pulsar pasture]

okay

finitely many fractions of the form a/b for a fixed b

should i use the thing thats like

every finite set contains its infimum n supremum

no nvm i dont think thats useful

[runic hamlet]

well its basically that, yes

but lets not overkill it with the precision

[pulsar pasture]

how do i use that?!

okay

[runic hamlet]

you want the minimum of the set {|x-a/b|}

which is a finite set

[pulsar pasture]

ohhhhhh

[runic hamlet]

of numbers > 0

so the min is also >0

[pulsar pasture]

that makes sense

[runic hamlet]

(because x is irrational)

[pulsar pasture]

so essentially my delta is just the minimum of the distances between x& all of the fractions w/ denominator n

with epsilon := 1/n

$\delta=\min

oopsie

$\delta=\min{|x-\frac{a}{n}|}, a\in[0,n]\cap\mathbb{N},\epsilon:=\frac{1}{n}$

[runic hamlet]

a should be in [0,n]

[pulsar pasture]

oh shit yea

[runic hamlet]

and that bit of the notation should either be in the set or under the min

[grand pond]

george clooney real account

[pulsar pasture]

either in the set or under the min?

wdym

[runic hamlet]

either $\delta=\min_{a\in{0,1,\ldots,n}} {\abs{x-\frac a n}}$ or $\delta=\min{\abs{x-\frac a n}: a\in{0, 1, \ldots, n}}$

[grand pond]

Denascite

[pulsar pasture]

uh

whats the difference

[runic hamlet]

well you wrote three separate things

just connected with commas

but if you are reading the first thing, you dont actually know what a is

[pulsar pasture]

ah oka oka

[runic hamlet]

and thats kinda important cause the a is what you are doing the minimum over

[pulsar pasture]

okay thanku sm

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[cyan dagger]

Just started college trig and the professor gave this as a question but hasn't shown a single example before.

[cyan dagger]

Is there a way to solve for y first like the problem states or do we need x before that?

I've never taken a trigonometry class so I'm kind of lost on how you get y first based on what he's already taught us

[azure basin]

I think you do have to find x

first

[cyan dagger]

So is the problem just wrong?

Because it says use y to get the other variables but I don't understand how that would work without having x

[azure basin]

oh i didnt see that

I can see how to solve x, but not y or z

[cyan dagger]

I'm guessing I have to add a parallel line to setup a transversal so I'll try that first

nvm that seems like it just creates more than i have to do

im lost on this lol

[marble yew]

with what

against point B

[cyan dagger]

yeah that's what I tried

but I don't think that's it unless I'm wrong

[marble yew]

i mean i think it could be a law of sines

[cyan dagger]

I wouldn't know what that is yet because he hasn't covered it.

[marble yew]

ok nvm

[cyan dagger]

He's had a few problems like this so far where he didn't have it in the lecture...

[marble yew]

i think you have to set up a system of equations where it involes those variables

and substitute and solve for y

but that is a little complicated

or waittry flipping it to the right

you will get a big right triangle

[cyan dagger]

you mean like splitting it so it's two triangles?

or so z is the base?

[marble yew]

yeah

[cyan dagger]

which one?

[marble yew]

hold on

the thing is if you knew a angle this would be light

what did he teach you so far

[cyan dagger]

Vertical, corresponding, and alternate interior/exterior angles. All angles of a triangle add up to 180. The concept of similar triangles. Finding unknown sides of a triangle (but the examples had at least two sides solved for one triangle and the other triangle had one side solved) by setting up a proportion/ratio.

[marble yew]

ok

so you need to like do pythagorean theorum for three triangles

the big one

the two small ones

you substitute until you get y

so you have z^2 = x^2 + y^2

and then you have x^2 = 17^2 + 15^2

and then you also have (15+y)^2 = 17^2 + z^2

you can solve it from there

i think you get 578/30 for y

[cyan dagger]

alright I'll try to solve it then

thanks!

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[cosmic river]

sin (pi - pi/2)

[cosmic river]

what allows us to remove the pi and make it sin (pi/2)?

