precalculus

[peak sinew]

Yup

[static canopy]

30 degree assumption also?

nice

[peak sinew]

Oh wait

Lemme see the question

💀

[static canopy]

dude lmao

thanks for taking the time though

[peak sinew]

Man I love differentiation

I hate trigno tbh

💀

[peak sinew]

And integration

[static canopy]

i'm too early in to have favorites

but fingers crossed I may get good sometime

[peak sinew]

Its easy lmao

The only thing I fear

Is trigonometry in quadrants 💀

Bro I remember doing that 2 yrs ago and I mugged everything up

Trigno in calculus gud tho

👼

Me when I see trigonometry outside the chapter trigonometry:

Me when I see trigonometry in the chapter trigonometry:

[static canopy]

the first one was okayish, at least I didnt get completely lost

but man the b) one not able to make it work

at a) alpha=1/2 was specified so degree 30 assumption made

[peak sinew]

Tan alpha is root3/3

Means tana is 1/root3

Hmm idk why tf is quadrant shit even there

[static canopy]

is this correct?

[peak sinew]

I told ya I don't remember shit abt quadrants anymore 💀

Man ig I have to revise smh

[static canopy]

ah okay dw

[peak sinew]

Wait

Do we even need quadrants in this question?

You have tan bro

Get everything out ez

[static canopy]

tan is sin/cos

i have tan

[peak sinew]

Ye

[static canopy]

but I don't have alpha

[peak sinew]

You know pt ryt

Pythagorean

Use tan a to get sin a and cos a

Ez

[static canopy]

whats formula haha

i tried brute force sin/cos combinations

none equal to tan

[summer ruin]

you're supposed to be familiar with all the table values if you want to do trig, plus there's also a trig circle that features tangent and cotangent

[static canopy]

from 0 to 90*

[peak sinew]

h²=b²+p²

[peak sinew]

Slide me some vids smh

I forgot everything I gotta revise

[peak sinew]

AYO THIS LOOKS LIKE A WATER WHEEL'S INSIDE 💀

@summer ruin

Can't we just get out the values normally

Without quadrant shit?

This transparent guy comes online once then gets transparent again 💀

[static canopy]

so if tan(alpha)=sqrt(3)/2 then alpha=30degrees?

[summer ruin]

it's sqrt(3)/3 and yes

[peak sinew]

Yup 30

Degrees

Or pi/6 rads whatever ya like

@static canopy slide ans when ya done

[static canopy]

@peak sinew i'll do c,d,e also quickly since I think I got the gist of it

[peak sinew]

oki

[strong plover]

do u mind checking some work i did

its just an optimisation question

[peak sinew]

Oki

[strong plover]

thank u so much

[peak sinew]

If its understandable by my side

[strong plover]

this is the question

[peak sinew]

Imagine man sending some high tech integration I'll die 💀

[strong plover]

im sending my working out now

nah nah im young

not hard question

[peak sinew]

OH FUC ITS MAXIMA MINIMA

💀

Wait its something else

Idk smh

Not maxima minima

[strong plover]

its just an ordinary optimization question im pretty sure

[peak sinew]

Something they never taught me

That's y I hate education

[strong plover]

oh lol

[peak sinew]

Why isn't everything uniform

[strong plover]

wdym

[peak sinew]

Like I'm an indian

[strong plover]

ah

[peak sinew]

They teach me shit that doesn't match with outside world

And I hate it smh

[strong plover]

lol its okay

thank u for trying

[peak sinew]

I didn't even apply my brain smh 💀

@static canopy you stuck?

[static canopy]

if sec alpha = 3 find sin(alpha) and csc(alpha)

can't figure out which degree it is

sec = 1/cos

[peak sinew]

When da hell

Sec is 3

Wtf

💀

[summer ruin]

there doesn't exist an exact representation of that angle like pi/3 or pi/6

[static canopy]

but cos(alpha) should be 1/3

[viscid thistle]

You could use a calculator to evaluate the side length ratio and the answer would be rounded

[summer ruin]

yes, but there is no table that can answer what angle produces cos(alpha) = 1/3

you have to use inverse function to represent the angle or figure out how to transform given equation to answer the questions about sine and cosecant

[static canopy]

if sec(alpha)=3
cos(alpha) = 1/3
can sin(alpha) be found?

