help-19

[wooden cypress]

Just take the reciprocals of these?

cot x = 1 / tan x = b / a

etc

[ocean bramble]

x is measured as an arc length. As in the ratio of the arc length covered divided by the radius

so x is usually called "angle"

[shrewd trellis]

Is sin x same as sin theta?

[ocean bramble]

y

tan(x) is the tangent of said arc

[wooden cypress]

yes, x and theta are just variables

They don't mean anything more

[ocean bramble]

tan^-1(x) means the arc with a tangent of x

[shrewd trellis]

So for finding reciprocal of sin theta, wee get the value and do 1/that value we just found from sin theta

[ocean bramble]

so tan^-1(tan[x]) means the arc with a tangent of the tangent of x, which is x

[wooden cypress]

If you do that you will get cosec theta yes

[shrewd trellis]

But how is that same to hyp/opp

Do they give u same value?

[wooden cypress]

If you look at the diagram I sent

sin x = opp / hyp

So cosec x = 1 / sin x = hyp / opp

Everything you need is in the diagram and in this message

[shrewd trellis]

alr I understand now

essentially trig ratios are basically like fractions

[wooden cypress]

Yeah exactly

a, b, and c aren't exactly defined

Because you could for example double them all

[shrewd trellis]

It looks at similar triangles that has same ratios

[wooden cypress]

But their ratios are defined, and those ratios are the trig functions

[shrewd trellis]

Or diff triangles

with diff ratios

[wooden cypress]

Ye

[shrewd trellis]

Wdym

[wooden cypress]

Well if for example x = 45 degrees

Then you could draw a triangle where a = b = 1, and c = sqrt 2

But you could also draw a triangle where a = b = 2, and c = 2 sqrt 2

So you can't just say what a is

But in both cases, a / b = 1

So tan (45 degrees) is 1

[shrewd trellis]

Why did u make a = b

[wooden cypress]

Becuse that's what 45 degree triangles look like

Try drawing one

[shrewd trellis]

I mean what I’m trying to say is I don’t understand what you mean

[wooden cypress]

Okay let's say we've got a triangle like this

Exactly the same as the previous diagram, but with x = 45 degrees

Then what is the angle marked with a ?

[shrewd trellis]

Well we could find that by trig ratios if atleast two sides of the triangles are known

[wooden cypress]

Nope you don't need any trig

Just basic geometry

But you're right

If you know two of the sides, you can work out the other angle with trig

What do the angles in a triangle add up to?

[shrewd trellis]

180

[wooden cypress]

Good

So what is the angle?

[shrewd trellis]

Oh yea 45 + 90 + x = 180

solve for x

[wooden cypress]

Good

So what is x?

[shrewd trellis]

40

[wooden cypress]

Try again

[shrewd trellis]

55

[wooden cypress]

Try again

You're close

[shrewd trellis]

45

[wooden cypress]

Much better

So this is what the triangle looks like now

What kind of triangle is it?

[shrewd trellis]

Right angle triangle

[wooden cypress]

Yes but what else?

It's a very specific kind of right angled triangle

[shrewd trellis]

Isiscikes

[wooden cypress]

lol

isosceles

[shrewd trellis]

Iscoscoles

[wooden cypress]

But yes it is

It's okay nobody really knows how to spell it haha

So what does that tell you about a and b?

[shrewd trellis]

They are equal

[wooden cypress]

Exactly

[wooden cypress]

Does that answer your question?

[shrewd trellis]

Oh yep, now I need to understand after that

[shrewd trellis]

I don’t understand this and the sentence after it

[wooden cypress]

My honest advice would be to really make sure you have a solid handle on geometry like that before you move on to trig, otherwise it might just confuse you

But the fact that a = b means that tan 45 = 1

Okay yeah

so

If we want, we can just declare that a = 1

That make sense?

Then from that, you know what b is

Then you can use pythagoras to work out what c is

But equally, you can declare that a = 2, or 3, or any other (positive) number you can possibly think of

Then from that, you know what b is

Then you can use pythagoras to work out what c is

[shrewd trellis]

Why did u make a =1

[wooden cypress]

Just arbitrary

That's my piont

It doesn't matter at all what a is

[shrewd trellis]

Oh

[wooden cypress]

Just some positive number

1 is just a really nice number to work with

Often, for reasons that won't make sense to you for another few years, mathematicians like to set c = 1

That has some pretty nice properties

But ultimately it doesn't matter one bit

[shrewd trellis]

U said something about these variables aren’t defined, and why can’t we say it’s just what a is

[wooden cypress]

Well in this example, a = 1

[wooden cypress]

But in this example, a = 2

Those are both right angled triangles with an angle of 45 degrees

But they don't have the same a value

So the angle alone is not enough to work out a

You need more information than that

[odd edge]

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[maiden delta]

help

[maiden delta]

can i get some help

[agile sinew]

what's ur question 🙏

[green elm]

not unless you ask a question

[turbid parcel]

@maiden delta

[maiden delta]

oh wait

[turbid parcel]

let's say we had 3/6

what would you do

[maiden delta]

divide it

[turbid parcel]

by?

[maiden delta]

2

3

i meant 3

[turbid parcel]

and it would become?