[marble yew]

pi = 2pi/2

[steep hinge]

you have removed pi-

[cosmic river]

how do we use this to remove the pi

[steep hinge]

in this case you can just sum the two values without remove anything

[marble yew]

fractions

because if you do division

2pi/2 = pi

you are just making common denominator

woops

[cosmic river]

ok so I can just do 2pi/2 - pi/2) which is what gives us that

what about this

how does the limit just give pi - pi/2

we just plugin pi into x ?

no additional operations

[marble yew]

yeah

[steep hinge]

yes because x-->x is a continuous function

[marble yew]

sometimes it is a easy substitution

but other times you may have to reduce and other wonky stuff

this is one of the easy ones

[cosmic river]

ok thanks

[midnight plank]

@cosmic river Has your question been resolved?

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[fluid swan]

any help w/ these two?

[wary thorn]

What have you tried

[fluid swan]

idek how to begin them

and what steps to follow

[wary thorn]

Have you found the area beneath curves before?

[fluid swan]

not beneath, but between yes

[wary thorn]

What do you mean not beneath

[fluid swan]

like these

[wary thorn]

Okay so if you've done that

what is confusing you about these ones above

[fluid swan]

how would you set up 2 ? bc w/ the one that i already did you would replace a and b

[tribal tartan]

well so howd you calculate the area for 1

like what was your setup

[midnight plank]

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[cosmic river]

whats the first thing to do ?

[crude pier]

this is a polynomial limit so you can try factoring out a h^{1/3} from the numerator and denominator

[cosmic river]

how do I go about it

[crude pier]

first a question

how can you write h in terms of h^{1/3}'s ?

[cosmic river]

3sqrt{h}?

🙏

[crude pier]

no

that would be 3h^{1/2}

[cosmic river]

I don't get in terms of

[crude pier]

like, how can you write the term h^{1/3} so that it equals h

[cosmic river]

exponent of 3/1?

I don't know

[crude pier]

hint: $h = h^{1}; 3\cdot \frac{1}{3} = 1$

[grand pond]

Triaxyz

[crude pier]

remember your rules of exponentiation

[cosmic river]

this?

but multiply

h^1/3 ^3

h^1/3 * 3

[crude pier]

yes

how do you write that such that you can only see terms that look like h^{1/3}

remember when cubing you multiply something by itself 3 times

[cosmic river]

I don't know

)):

am I supposed to change the denominator also

[crude pier]

$(h^{\frac{1}{3}})^{3} = h^{\frac{1}{3}}\cdot h^{\frac{1}{3}} \cdot h^{\frac{1}{3}}$

[grand pond]

Triaxyz

[crude pier]

which is equal to 1 if you recall your rules of exponents

$x^a \cdot x^b = x^{a+b}$

[grand pond]

Triaxyz

[cosmic river]

yes

h / h^3

??

h / h^1^(3)

[crude pier]

so your original limit entry turns to: $\frac{h^{\frac{1}{3}}}{h^{\frac{1}{3}}\cdot h^{\frac{1}{3}}\cdot h^{\frac{1}{3}}}$

[grand pond]

Triaxyz

[crude pier]

from here the next step should be extremely obvious

[cosmic river]

multiply by 3

[crude pier]

dog

[cosmic river]

exponent of 3

[crude pier]

you are able to cancel out one term of h^{1/3}

[cosmic river]

ok

1/h^2/3

[crude pier]

yes

[cosmic river]

we did all of that for the numerator

why is it in the denominator now

[crude pier]

we did that for the denominator

[cosmic river]

h^1/3 / h^1

?

[crude pier]

the numerator stayed the same

we just manipulated the denominator so that it was in terms of h^{1/3} to make the division (cancellation) make slightly more sense

[cosmic river]

ok

h^1/3 / h^1

so what operations did you do to the denominator

how come nothing happened to the numerator

[crude pier]

what we just did exactly 6 minutes ago

because we want all terms to be able to factor out a h^{1/3} so that you can cancel it

what I did wasn't the only way to do it but it should have made the process eaasier to understand

[cosmic river]

Sorry I was under the impression that you had to multiply by 1/1, e.g., ^3 to both

so you multiply denominator only

[crude pier]

or you can just do $\frac{h^{\frac{1}{3}}}{h}=h^{\frac{1}{3}-1}$ which is probbably way easier

[grand pond]

Triaxyz

[crude pier]

you dont multiply anything

[cosmic river]

exponent

[crude pier]

if by multiply you mean manipulating the exponent then yes

[crude pier]

just stick to this and move on

[cosmic river]

So given a fraction

4/5

You could do any operation you want to either side to allow you to find a way to cancel?