[summer ruin]

well otherwise this wouldn't be on a problem list

[static canopy]

but there seems no function formula

that fits the bill to get sin

tg seems close since it includes sin/cos but I don't know tangent value

ignoring degrees, using this formula to replace cos with 1/3
sin becomes 2/3? then csc is found naturally

[peak sinew]

Pythagorean ?

@summer ruin can't he use that?

[static canopy]

phone died, no camera on pc so I can't share answers immediately...

it's just homework of last year curriculum(which is pretty much the same this year)

[static canopy]

source:
http://www2.clarku.edu/faculty/djoyce/trig/cosines.html#:~:text=Generally%2C for any angle θ,(90° – θ).&text=cos θ %3D sin (π%2F2 – θ).

@peak sinew

no combination of standard degrees sin/cos make up to a tan of 2

oh, I think I have to look towards 270degrees too

[peak sinew]

Ah yes

[viscid thistle]

whats so hard then

[peak sinew]

Jesus da hell

[static canopy]

i solved that, I'm stuck on finding sin/cos if tan=2

[viscid thistle]

what

[static canopy]

and

[viscid thistle]

tan = sin/cos already

[peak sinew]

Just use Pythagorean ig

[peak sinew]

No he meant ques says tan equals 2, find sin and cos

[peak sinew]

When theta is

I don't remember shit abt quadrants smh

[viscid thistle]

bro just use the ratios and get the answer

tan = perpendicular/base = 2

[peak sinew]

Fr

Use Pythagorean

[static canopy]

i don't have the triangle

[viscid thistle]

exactly

[peak sinew]

Create oneeee

You have tannnn

[viscid thistle]

createeee

one ratio is enough cause sir pythagoras lived in this world

[peak sinew]

💀tf

[viscid thistle]

idk why you are making the simple work complex

wait lemme send you the steps

[peak sinew]

Nice

[static canopy]

I'll follow this video: https://www.youtube.com/watch?v=IBKk7eHove8
maybe it'll clear things up

[peak sinew]

Ok ig

[static canopy]

why perpendicular is 1 and base 2?

[viscid thistle]

*2,1

and bro thats the basic definition of tangent, a trigonometric ratio 🫥

[peak sinew]

@viscid thistle

Brooo

💀

I'M DYING

He did all those shit to get the value of theta

But at the end of the day man applies Pythagorean

💀

[viscid thistle]

Lol

This is pro level maths

You seem to be Indian @peak sinew

[peak sinew]

I am

[viscid thistle]

Why are you crying man

[peak sinew]

Idk bro

[viscid thistle]

I am an Indian too

[peak sinew]

Areee

Yaar I have bst project to do

Wed dena hai

I didn't even complete 50%

💀

[viscid thistle]

Bhai gajab

[peak sinew]

I too have to give accs and maths

I didn't even touch em

Vo bhi wed

[viscid thistle]

Accs?

Accounts

?

[peak sinew]

Yeah

[viscid thistle]

Ah I see

To bhai Commerce me ho?

[peak sinew]

Yes

[viscid thistle]

To bhai lag ja

Warna

[peak sinew]

Ikik

💀

[viscid thistle]

You know it better

[viscid thistle]

Unfortunately

And fortunately

I am from Science 🔭

[peak sinew]

💀

[peak sinew]

Nice nice

11 ya 12?

[viscid thistle]

11th

[peak sinew]

Lucky smh

Bc I have boards in 3 months

[viscid thistle]

Kyo

[peak sinew]

YAARRR I'M SCAREDDD

💀

[viscid thistle]

Oh you're my senior

[peak sinew]

Doesn't matter much lol

[viscid thistle]

Koi nhi bhaiya, boards hi to hai

[peak sinew]

Agle saal I'll say same to u

💀

[viscid thistle]

Are are

[peak sinew]

Nvm pcm ya pcb?