[maiden delta]

2

cuz 6 divided by 3 is 2

[turbid parcel]

but i gave you 3 divided by 6 😄

[maiden delta]

so 2

[turbid parcel]

does this make sense to you

[maiden delta]

how did the 6 turn into 3x2

[turbid parcel]

what is 3x2 equal to

[maiden delta]

6

[turbid parcel]

so can i rewrite 6 as 3*2

[maiden delta]

but ontop u just copied 3 right?

[turbid parcel]

does this make sense to you

[maiden delta]

lil bit

if u cut 3 how did it become 1

[turbid parcel]

in a fraction if you multiply or divide BOTH the top (numerator) and bottom (denominator) by the SAME thing the fraction value remains the same

so let's say i had 1/2

2/4 is the same thing as 1/2

[maiden delta]

wait so basically 3 had an x and u cut 3 from x and x is a visual representation of 1 so u wrote one and u cut 3 from x2 so u copied 2

or

[turbid parcel]

x was a multiply sign...

[maiden delta]

when u cut top 3 and cut down 3 it remained x2 but since theres no top number x became 1 and 2 become 2

[maiden delta]

oh i thought it was a variable

man nun of these making sense to me

i still dont get this

[turbid parcel]

we'll get to it

you need to understand fractions first

your core concept is lacking which we need to address

this is what i did if the 3x2 didnt make sense to you

3 divided by 3 is 1
6 divided by 3 is 2

[maiden delta]

3 divide by 3 is 1 and 6 by 3 is 2

[turbid parcel]

so we got 1/2

yes brilliant

now

do you know that a^2 means a*a

a multiplied by a

[maiden delta]

a squared?

[turbid parcel]

yes

[maiden delta]

yes

[turbid parcel]

so a^3 (a cubed)

is a*a*a

correct?

[maiden delta]

yea

[turbid parcel]

so a^4 would be

[maiden delta]

for every * is a squared or an exponent?

so aaa* is a cubed

i get it

yo

whered u go

[turbid parcel]

sorry i had to attend to something

okay so

[maiden delta]

ok

[turbid parcel]

now

[maiden delta]

ok

[turbid parcel]

we've established that a^2 is a times a

what if i asked you

evaluate this

what can we do here

[maiden delta]

a times a and a

[turbid parcel]

perfect

and now we can?

[maiden delta]

a times a/ a

can

times it

[turbid parcel]

because it's the same thing

remember that when we had 3/(3*2)

[maiden delta]

so 0 times 0 and 0?

[turbid parcel]

we could just cancel the 3s because what we were doing was

dividing by 3 on top and at the bottom

correct?

and we were left with 1

[maiden delta]

this?

[turbid parcel]

yes

[sturdy cape]

[dividing by zero is almost always dangerous]

[maiden delta]

nothing times nothing

[maiden delta]

yea i get it

[turbid parcel]

perfect so now we go to your question

a^4/a^7 can be written out as

(i want you to write it out)

[sturdy cape]

That's fine, but seeing that it came after a fraction, it reads like you plugged in a =
0, so be careful]

[maiden delta]

a times a times a times a times a times a times a times a times a times a times a times a times however many left

[turbid parcel]

do you see what we can do now

[maiden delta]

cut it out?

so it becomes 1

[maiden delta]

since they are all the same?

holup i gotta take a piss

[turbid parcel]

and that simplifies to?

[maiden delta]

im back

[maiden delta]

1/3?

[turbid parcel]

a times a was a^2

we have a times a times a

[maiden delta]

theres 3 a?

1/cubed?

[turbid parcel]

1/(a cubed)

specifically a

[maiden delta]

yea

[turbid parcel]

if you dont mind me asking, how old are you?

[maiden delta]

il get to that after we answer this

[turbid parcel]

we already did

[maiden delta]

oh

so the answer to this is 1?

[turbid parcel]

and i waited until we were done answering it so i could ask you

[turbid parcel]

what was this an answer to

[maiden delta]

1 cubed

1 a cubed

[turbid parcel]

1 OVER

specifically

in a fraction

[maiden delta]

1 over a cubed?

[turbid parcel]

yes

now can i ask how old you are if you dont mind

[maiden delta]

14

[turbid parcel]

ah alright no worries

[maiden delta]

wby

wbu

[turbid parcel]

i just turned 18

well

if your question is resolved

!done

[odd edge]

If you are done with this channel, please mark your problem as solved by typing .close

[maiden delta]

im gonna ask more later

[turbid parcel]

alright

[odd edge]

@maiden delta Has your question been resolved?

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[humble jungle]

Can someone tell me when do we consider the special case of (n-1)!/2 in circular permutations?

[humble jungle]

I can't visualise it

Ik it happens when mirror images are equal like on a necklace

But how exactly it differs from the case where we take (n-1)!

Like isn't that a circular permutation too

I think (n-1)! Is used when anti clockwise and clockwise direction matters

[pallid badge]

Its because you can flip a necklace or a garland

[humble jungle]

And (n-1)!/2 is used when it doesnt matter

When you can flip in the third 3rd dimension

And make anti clockwise equal to clockwise

[humble jungle]

1,2,3 and 1,3,2 are different in table arrangement

But why are they different

U can just go from the opposite direction in 1,3,2 and they will be same

Ik in a necklace u can go from both directions

Because they can be "flipped over"

And "tables can't be flipped over"

Ugh

So direction in circular arrangement only matters till they can't be flipped over

And made equal?

[odd edge]

@humble jungle Has your question been resolved?