I thought any operation you did had to be 1/1

so it doesn't break the rules of algebra

or is that only for linear equation

[crude pier]

you are seriously misinterpreting what I am saying

here

$h^1 =(h^{\frac{1}{3}})^{3} = h^{\frac{1}{3}}\cdot h^{\frac{1}{3}} \cdot h^{\frac{1}{3}}$

[grand pond]

Triaxyz

[crude pier]

these three things are exactly the same thing

it does not matter if you write them the first way, second, or third

they mean exactly the same thing

h^1

[cosmic river]

gotcha

[crude pier]

therefore, nothing breaks once you rewrite them as something equivalent

you are just rewriting the term

[cosmic river]

sorry mate am bad at math

[crude pier]

anyway now that you have the simplified fraction

$\frac{1}{h^\frac{2}{3}}$

mf

1sec

[grand pond]

Triaxyz

[crude pier]

there

now that you have this

need to turn to the concept of even vs odd functions

even functions mean that some function f(x) = f(-x)

aka upon plugging in a negative value you get the same as you would with its positive

[cosmic river]

ok

[crude pier]

this function is even

because anything that gets plugged in will be squared by that power of 2

so f(x) = f(-x) here

important because it shows that this wont diverge to both -inf and inf at x = 0 like 1/x for example

[cosmic river]

alright

So I tell if a function is even by the power on the independent variable

[crude pier]

and as we see there is no negative sign on the function, and any value plugged in will be positive, so this will tend to +inf as h approaches 0

[crude pier]

I would look more into even vs odd functions because this has a few exceptions

but as an introduction yes

[crude pier]

anyway this is basically the final solution

limit approaches +inf from the left, limit approaches +inf from the right, both sides tend to the same sign of inf, therefore the limit is +infinity at h = 0

[cosmic river]

Okay thank you

I'm gonna post another question but you don't have to help if you don't have time

First I tried to use the special limit sinx/x = 1

Now I don't know what to do to use 1-cosx/x = 0

[crude pier]

$\lim_{x\rightarrow a}[f(x)g(x)]=\lim_{x\rightarrow a}f(x)\cdot \lim_{x \rightarrow a}g(x)$ ONLY APPLICABLE IF BOTH LIMITS OF f(x), g(x) EXIST

[grand pond]

Triaxyz

[crude pier]

this should be somewhat useful

other than that I gtg

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@cosmic river Has your question been resolved?

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[river ridge]

I need help with this question

[wide marsh]

try rewrting tan as sin/cos and rearrnage using the sinx/x=1 identity

[midnight plank]

@river ridge Has your question been resolved?

[midnight plank]

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[tranquil wagon]

math aint mathin

[tranquil wagon]

full

[last slate]

u get 147.030 if you dont square 9.8

[tranquil wagon]

yup

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[glad venture]

Is this correct?

[glad venture]

am i allowed to do that

the canceling

[cloud wadi]

what did you do?

[glad venture]

idk if this is the correct term for it but i canceled the e^x with the 6e^x

so it became 5e^x

and 5e^x/1 is the same as 5e^x

[cloud wadi]

uh

i dont think that is a mathematical operation

[glad venture]

like this thing

i swear its a thing

[cloud wadi]

but there isnt a x+1 here..

ik i am dumb but this is just sad for me

[glad venture]

but the answer is correct

so how is it not correct

[azure basin]

is x/x+1 + x+1/x+1

so then x/x+1 + 1

or am i being silly

[tribal tartan]

what happened here is that they multiplied 1 + e^x to the other and subtracted e^x from both sides

[cloud wadi]

we are aware

but..

[cloud wadi]

..

[glad venture]

oh wait

i should probably write the intermediate step

this has to be correct

[cloud wadi]

yes

that is correct

[glad venture]

we aint making it outta the exam with this one

.close

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[old shell]

How do you simplify log10/log2 (log8) by chance?

[old shell]

Im currently a bit stuck, i was thinking of doing (log10xlog8)/log2 but the answer says its log8/log2

[frail burrow]

Whats the base here

10?