[viscid thistle]

Muze kyo toda

PCM

[peak sinew]

OHHH

Nice nice

Future engineer

[viscid thistle]

Kya lagta hai me PCB me hounga 😂😅

[peak sinew]

Idk man

I know some pros who have pcmb with economics

[viscid thistle]

Ha bhai, I aspire to be an IITIAN

[peak sinew]

[viscid thistle]

Death

That's the only word that comes to my mind

[peak sinew]

Ikr

I was like

Zoor se

In whole corridor

"bsdk pagal ho gaya kai kya"

💀

[viscid thistle]

Lol

This is scary combination

[peak sinew]

It is

[viscid thistle]

Waise muze economics bohot pasand hai

[peak sinew]

Its better not to have it ngl

[viscid thistle]

Par abhi to time nhi isliye nhi liya

Are yar

[peak sinew]

Its good for future but

Its hard for sci kids

[viscid thistle]

Aisi bat nhi muze interest ata h

[peak sinew]

Qki u guys can't connect it with any other subs

Like we can with accs, bst etc

[viscid thistle]

Maybe

Commerce wale log shi mein legend h

*Serious Commerce Students

[peak sinew]

Yup us drawing lines for 1h in a 3h paper

💀

[viscid thistle]

Umm

Idk man

[peak sinew]

Accs

Is full of tables and shits

[viscid thistle]

I have no idea abt accs

I just know there are a lot of calculations

[peak sinew]

Lemme send you one image

[viscid thistle]

Please

[peak sinew]

Dekh this is one 5 mark question

Saala aadha life tables banane mai lag jaata hai

You will now say bro its just a few lines

[viscid thistle]

Yeh to kuch jyada hi hai re baba

[peak sinew]

But bc imagine drawing multiple tables for each sum you do

Smh*

💀

[viscid thistle]

Nhi mene Statistics phadhi hai 😂

[peak sinew]

💀

[viscid thistle]

Statistics me table bana bana ke mein 10th me pagal hi ho gya tha

[peak sinew]

So you can feel that pain

Good.

[viscid thistle]

Abhi hamara Maths ka last chapter again Stats hone wala hai 🥲

[peak sinew]

💀💀💀💀

[peak sinew]

Class 12 mai probability is there

With trigno innit ig

💀

Someone said me ig

💀

[viscid thistle]

Probability is good ig, cause I like Permutation and Combinations

[peak sinew]

I have to check if there actually is

[peak sinew]

Aree bhai my fav class 11 chapter

[viscid thistle]

Gajab

Abhi meri trigo bohot kamzor hai but 12th me ane se pehle accha kar lunga

[viscid thistle]

Kinda Same for me

Kyonki usme koi calculations nhi 🌛

And bas thoda bohot dimag lagana padta hai

[peak sinew]

Buai

Bhai*

Trigno hi toh change ho jaata hai 12th mai aake 💀

[viscid thistle]

Kaise

[peak sinew]

You don't even need trigno ka concepts

Bas formula bc

[viscid thistle]

Bhaisaab

[peak sinew]

And few quadrant shit for inverse trigno

Vo bhi I can do without quadrants for some reason 💀

[viscid thistle]

Lol

[peak sinew]

So the life changes

10 ka trigno was life threatening for me

11 ka was hard

[viscid thistle]

Mereko wait nhi ho rha Calculus phadne ka 🥲

Or 12th ka easy 😂

[peak sinew]

12 mai aake I'm like wtf where did it go 👁️👄👁️

[viscid thistle]

Lol

[peak sinew]

12th is easy rehh

Just be aware of fkin theory subjects

Vahi le dubta hai

[static canopy]

if it's limitited to 180degree to 270*
-1,-1 should be used right

[viscid thistle]

Thoda seh lenge 🥲

[peak sinew]

Here comes quadrants

Help him brodar

💀

[viscid thistle]

hello how would i solve 9^log3(15)

i cant wrap my head around this... i would be very glad if someone could help explain it to me

[viscid thistle]

Very simple

Wait lemme send it to you

okay

@static canopy bro I will get to you, wait a min

Just used a log property

If you know it u know it

oh what

thank you

but

wouldnt the answer in this case be

15^2

Fk I am sorry

Yeah correct

its ok now i understand the problem

thank you a lot

Ig I should sleep now

My mind turning off

[viscid thistle]

Welcome

[viscid thistle]

Bro

Noe

Wait lemee see your problem again

[viscid thistle]

What's the answer?