[humble jungle]

Why is combination with unlimited repetition similar to permutation with limited repetition

[narrow crypt]

i beg ur pardon?

[humble jungle]

Combination with unlimited repetition => n+(r-1)C(r-1) has the same form as the Mississippi problem where u scramble all the letters and find all the arrangements of the word

Am i noticing

Or completely off

[narrow crypt]

this means that one 's' is not the same as the other 's'

[humble jungle]

U gotta account for identical letters

[narrow crypt]

if u account for the identity letters then

divide by 4!4!2!

[humble jungle]

Isn't it similar to combination with unlimited repetition

Like the identical chocolate distribution problem

Nvm I'm holding this channel for silly shit that's probably not true

.close

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[glacial loom]

does anyone know where i can find solutions to serge lang basic maths????

[odd edge]

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[echo relic]

If the divider is removed, what is the height of the water

[narrow crypt]

the combined volume remains constant

!status

[odd edge]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[narrow crypt]

@echo relic

[wooden python]

hmm OP is offline

[narrow crypt]

i got ghosted ):

[odd edge]

@echo relic Has your question been resolved?

[odd edge]

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[frail lintel]

Can some please help me with this question

Also the angle which angle is it

Theta or alpha

[tacit haven]

ive never seen this in my life but im just guessing its the angle of intersection between the tangent lines

[narrow crypt]

,rccw

[frail lintel]

Igot this till here

But what should be the best possible substitution

[cold cobalt]

Bro what chapter is this 😭

[frail lintel]

Ahh

[frail lintel]

Application of derivatives

[narrow crypt]

,rccw

[cold cobalt]

No way

Alright you can find x or y from eq 1

[frail lintel]

Can i do it any other way

[cold cobalt]

Then find the other from putting it in other eq

[cold cobalt]

How do u wanna do it

Show full working from the start

[frail lintel]

I dont know maybe an easier substitution

Ok

[cold cobalt]

,rccw

[cold cobalt]

Theek toh kar rahe the

[frail lintel]

Ah nvm i got it....i can jus substitute it as a cos theta and b sin theta

[cold cobalt]

U just have to combine this both

[frail lintel]

Ahhh

[cold cobalt]

Alright ig

[frail lintel]

.close

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[frigid isle]

Wtf

[odd edge]

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[wide pollen]

how can i proof that this polynomial have no roots in the interval (−∞,−1]

[wide pollen]

any hint (no full answer) will be great

thats what ive found so far

[narrow crypt]

Derivative?

[frigid isle]

Yes

Just check where the function is decreasing

[wide pollen]

i need to show that theres no solutions for px=0 in this interval

(−∞,−1]

i cant differentiate a function yet

[narrow crypt]

So u can only use limit?

[wide pollen]

yep

[narrow crypt]

U can’t use differentiation?

[wide pollen]

no

[narrow crypt]

The main idea that I have is to show that the function is bounded below by 1 ;-;

Over that interval

[wide pollen]

i cant use yet upper/lower bounds if thats what you mean.. :/

[wide pollen]

.

[narrow crypt]

Oh waittt

0 = x^4 - x - 1

1 = x(x^3 - 1)

[wide pollen]

only hints plz btw

[narrow crypt]

This function is x^4 - x shifted up by 1

[wide pollen]

u mean it was shifted down by 1?

cuz the minus one

[narrow crypt]

oh rihgt

nvm

the idea doesnt work now ):

[wide pollen]

:/

[narrow crypt]

or does it

x(x-1)(x^2 + x + 1) - 1

[frigid isle]

Just show

That the function decreases/increases in that interval

[narrow crypt]

we cant use derivative ):

[frigid isle]

And if so

Then check value to -1

U could also just lmvt

🗣️

[narrow crypt]

can u use that?

[wide pollen]

cant anything related to derivatives

[wide pollen]

so cant use that

[merry finch]

,w x^4 - x - 1

[clever fjord]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by frosst

[narrow crypt]

it is true

[wide pollen]

btw showing that there are roots between other intervals was pretty easy using intermediate value theorem

[narrow crypt]

x + 1 = x^4

x^4 > x + 1 for x < -1

[narrow crypt]

So there should be no intersection

[merry finch]

ooh can you show that there doesn't exist a solution between -2 and -1

[narrow crypt]

Or lhs is negative and rhs is positive so no possible intersection

[merry finch]

if you can then you can use cauchy's bound to show all solutions must be between -1 and 2 meaning there are no solutions in -∞ and -1

[frigid isle]

Oof

[narrow crypt]

@wide pollen is this a valid response

[narrow crypt]

[frigid isle]

Idk what is the use of restricting students

[merry finch]

hey it was a good idea, if the problem was from -∞ to -2 you could check -2 then use cauchy's bound

[narrow crypt]

To uhh

I don’t even know what a Cauchy hound is😭

Is it from ra

[frigid isle]

😨😨😨

[merry finch]

1 + max {|a_n-1/a_n|, |a_n-2/a_n|, ..., |a_0/a_n|}

[narrow crypt]

Unoptimize a project

[wide pollen]

cant use cauchy didnt learn it yet

[frigid isle]

💀

[narrow crypt]

How abt this 🥀

[merry finch]

that's the upper bound for the distance of all roots in any complex polynomials

[frigid isle]

U think they would let the use of cauchy but not derivatives

[wide pollen]

lmao

[wide pollen]

checking it

[frigid isle]

Just

Uhh

what are u allowed to do

[narrow crypt]

Use math

Duh

[frigid isle]

Not allowed

I didnt learn it

😔

[wide pollen]

lmaoo

[wide pollen]

in calculus one we reached continous of functions

[frigid isle]

If i was u i would go to the teacher and ask he/she to plot the entire graph without the use of anything but basic arithmetic 🗣️🗣️

[wide pollen]

sry for my bad english

[narrow crypt]

Built like desmos😎

[wide pollen]

its just week 2 of calculus one :/

[narrow crypt]

So..