[old shell]

Yes

[frail burrow]

So whats log(10)

[old shell]

Oh

Thank you very much

[frail burrow]

Np

[old shell]

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[prisma trout]

help

[prisma trout]

plz

[prisma trout]

do I have to pay for the math thing

blud clam tf down

what is pie?

3.14? Right

[twin stump]

lmao

ok

[prisma trout]

no help I swear

<@&268886789983436800> he crused at me

[twin stump]

pi

is an irrational

approx equal to 3.14

[twin stump]

bro chill, i wasnt serious

[prisma trout]

okay thank you

[fluid elm]

so?

don't be mean guys!!! Lets all be friends!!

[midnight plank]

@prisma trout Has your question been resolved?

[pearl idol]

No

It's based on volunteer work, just ask your question

[midnight plank]

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[unique stream]

Hi I'm uncertain how to extract the taylor series for arcsin(x) at x=0

[quartz dove]

One trick you can use is to check if it is easier to find the Taylor series for the derivative of the function. If it is, then you can do that, and then integrate each term to find the Taylor series of arcsin(x).

[unique stream]

hm how would it be done via integration?

I started like this

fetching the first term which is 0

and then starting from the derivative as you mentioned

if I then expand it via binomial expansion I receive

then the top terms are always 0 when inserting 0 except for 2k=n

however (-1)^(n/2) wouldn't be defined in R for odd n

thereby the sum must be rewritten for all 2n instead of n

that's where I'm at

well (2n)! and (2n+1)! can be simplified

but not sure where to go from there

[quartz dove]

Right, it might just work to do it directly as well, but the fractional binomial looks a bit gnarly, yeah.

[unique stream]

when I look up the formula it says

the x^(2n+1) and div by (2n+1) overlap

[quartz dove]

So you're somewhat close

[unique stream]

but I'm not sure how to get (2n over n)/4^n

@quartz dove where does one get the (2n over n) when using the binomial?

[quartz dove]

I'm not sure. Do you get it if you expand the fractional binomial (-1/2 over n) ? At least the (-1)^n should disappear.

$\binom{-1/2}{n} = \frac{(-\frac{1}{2})(-\frac{3}{2})\cdots(-\frac{1}{2}-(n-1))}{n!}$

[grand pond]

OneTrackPony

[quartz dove]

It'll be something like $(-1)^n\frac{1\cdot 3\cdots (2n-1)}{2^nn!}$

[grand pond]

OneTrackPony

[unique stream]

yeah this is the part I don't get

[quartz dove]

Let me see it I can get it to work.

,w binom(2n,n)1/(4^n(2n+1)) for n = 3

[grand pond]

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Requested by onetrackpony

[quartz dove]

,w -binom(-1/2,n)*(-1)^n/(2n+1) for n = 3

[grand pond]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by onetrackpony

[quartz dove]

Just sanity checking, so at least they agree for x = 1 and n = 3 (except for a sign).

[unique stream]

hm k

[quartz dove]

Right, I think I have it.

You know the double factorial notation? You just skip every other term, so (2n)!! = (2n)(2n-2)...2, and (2n-1)!! = (2n-1)(2n-3)...1

Like I wrote above, you have expand the fractional binomial to get
$\binom{-1/2}{n} = (-1)^n\frac{(2n-1)!!}{2^nn!}$

[grand pond]

OneTrackPony

[unique stream]

haven't seen it yet but I'll get used to it

ah k I'll try to write it out a sec

@quartz dove can the !! be rewritten in terms of !

I'm here, but would like to not use !!

for the product

[quartz dove]

\begin{align*}
\binom{-1/2}{n} &= (-1)^n\frac{(2n-1)!!}{2^nn!}\
&= (-1)^n\frac{2^nn!(2n-1)!!}{4^n(n!)^2}\
&= (-1)^n\frac{(2n)!!(2n-1)!!}{4^n(n!)^2}\
&= (-1)^n\frac{(2n)!}{4^n(n!)^2}\
&= (-1)^n \binom{2n}{n}\frac{1}{4^n}
\end{align*}

[grand pond]

OneTrackPony

[unique stream]

actually yeah wait

1 * ... * (1+2n-2)

is (2n-1)!

div by

(n-1)! * 2^(n-1)

which negates each second term

hm but that yields an offset of -1

hm that's odd, I don't know how to get rid of it directly

[quartz dove]

If you want, you can rewrite it, yeah. For the even case, you have (2n)!! = n!2^n

[unique stream]

the binomial is the same as:

right? by generalised binomial theorem

there I extracted the (-1)^n and 1/2^n

[quartz dove]

For the odd case (2n-1)!! = (2n-1)!/((n-1)!2^(n-1))

[quartz dove]

Yeah, looks good to me.