Ahh I see

The angle is mentioned

[static canopy]

sin = -1/sqrt(2

cos = -1/2sqrt(2)

[viscid thistle]

What

[peak sinew]

Jaadoo

[viscid thistle]

Where from the world sqrt(2) come from

[static canopy]

sqrt( -1**2 + -1**2)

from a triangle -1,-1

[viscid thistle]

I would agree if the answer would be sin alpha = -2/sqrt(5) and cos alpha = -1/sqrt(5)

[viscid thistle]

Why did you form the triangle of -1,-1

When tan = 2 is mentioned

[static canopy]

it's limited to the 180degree to 270* degrees

[viscid thistle]

The triangle should be this

And as in 3rd quadrant sin and cos are negative

My answer is missing the negative sign

But I can't think anything other than that

[static canopy]

the answer limits the triangle in that area

therefore: -1,-1

you made a triangle not considering the 0-360 circle

[peak sinew]

Thank god quadrants left my life

[viscid thistle]

What is -1,-1 could you explain

[viscid thistle]

Yes of course

[static canopy]

x -1, y -1 represent lines perpendicular and base

[viscid thistle]

I played with the magnitude

[static canopy]

that create the triangle

leaving hypotenuse to be solved

[peak sinew]

What the hell?

[viscid thistle]

Bro I can't understand anything you are talking

Especially this -1,-1 stuff

I couldn't help you with this actually

[peak sinew]

Told ya

Jadoo

[viscid thistle]

You could just watch the video

Jadoo ha bhai

lol

[peak sinew]

Not something we did so-

[viscid thistle]

CRY

Bro btw

Aren't you really liking the way your 12th is going

[peak sinew]

No.

[viscid thistle]

Why so

[peak sinew]

Lifes fucked up

From every angle you can imagine

💀

[viscid thistle]

Sed

[peak sinew]

Chal jaane de lemme complete the project smh

[viscid thistle]

Waise apne future ka kya socha hai

[peak sinew]

Marks toh aane de pehele 💀

[viscid thistle]

Chalo bhaiya kar lo ap project, warna

Bye

[peak sinew]

Oki

Gn

[viscid thistle]

GN

[karmic condor]

g(x) = sin(2x) / cos x
g´(x) =
how do you use the u´v + uv´thing?

[open hemlock]

how do i solve this

[peak sinew]

Its a property

https://youtu.be/5sWGXReuQfc

Or just watch this better

[peak sinew]

Btw u don't even need that here

Sin2x = 2sinxcosx

You know that ryt

cancel out cosx

Now remains 2sinx

I hope ya know how to diff 2sinx

[viscid thistle]

Is that the quotient rule

[peak sinew]

Ig you can call that idk

I just call that u by v rule

Or division rule

[static canopy]

maybe this belongs here:
#calculus message

[tawdry pelican]

hello,
im working on the infinite behaviours of an inverse function
i know that the horizontal asymptote is 1. im trying to algebraically find whether y=1+ or y=1- when x tends to + and - infinity

[balmy blaze]

Yeah it is

[viscid thistle]

I don't think there's a directly algebraic way of finding it, but what you do is find your dominating terms on the numerator and denominator, the ones that like grow faster than the others. when you have like a poly times a poly you can judt multiply the dominating terms in each together, and every other term as you trend to infinities contributes far less than those dominating terms. in your case it comes to doing x*x on the top and bottom which simplifies to function looking like x^2 / x^2 at the infinities. cancel them out and it just looks like positive 1.

this is however times when it changes at the infinities though

I mean like

like it's not always going to be the same at both infinities

[kindred lagoon]

Can someone help me through the steps of prooving that d'(x)=-d(x)/x+10 when d(0)=10000?

[willow bear]

what is d(x)?

we're missing a lot of information here. almost the entire problem, in fact. @kindred lagoon

[viscid thistle]

What does the act of getting banned from this server?

Ban Theta( misspelling of TAN theta) hehehe lol

[vapid plaza]

Didn’t you say almost the exact same thing 3 months ago #geometry-and-trigonometry message

… at least the laugh was less exaggerated this time

[tawdry pelican]

@viscid thistle i agree. thanks for the help!

[hasty haven]

What are the steps to solving this?

Really not sure if im doing this right

[viscid thistle]

unsure exactly how this works butttt.. I have about two or three math problems i need help with

[peak sinew]

From sec

Get cos

Cos2x equals 2sinxcosx

So get sin from Pythagorean

Multiply and get em

Ig

Lemme try yk

Ah yes I'm right

[ivory trout]

Very confused

[hasty haven]

Where does this come from?

[peak sinew]

Ok so

Let us make miu as x

Coz I don't have that symbol in my keyboard lol

So secx=-2 is given

Ryt? @hasty haven

[hasty haven]

Yeah

[peak sinew]

So what's cosx?