[frigid isle]

So only limits are allowed?

[narrow crypt]

https://tenor.com/view/please7tv-please-beg-pray-hope-gif-3860103425950934673

[narrow crypt]

Limits + continuity

I think

[wide pollen]

yes

[wide pollen]

.

[frigid isle]

Uhhh

Continuity is useless af here

😔

[narrow crypt]

Plz accept this as a response

;-;

[wide pollen]

how can i prove it

[narrow crypt]

x^4 >= 0 is true in general

[wide pollen]

i understood that u mean that x^4-(x+1)>0 for x<-1

am i right?

[narrow crypt]

Yes

[wide pollen]

this looks good

any hints for proving it

[narrow crypt]

Since x < -1

[narrow crypt]

Might want to rearrange this👀

[narrow crypt]

With this

[wide pollen]

ok just a secd

@narrow crypt is it smth like that

how can i prove better the green barracks?

[narrow crypt]

Equality only holds when x = 0

Since x is never 0 here

Strictly inequality is allowed

[wide pollen]

oh and thats it?

[wide pollen]

can i just say it in words

[amber veldt]

sure

doesnt have to be written in symbols to be math

[wide pollen]

thx

@narrow crypt the solution worked for me thx

[narrow crypt]

Wonderful

[wide pollen]

.close

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[dire belfry]

I'm learning about improper integrals of type 2 in my second semester at university. One of the examples in the lecture slides shows a function with a discontinuity at a point c∈(a,b), and they write that f(x)is continuous on (a,c) and (c,b)

But this confused me, from my understanding, writing (a,c) and (c,b) implies that f(x) is not defined at a and b either, which would make both sub-integrals improper. Wouldn't it be more accurate to write [a,c)and (c,b] instead? That way, it's clear the only discontinuity is at c, and f(x) is fine at the endpoints.

Is there a reason why my lecturer used round brackets.

[sturdy cape]

Logically, the sum of the area under the curve at the point a (i.e. a singular point) is fundamentally 0

Because the interval [a,a] = {a} has measure 0

It's slightly bleeding into Measure Theory (cf. Lebesgue integration) at this point, suffice it to say that we don't necessarily have to have the boundaries explicitly defined on the function for it to be integrable

Thus, integrating "from a to b" amounts to intgrating over the open interval (a,b)

It's not that f(a) and f(b) don't exist; it's more that it doesn't matter if they don't

The definition here is trying to explain something related but essentially different

Namely, even if the interval you're integrating over has a discontinuity somewhere (call it c), we can still integrate it, but we need to play it safe

The limits there have to be specified anyways because the two limits don't necessarily have to agree

[dire belfry]

ok

Thanks

.close

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[covert root]

$\lim _{x\to 1+}\left(sin\left(3x-3\right)^{ctg\left(3x-3\right)}\right)$

[clever fjord]

Rubix

[covert root]

first natural log then lhopital?

[stable sequoia]

ctg as in cot?

[covert root]

yes

or what if its taken as x^0 = 1

since one is from the right

symbolab and wolfram cant solve this

[covert root]

and by this route i still get indeterminate forms after first derivatives

[odd edge]

@covert root Has your question been resolved?

[woeful vine]

Can you show?

[woeful vine]

L'Hôpital rule is for ratios, not for products, you can't just apply it to cot(3x-3)log(sin(3x-3)) like that

[covert root]

ill try applying to the last form i got

[woeful vine]

do you know what L'Hôpital's rule says?

[covert root]

we find the derivative of the ratios

[woeful vine]

not really, no

[covert root]

if its 0/0 or inf/inf

[woeful vine]

(Under some right hypotheses)
$$
\lim_{x\to x_0} \frac{f(x)}{g(x)} = \lim_{x \to x_0} \frac{f'(x)}{g'(x)}
$$

[clever fjord]

Luigi

[woeful vine]

that is not the derivative of the ratio, but the ratio of the derivatives

[covert root]

my bad fam

lemme resolve

We good fam?

Think we good, sorry for my braindead theorem executions

[woeful vine]

you missed a ⨯3 in the derivative of the denominator

also, the derivative of tan is sec², not csc²

remember also that whatever you get is not the final result, you applied log at the beginning, so you need a final exp

[covert root]

Right thanks

[woeful vine]

Just have to have to fix the mistakes I mentioned

[covert root]

Better?

[woeful vine]

There are still few weird steps

[covert root]

I didnt know what to do with 3cos^3/3sin so i went another way

[woeful vine]

red --> that should not be an equal sign, you want to say “let's study lim log (...)”
blue --> just what happened there?

[woeful vine]

what's cos³(3x-3) as x --> 1⁺?

[covert root]

1

Blue is the new path i mentioned

[woeful vine]

blue doesn't make much sense

[covert root]

Wait

[woeful vine]

you have cos³(3x-3)/sin(3x-3), what do the numerator and denominator tend to as x --> 1⁺?