[unique stream]

I'm not sure why this doesn't result in the same

extract the (-1)^n:

extract the 1/2^n:

[quartz dove]

It's the same thing, isn't it? 🤔

[unique stream]

and that would give

everything the same except everywhere is a -1 :D

[quartz dove]

Oh :d

Where is the extra -1?

[unique stream]

well if it were (2n)!/(n!*2^n) then it's correct

index offset by 1

[quartz dove]

So from here, it's (-1)^n/2^n * (1*3*...*(2n-1))

[unique stream]

ys

oh wait

I can shift at the end

I can simply add the last term

and negate it as well

🦇

[quartz dove]

Yeah,

[unique stream]

weehee done

probably one of the worst possible proofs for taylor series of arcsin

[quartz dove]

That's some nice brute-forcing too.

Yeah, that's why I was thinking it would be easier to find the Taylor series of 1/sqrt(1-x).

[unique stream]

well less or more I did that

[quartz dove]

Pop in x^2 instead of x of course.

Yeah, it's part of your proof in a sense.

[unique stream]

yeah the official one doesn't maintain everything in a single term

[quartz dove]

Funny they don't write it as (2n over n), it's so tempting.

[unique stream]

I do the same in essence except that the binomial expansion are 10 steps in mine and instead of the integral everything is directly inserted hm

nywys I'll keep it that way lol

thx for the dedication 🙂 @quartz dove

[quartz dove]

No problem. 🙂

[unique stream]

.close

[midnight plank]

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[midnight plank]

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[prisma trout]

Help

[prisma trout]

with this

[waxen willow]

What exactly?

Which part

[prisma trout]

The first one plz

7x2 -13x+3x2

thatone

<@&286206848099549185>

someone plz help me

Still wating

[vague remnant]

you know that you can do minus if the x are in same power like 5x-4x=x

So if they x²

Do same

[prisma trout]

thank you

[midnight plank]

@prisma trout Has your question been resolved?

[midnight plank]

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[midnight plank]

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[strange coyote]

what method would i use to find the roots of a rational function if p(x) is expressed as “1”? I tried looking online but cant seem to find an answer that helps me with this specific scenario. Im in accel. AGS III so if this is too complicated it may be out of my curriculum, but it feels odd that it was asked of me.

[slender walrus]

wdym by expressed as "1"

[strange coyote]

when i search online for answers i always get how to find the roots for a function like (x-1)/(x+2) where p(x) has an x term in it, but in all of the problems im given p(x) has no x term and is always equal to 1

[slender walrus]

you mean if the numerator is 1?

[strange coyote]

yes

[cloud wadi]

man that confused me

[slender walrus]

fraction can only be 0 if the numerator is 0

if the numerator is a non-zero constant, then it can never be 0 and will have no roots

[strange coyote]

ohh ok that makes sense

in that case let me ask, how would i find the x-intercepts of a function like this

[cloud wadi]

well

[thick parcel]

There would not be

[cloud wadi]

if it is intercepting x, that would mean it has a root

[slender walrus]

in general,
set equal to 0
solve
exclude domain violations

[strange coyote]

thats what i originally thought, but i plugged it into desmos to check and i saw there were two x intercepts,. but i just checked again, and there arent, must have made a typo somehow 😔

anyway thanks for the help i understand what i need now

.close

[midnight plank]

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[quartz sage]

Hey there folks, got a question about tripe integrals, and this case here: b) f(x, y, z) = x, U: xyz = 0 i 2x + 2y + z − 2 = 0;. My main concern is if it is possible to claim that

0 <= y <= 1-x
0 <= z <= 2 - 2x - 2y
```?