[hasty haven]

-1/2

[peak sinew]

Yes

You should know that cos(2π/3)=-1/2

So

It makes cosx=-1/2

[hasty haven]

Ok I get that

[peak sinew]

Then cosx=cos(2π/3)

X=2π/3

Then we know

Cos2x

Replacing x

Cos(2*2π/3)

And I hope ya can find the value of cos(4π/3)

Using the quadrant method or whichever method that has been taught to u

[hasty haven]

Is it -sqrt2/sqrt2?

[peak sinew]

Nah -1/2

Lol

💀

[hasty haven]

Bro…

[peak sinew]

Cos(4π/3)

[hasty haven]

I got a test tomorrow

[peak sinew]

Cos(π+π/3)

Ryt?

Use cos(a+b)

[hasty haven]

O i see

I was reading unit circle wrong

[peak sinew]

💀

[hasty haven]

Alright is correct, thanks

[peak sinew]

Lol

[peak sinew]

Imagine I said this before like a dumb shit

[peak sinew]

@ivory trout

[ivory trout]

I figured it out

[peak sinew]

Ah oki

[ivory trout]

I have another question tho

[peak sinew]

The answer is 12i ryt?

[peak sinew]

Slide

[ivory trout]

Yes

[peak sinew]

Solve for k?

[ivory trout]

that’s the answer

but idk how

[peak sinew]

Lemme try

Ok lemme try while trying to make u understand

Lets simplify it first

10k²=-80

Ryt?

[ivory trout]

Yes i have that

[peak sinew]

x²=-8

Simple division by 10 on both sides

[ivory trout]

yes

[peak sinew]

Now

Let's take an example

If y²=4

What's the value of y?

[ivory trout]

2?

[peak sinew]

No

±2

Forgot?

[ivory trout]

OH

yes

[peak sinew]

In the same way

[peak sinew]

This

[ivory trout]

so you would root 8

[peak sinew]

Yes

±√-8

[ivory trout]

why imaginary number

[peak sinew]

Because the chapter is imaginary numbers

Lol

We are dealing with iota here remember?

[ivory trout]

Yes

So i just add it

[peak sinew]

So x=±√-8

Then

Let's take another example

[ivory trout]

OHH we square root both sides

So that’s why it’s that

Okay i understand

[peak sinew]

Try simplify z=√8

z=2√2 ryt?

[ivory trout]

yes

[peak sinew]

Similarly √-8

Is √2•2•-2

Wtf

Lol

[ivory trout]

Yes i understand

I just forgot i was supposed to square root

[peak sinew]

Ye lol

Yeah

So k is ±2√-2

[ivory trout]

Yes i got that

[peak sinew]

And then we take √-2 and √2i since i equals √-1

And doneee

K=±2√2i

[ivory trout]

thank you

[half fulcrum]

anyone know any tips for when solving for exact values for trig identities

its the one thing i seem to struggle with

[peak sinew]

What do u mean my exactly values?

[viscid thistle]

quick question but in the piecewise definition of |x| how come -x is only for x<0 and not x<=0

[summer ruin]

it doesn't matter

you can define |x| = x for x > 0 and |x| = -x for x <= 0

it's just that you don't want your function to have two definitions at one point

[viscid thistle]

is there a reason for why a function shouldnt have 2 definitions at a point?

[summer ruin]

because it's not a function anymore once that happens

for one input you have two outputs

[coral tartan]

can anyone give a brief summary on absolute value functions

i understand absolute values but what about absolute value functions and equations

[cosmic girder]

it's not a function though lol

it's a multi valued mapping or w/e

but definitely not a function

unless of course you say $\ln : \bC \to \mathfrak{P}(\bC)$

[obsidian monolith]

illuminator3 (I/you)

[eternal thistle]

Let 2^x = a, 2^y = b, rewrite the system in terms of a and b

[kindred sluice]

Ok so i did that.
Then i manipulated the other equation and got
2(2^x + 2^y) = 68
I subbed in a and b
and got 2(a + b) = 68

then i manipulated the first equation
and got a = 10 - b
sub it in

2(10-b) + b = 68
20 - b = 68
-b = 48
b= = -48

but i cant take a log of that :/ did i do something wrong?