[covert root]

1/0

[woeful vine]

specifically 1/0⁺

[covert root]

so +inf?

[woeful vine]

yes

[covert root]

this is what i did, i fixed my mistake and still get cos^2 of (3x-3)/ 3sin(3x-3)

[woeful vine]

this is wrong

[covert root]

so the result is e^inf == inf

[woeful vine]

sec² is at the denominator, not numerator

you can't just move it up and down

[covert root]

yeah

[woeful vine]

this also doesn't track, 3 should cancel out and it should be cos³

(Note that writing “cos^2 of (...)” makes it sound like the whole thing coming is the argument of cos², which I don't think is what you meant)

[covert root]

yeah fair, forgot the 3, in this case however it doesnt change the outcome

think thats it, its inf

[woeful vine]

but if it did you would be like “why is this wrong?”
you can't know if something changes the outcome until someone tells you the correct outcome

Just saying, let's try to avoid computational mistakes

[covert root]

im not justifying my mistakes xd just higlighting them to be clear

thanks a lot you've been very helpful

.close

[odd edge]

Channel closed

Closed by @covert root

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

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Remember:
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[sharp bridge]

it said the answer was (−∞,1)∪(3,4).

[sharp bridge]

just wanna know how this is negative infinity

ik this is like special needs math

[quasi sparrow]

do you know what decreasing means?

[sharp bridge]

dont be condescending in a tutoring server

[quasi sparrow]

i wasn't being condescending

simple yes would be fine

[sharp bridge]

are intervals not written (x,y)?

this one is (-∞,3)
which is written (y,x) no?

[quasi sparrow]

no, not all intervals can be written as (x, y)

[sharp bridge]

if the -∞ is x where did 3 come from

or am i only mapping x

[quasi sparrow]

also this isn't a "tutoring server"

no one's getting paid here

[sharp bridge]

im not gonna argue the logistics of tutoring w you i just want help w my math

[quasi sparrow]

¯_(ツ)_/¯

[sharp bridge]

bro are you trolling what is happening

[quasi sparrow]

don't say so many wrong things

[sharp bridge]

jesus i bet your fun at parties

[sharp bridge]

nah i understand that one

im on 2 now

[quasi sparrow]

so what's with not understanding the 3?

[sharp bridge]

how is it 3 if the x is neg infinity

am i mapping x,x

[quasi sparrow]

do you know what $\cup$ symbol means?

[clever fjord]

riemann

[sharp bridge]

no actually

assuming its the direction of the parabola?

[quasi sparrow]

[sharp bridge]

okay bro go fuck yourself

go somewhere else

[quasi sparrow]

that's exactly why i wasn't being condescending here

[sharp bridge]

nah go somewhere else

[quasi sparrow]

be less snowflakey for the next helper

[sharp bridge]

i dont want your help at all

your just a dick

[radiant oriole]

Its - infinity to 1 because 1 is where it starts increasing i think

and since this is an angled line it goes infinitely forever that way

i think

[sharp bridge]

im on 2

[radiant oriole]

ah

mb

[sharp bridge]

thanks thouth

[radiant oriole]

is the parabola 2?

its just - infinity and 3 then for that one

[sharp bridge]

yeah but am i mapping x,x

[radiant oriole]

oh

no clue what that means lol

[sharp bridge]

well like normally it would be mapped x,y for data points

so i put (-infinity,-6)

x,y

how did you know to use x,x

[radiant oriole]

its just like at what x value does y start decreasing and what x value does it stop decreasing

[sharp bridge]

ohh

[radiant oriole]

its just asking when x starts and stops decreasing, so both values should be x i think

[north sparrow]

(x,y) can describe two things a point in the plane and an interval of values like here (-infty,1) is the set of x values from -infty to 1 excluding 1

the U symbol is used to combine two intervals

[sharp bridge]

yea did a little chatgpt refresher on union and intersection totally forgot that was a thing

[north sparrow]

here it's assumed the parabola y(x) keeps going up when x becomes less than 0. All they want then is for you to describe the set of x values you could plug in y(x). Maybe this picture will make more sense

[sharp bridge]

I put (-inf,1)U(1,4)

[sharp bridge]

yea that makes way more sense

[radiant oriole]

i mean that one is just (1,4) right

cause it starts decreasing at 1 and stops at 4

[north sparrow]

idk why you put (-inf,1) but (1,4) is good

[sharp bridge]

do i ignore the infinity on these?

[radiant oriole]

cause its infinitely going up

not down

[red perch]

we use f'(x)=0

and just the number lines

[sharp bridge]

what about the other infinity??

[radiant oriole]

wdym

[red perch]

if is - , its downwards (which decreasing)

[north sparrow]

f is not explicitely given

[sharp bridge]

like this one is (-6,-2)U(1,inf)

so why is infinity mapped here and not the other one

[radiant oriole]

because this one is asking for increasing

and you can tell that it starts increasing infinitely at 1

and as far as you know it doesnt stop

[sharp bridge]

no i understand that but theres no difference between this being pos infinity and the last one including negative infinity do i just ignore the left side infinity? im confused

[radiant oriole]

For this one, if you increase x it goes up until 1

and then it keeps going up

at 5

so when its at 5 and it keeps going up itll go to 6,7,8 etc, these are all positive numbers, there cant be a negative number there

but for the other one

[sharp bridge]

but wouldnt it start at neg infinity

[north sparrow]

increasing means that whatever x and y you pick on this range of values x > y imply f(x) >= f(y).

[radiant oriole]

the parabola starts decreasing at negative infinity

lets just say that it starts decreasing at x = -2,

[north sparrow]

but that might be more confusing

[sharp bridge]

yk what i see it im just slow asf

i looked at it wrong

mb

[radiant oriole]

oh lol

i keep reading whole questions wrong so your fine

lol

[sharp bridge]

i appreciate the help[

[radiant oriole]

🙂

[sharp bridge]

i finished it

i understand all of it now i was like subconsciously plotting y everytime

1 assignment down 7 more and the exam to go

[north sparrow]

.close

[odd edge]

Channel closed

Closed by @north sparrow

Use .reopen if this was a mistake.

[north sparrow]

oh sorry

.reopen

[odd edge]

✅

[north sparrow]

!done

[odd edge]

If you are done with this channel, please mark your problem as solved by typing .close

[sharp bridge]

confused as to what im doing here

[limpid adder]

do you understand what (g/f)(x) is saying?

[sharp bridge]

for reference i missed 6 classes in a row bc i was camping in yellowstone so i just dont know the content its all new to me

[limpid adder]

oh alr

[sharp bridge]

no

[limpid adder]

ok so it means (g/f)(x)=g(x)/f(x)

[sharp bridge]

are g and f just meaningless variables

[limpid adder]

oh they are considered functions

[sharp bridge]

how does the assumption change the problem

[limpid adder]

like f(x)=x that is a function

g(x)=x^2-1 is another function

the reason why theyre different is because they are different functions

so you assign a different name which is g(x)

the x inside the parenthesis means it is the value you plug in

aka the independent variable

[sharp bridge]

makes sense

[limpid adder]

so (g/f)(x) is like a different way of writing g(x)/f(x)

basically you are dividing g(x) by f(x)

[sharp bridge]

how does the assumption affect the problem

[limpid adder]

which assumption

[sharp bridge]

x does not equal 1

[limpid adder]

its because when you plug x=1 into (g/f)(x) it is undefined

[sharp bridge]

wym

[limpid adder]

0/0 is undefined

also i need to go eat sorry i hope someone else here helps 😭

[tawny lake]

well we know what f is

and what g is

[north sparrow]

try plugin in x=1 in (f/g)(x)=f(x)/g(x)

and see for yourself

[tawny lake]

so lets write g(x) / f(x)

wrong way around brochacho

[sharp bridge]

im on a new problem now hold on

Note that we had to assume x≠1 , because if x was equal to 1
, we would have had a denominator equal to zero, making the function undefined.

what does this mean in laymans

[velvet gull]

What would 5 divided by 0 equal to?

[hidden token]

You know that if the denominator of a fraction is 0, it is undefined?

[sharp bridge]

0

[velvet gull]

No, it's undefined

[tawny lake]

please first write g(x) / f(x)

[velvet gull]

It does not have an answer

[mystic saffron]

Bro there are certain things u gotta assume and accept in maths to proceed otherwise, u can't solve problems

[sharp bridge]

huh

ive taken stats and stuff so its not like im incapable i just havent touched algebra since like 10th grade

and i missed 6 lectures

so im teaching myself from scratch

[mystic saffron]

So basically for fx/gx to be equal to f/g (x), there has to be a condition that is g(x) can't be equal to 0 since dividing by 0 will give an undefined result

[mystic saffron]

That's a nice initiative

[abstract harbor]

do you know what (g/f) (x) is ?

[mystic saffron]

Do u understand this part?

[sharp bridge]

cant be 0 bc its impossible?

[mystic saffron]

See, I'll give u a simple exercise

[abstract harbor]

yes dividing anything by 0 is impossible, the answer is undefined

[mystic saffron]

Try dividing 2 by 0

[sharp bridge]

error

[mystic saffron]

Do it manually and tell me the answer

[mystic saffron]

Not by any calculator

Try to divide 2 by 0

[sharp bridge]

uh you physically cant

[mystic saffron]

Why can't u?

U obviously can

If u go by the assumption dividing by 0 will give 0, u should obviously be able to right?

So let's try dividing it?

2/0

Let's try 0*1

[sharp bridge]

2

0

nothing x nothing is nothing

[mystic saffron]

We will try to multiply a number with 0 so that we reach 2

Now try to multiply 200

0*200

[sharp bridge]

still nothing

[mystic saffron]

0 right?

[sharp bridge]

im not special needs im just teaching myself from scratch

[mystic saffron]

Now 999999*0

[mystic saffron]

Okk bear with me

[mystic saffron]

What's the answer?

[sharp bridge]

the number doesnt matter if you x0 its nothing

[mystic saffron]

Yup

So no matter how big the number u take it's still never gonna be 2

So what is the quotient of the division?

Something that is veeeery large

How large?

We don't know

So we call it undefined

To understand the undefined part u need to go deeper but for now this explanation will be ok for u

[abstract harbor]

bros really breaking it down

[mystic saffron]

I'm trying lol

[limpid adder]

you could also do this to show that it will always stay 2, therefore having a large number as the answer but it wont be because 0x=0 so we call it undefined

[sharp bridge]

i think math theory is gay i just want a decent grade on my exam that i have to take in 9 hours

[mystic saffron]

Absolutely

[abstract harbor]

how well do you understand functions?