[eternal thistle]

your equations are wrong

its a^2 + b^2 = 68

a + b = 10

[kindred sluice]

oh crap I see

[eternal thistle]

yeah

8 and 2 is a solution to that btw

just by eyeballing it

there might be another too

[kindred sluice]

thank you. Dang you can eyeball that, your good lol

[eternal thistle]

no

i just tried 8 and 2 because they were powers of 2

and it works

[kindred sluice]

ahh I see. appreciate it

[eternal thistle]

np

[naive stream]

im so dead i do not get how grpahing logs works

is it just hey first make it exponential graph that and then the log is that equation but reflected over y = x

[viscid thistle]

ye

the inverse

[static canopy]

should it be x squared here?

[vapid plaza]

probably

[viscid thistle]

Yep

[viscid thistle]

any idea how to solve this limit

[willow bear]

the correct answer seems to be none of the above lmao

the denominator approaches 0 so if the numerator goes to anything but 0 the limit will explode to infinity

so f(x) has to approach -4

but we don't see that in the options

[bitter egret]

Wait how do x and y cancel each other?

Radius of circle?

Then why is it just "(5/3)^2"?

Oh wait wasn't x and y = 0? Because the circle was lying on the x axis?

Yep.

Got it.

So hold up x and y are the point of intersection?

Ah sure.

[obsidian monolith]

rmu

[bitter egret]

Understood.

Ye I am

Lemme just

But wait there is just one coordinate.

$\sqrt{\left(\frac{5}{3} - x_1\right)^2 + \left(0 - y_1\right)^2} = \frac{5}{3}$

Wait minus not plus

[obsidian monolith]

V01D3D

[bitter egret]

So would this be correct?

Got it.

Wait equation for the circle? What does that exactly mean? The coordinate of the end point of radius?

Wait maybe just coordinates of the point on the circle.

With that consideration, I get it.

What happens after this though?

Wait how do I know which points can do that? do I assume a random number?

This part kinda flew over my head.

(0,0), (10/3,0), (5/3,5/3), (5/3.-(5/3)), I may have messed up I'm on choosing perpendicular points.

Wdym exactly?

All I know is that they can follow the circumference of a circle (since circle has the radius of 5/3)

FINALLY GOT IT LOL.

Brb

[obsidian monolith]

rmu

rmu

[bitter egret]

What problems should I work with to be comfortable?

[bitter egret]

I'll try learning them lol.

Aren't lines-parabola intersections related to quadratic equations?

Mind giving me some problems for Depressed-cubics then?

I never really solved cubics so let's try.

[vapid plaza]

in my honest opinion, it's not worth learning the "general method" for solving cubics (e.g. w/ the cubic formula), but it is still useful to know how to identify rational roots of cubics, as well as to factor cubics with 1 known root.

[still umbra]

Tan B = ⅔ where pi < B < 3pi/2 Does anyone know the solution to this problem?

[weary bramble]

the inverse function of tan for 2/3 radians is the answer for the first quadrant

since tan is first and second quadrant, you do 180-B to find both answers

to understand this, make sure you look on youtube what functions, inverse functions, and quadrants are

[obsidian monolith]

nick!

[astral bronze]

How do I solve for c on a double integral numerically?

[viscid thistle]

I think the answer might be D. I am not sure tho.

[muted vigil]

24x^4y^5

when you look for the lcd, you want to take the highest exponents from the denominators, which is 4 and 5 and cannot exceed as it did in your choice

[strange echo]

you can just look at the numbers and see that the lcm of 8 and 6 is 24, considering that all the answers have different coeficcients

kinda an L move on the teacher but whatever 💀

[boreal saddle]

guys, how do i clear sinh (2t) from an equation?

$s=\frac{\sqrt{32}}{2}\sinh(2t)$

[obsidian monolith]

Aylou-210

[viscid thistle]

$y=a(tan)(x-b)+2$

$y=atan(x-b)+2$

[obsidian monolith]

milky

[viscid thistle]

$y=atan(x-b)+c$

[obsidian monolith]

milky

[surreal berry]

you need some sort of initial condition

[restive flame]

hey guys im having trouble determining the equation of a function from its graph, the form is y = ab^x

I can send a picture of the given graph

these are the two points ive used to try to solve for b
f(-1)=15
f(0)=3

[summer ruin]

what's the problem

[restive flame]

I'm trying to determine the equation of the graph

[summer ruin]

and what is the problem you're having with it?