[sharp bridge]

i understand how to translate the problem and simplify it

[abstract harbor]

what do you get

[mystic saffron]

Well maths isn't a 1 day thing and more so if u want to understand all the concepts in 9 hrs

So nothing much can help u bro

Good luck

[abstract harbor]

dw ill take over

[limpid adder]

you just gotta take things one at a time

[sharp bridge]

it sjust college algebra you acting like its a death sentence

its not hard i just need the concepts explained so i can identidfy what the steps are on each problem

[abstract harbor]

show me what you've written for the question so far

[abstract harbor]

yeah show me how far you've gotten on the question at hand so I can see how much you understand

if you don't know how to start then that's fine

[sharp bridge]

gotta download phone discord hold on

[limpid adder]

you could type it here

[abstract harbor]

oh no problem you can explain it as well

[sharp bridge]

f+g(10)= (x+4)(x^2+2)

adn then simplify

[limpid adder]

oh another question

[sharp bridge]

yea im on this one

[abstract harbor]

oh you solved the other one or just pushed it aside for now?

[limpid adder]

do you know what (f+g)(x) means

[sharp bridge]

f+g = x?

[limpid adder]

ok uh

you see how it gives you f(x) and g(x)

those are the functions for f and g

think of f and g as like a name to the function

[sharp bridge]

yea

[abstract harbor]

yeah the way i like to think about it

f(x) just means what would F output if we plug x into it

f(x) = x + 1

[limpid adder]

its also like a y value in a graph

f(x)=x and y=x the same thing

[sharp bridge]

so this 1428?

[abstract harbor]

try solve this f(x) = x + 1 where x = 1

or what is f(1)

[limpid adder]

f(1)

yea

the number in the parenthesis is what you substitute for the variable

[limpid adder]

its quite blurry

[abstract harbor]

no you don't multiply them

[sharp bridge]

sry not super legible

[abstract harbor]

you actually add the functions

[sharp bridge]

this is the example

they multiplied

[abstract harbor]

is this a different question

[sharp bridge]

yea this is the example

[velvet gull]

It does say f + g

[abstract harbor]

let's try to stick to 1 question

[sharp bridge]

ohhhhhhh

so that determines whether i multiple/divide/add the variables

[abstract harbor]

Yes exactly

[sharp bridge]

is f+g or f/g

okay that makes ssense

[abstract harbor]

yeah f represents whatever equation it's equal to

[sharp bridge]

so its 116

[abstract harbor]

g represents whatever equation it's equal to

for which question?

[sharp bridge]

this

[abstract harbor]

uhh 10+4+10^2+2

116 yeah

[limpid adder]

Addition: $(f+g)(x)=f(x)+g(x)$
Substraction: $(f-g)(x)=f(x)-g(x)$
Multiplication: $(f \cdot g)(x)=f(x) \cdot g(x)$
Division: $\left(\frac{g}{f}\right)(x)=\frac{g(x)}{f(x)}$

[clever fjord]

ava 💕

[limpid adder]

this may help

[sharp bridge]

it got more complicated

[abstract harbor]

don't be intimidated just stick to what you learned

you can see what each function f and g are equal to

and what you need to do with them

and what you need to substitute

[limpid adder]

its the same thing but longer equations

[tepid gust]

not really

as (6x^2+2x+2/3)(5x-2/3)(1/3)

[limpid adder]

youre thinking of distributing it

but you dont need to

[abstract harbor]

not needed

[abstract harbor]

1 sec

[north sparrow]

,rccw

[sharp bridge]

6(1/3)^2 = 2/3

[limpid adder]

what is 2.01

[sharp bridge]

2/3+2/3+2/3

[limpid adder]

yeah and that is equal to what

add the numerators

[sharp bridge]

i think the calc just did it wrong

[abstract harbor]

2.01 is your answer?

[limpid adder]

everything is correct

yoiu just gotta do 2/3+2/3+2/3

[sharp bridge]

it’s just 2x1

so 2

[abstract harbor]

(2/3 + 2/3 + 2/3) * ( 5/3 - 2/3)

[limpid adder]

yea

[abstract harbor]

do this again ^

[limpid adder]

they did 5/3-2/3

[sharp bridge]

its 2 i got it

[limpid adder]

thats what the 1 is there

yea

[abstract harbor]

oh yeah well done

im so confused where 2.01 came from

[sharp bridge]

idk i put it in the calc wrong

[abstract harbor]

oh im not sure if u need a calc for 2/3 + 2/3 + 2/3 lol u can just know its 6/3 which is 2

[limpid adder]

you know what to do here
apply what you know

[abstract harbor]

yeah just ping me when u want ur workings checked

[sharp bridge]

i put everything in the calc just so i dont do mental math wrong and get the whole question wrong

[abstract harbor]

do you guys not have non-calc papers in your country?

[limpid adder]

you can write:
2/3+2/3+2/3=3(2/3)=2

[sharp bridge]

yea but not for this class

so do i factor f-g?

[limpid adder]

write out f(x) - g(x)

[sharp bridge]

i got 3x^2-6x+3

[limpid adder]

uh thats wrong lemme get my paper

[abstract harbor]

not quite

you multiplied them?

it says to take them away

[sharp bridge]

i got it

[limpid adder]

make sure you distribute here!

[abstract harbor]

(3x^2 - 2x + 1) - (-4x + 2)

[sharp bridge]

yea i added them instead of subtracting them

its always silly shit like that that fucks me ovber

[limpid adder]

you just need to take your time

[abstract harbor]

happens to the best of us

[abstract harbor]

ur not at college level and helping a college student?

[sharp bridge]

the x3 x2 x are all there own variable so i cant divide them

[limpid adder]

i self taught myself

[abstract harbor]

oh nice

[sharp bridge]

tbf this is super simple math i just dont remember any of it

[limpid adder]

just put the function over the other one, plug the x value and bam!

[abstract harbor]

yeah in my country its high school

[limpid adder]

you dont need to divide the variables

[sharp bridge]

f/g?

[limpid adder]

thanks, im currently trying to study for IMB however im lazy

[limpid adder]

yes

[signal oar]

(f/g)(x) stands for f(x)/g(x)

Write that out and then see how you could continue

[sharp bridge]

i wrote it out im js confused as to what im dividing if none of the variables match up

[limpid adder]

you dont need to divide the variables

just simply plug the x value

oh wait

[sharp bridge]

x isnt given

[limpid adder]

shoot mb

this is gonna be hard to teach

[sharp bridge]

ill just get it wrong and read the explanation

[limpid adder]

https://www.youtube.com/watch?v=_FSXJmESFmQ

watch this

this will help quite a bit

[sharp bridge]

so simplify the x3 by subtracting x1 from the top and then the top and bottom cancel?

[limpid adder]

yea

wait hol up

ok yeah

[sharp bridge]

this is confusing me

so im finding h with one and then plugging the answer of h into f?

[limpid adder]

so if you see f(h(x)) it means to find the value of h(x) then use that value for f

[sharp bridge]

oh okay this is light

[mystic saffron]

Wow this doubt has been going on for a long time

[sharp bridge]

i have maybe 4 more hours of math to do

[limpid adder]

oh dear

[sharp bridge]

doing a whole unit in a day

[mystic saffron]

Good luck buddy

[sharp bridge]

light work ive done it many times before

[limpid adder]

i suggest watching the organic chemistry tutor on algebra topics

[sharp bridge]

im 3 hours in and i feel really good about everything so far

[mystic saffron]

But I suggest u to focus on stuff ur confident in

[mystic saffron]

But girlie this is college maths... Not that easy

[sharp bridge]

im gonna have a cheat sheet for the exam bc its an online honorlock exam

this is unit 1 so i wouldnt call it college math yet

[limpid adder]

i learned this by myself in 4th grade, so im sure others can do it too using that ytber

[mystic saffron]

Don't treat it lightly coz if u don't understand these, things will fly over ur head before long

[mystic saffron]

That's same for me too but what I'm surprised about is someone struggling with these in college

[limpid adder]

it could be the country

[mystic saffron]

And who knows u might be a genius unlike us commoners

🙇🏻‍♂️

[sharp bridge]

what did i do wrong

[limpid adder]

true except i dont understand any geometry concepts 😎 (only algebra and number theory by beloved)

[limpid adder]

you did f(x) first

you need to evaluate the inside which is g(x)

[sharp bridge]

i destroyed geo i had a 96

[limpid adder]

so find g(-1)

[sharp bridge]

tbh geometry is fun imo

i like the rules and the logic

[mystic saffron]

I'm sure this isn't the right way to solve this

[sharp bridge]

was i supposed to find g first and not f

[limpid adder]

yea

find g first

[sharp bridge]

o

[limpid adder]

evaluate from the inside

[mystic saffron]

Missy is right

U could think another way too

It says fg x

So first we put g in f

For the x in f, substitute the expression of g

And then u will get a final expression wherein u put x=-1 to solve

[sharp bridge]

so for FoG what do i plug in where

plug g into f or f into g

[mystic saffron]

By fog they mean f of g

[limpid adder]

its f(g(x))

[mystic saffron]

G goes into f

[sharp bridge]

sweet

what is wrong

[limpid adder]

i think you put f into g

insterad of g into f

[sharp bridge]

this one is GoF

[mystic saffron]

Yeah

[limpid adder]

oh

[limpid adder]

exponents before dsitributing

expand (4x+5)^2

[sharp bridge]

ohhhhh

pemdas

[limpid adder]

(a+b)^2=a^2+2ab+b^2

[sharp bridge]

is it 4x^2 or 16x

[limpid adder]

(4x+5)^2=16x^2+40x+25

you distribute the exponent to both

(ab)^n=a^n*b^n

[sharp bridge]

where did 40 come from

[limpid adder]

2ab

2(4x)(5)

2(20x)=40x

[sharp bridge]

(4x+5)^2 = 4x^2+20x+25??

[limpid adder]

uh no

use the formula

[limpid adder]

here

[sharp bridge]

i do not remember doing ts ever😭

[limpid adder]

$(4x+5)^2=(4x)^2+2(4x)(5)+(5)^2$

[clever fjord]

ava 💕

[limpid adder]

a=4x and b=5

you can also do this box method

[sharp bridge]

ohh okay i remember that

i was thinking of it wrong

oh wait so i do 20x twice>

[limpid adder]

yea because it is 2ab

[sharp bridge]

okay

[limpid adder]

2(4x)(5)=40x