[restive flame]

solving for b

in the form y = ab^x +k

[summer ruin]

the problem clearly states that the function has form y=ab^x, there's no k

[restive flame]

i solved it y = [(1/4)^(x-1)] - 1

[distant bolt]

How do you determine the inequality of a quadratic function

[dull aspen]

hellooo

does anyone know the answer to number 1

@everyone

[viscid thistle]

May you please give us an example?

[surreal swift]

expand using the formula of sin(x+y)

[viscid thistle]

good boi

hehehe

[surreal swift]

wavy curve method

[viscid thistle]

yes

wavy curve method

[viscid thistle]

https://www.youtube.com/watch?v=Kl3OcZvkZJA

[viscid thistle]

https://www.youtube.com/watch?v=-xSS0FQstoU

sorry bro, but the videos are in hindi. you should be able to understand from what is written on the board. so fat, this dude explains it the best from whoever I saw on youtube.

[slim steppe]

Sin (π/2 + x) = Cos x

Let x = π/3

Sin (90+60)= Cos (60)

Sin of 150 is 1/2, and cos of 60 is 1/2.

@dull aspen ^^^^^^

[bitter sable]

What is a real zero? Is that just another term for an x-intercept?

[peak pasture]

yes

@bitter sable

[bitter sable]

Thanks

[peak pasture]

anywhere it croses the x axis

anytime!

[tulip dune]

$s=\frac{\sqrt{32}}{2}\sinh(2t)$

[unkempt zinc]

I have a book that defines a conic as the set of all points P(x,y) in a plane such that the ratio of the distance from P to a fixed point and the distance from P to a fixed line is constant. This ratio is eccentricity e. For a parabola e = 1 because it can be defined as all points equidistant between a point and a line. This makes sense, but then it goes on to define the eccentricity of a circle, ellipse, and hyperbola in terms of vertices a and b. How does this fit the definition of a conic?

[viscid thistle]

it does

e = 0 circel

circle*

0 < e < 1 is ellipse

e = 1 is parabola

e > 1 is hyperbola

[unkempt zinc]

@viscid thistle but the definition given for an ellipse, circle, and hyperbola don't involve the distance from a point to line. It gave it in terms of distances to two points. Not a point and a line. Which is what the definition of conic mentions.

[coarse kernel]

it's just some smart transformations I never thought about

but it's most likely just simple analytic geometry

[lucid trench]

heres some cool precalc notes i took #4

[rocky dock]

oh my god

wow

you are neat

[lucid trench]

thank you! it all comes down to my mom who really made me lol

[rocky dock]

i kinda just use my notebook to jot down my thinking process

[lucid trench]

i like that idea

i think i just really need the organization though lol

[rocky dock]

yeah everyone works differently

[placid lagoon]

wow, nice notes!

[lucid trench]

thank you 😌

[hollow iris]

i love it

[viscid thistle]

nice

good handwriting buddy

[lucid trench]

ty

[viscid thistle]

keep it up

[opal tree]

My precalc notes, oh boy

Lemme show them

[viscid thistle]

Dam ez stuff

[raven cobalt]

idek whats going in precal rn lol

sin and cos waves are weird

but theyre pretty neat tho

[viscid thistle]

Nah they g

[lavish creek]

looks like a place i can hide in

[opal tree]

It's just ratios

There are weirder

,w Plot[x!, {x, -5, 5}]

Bruh

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by Umbraleviathan#3607

[viscid thistle]

lol

[tepid yew]

Can someone help me with these

[viscid thistle]

you can use trig functions and that will hopefully give you an equation to solve (question 5)

[tepid yew]

Yep I got 5-8 already

I need help with 10-12

[peak sinew]

@tepid yew

In number 11

Use formula of sin²theta

Sin²x=(1-cos2x)/2

So its like (sin²2x)²

Use formula ones then square it and use formula again if necessary

cos²x=(1+cos2x)/2

In number 11 and 12, divide and multiply the eqn by 2

And use the 2 in the num, to use formula 2cosacosb and 2cosasinb respectively

[peak sinew]

I'm so envious rn that i for real wanna own that lol

[viscid thistle]

haia guys

i'm doing calculus but i wanna know what if missed anything from precalc just because i'm a bit paranoid

So I thought to myself: a diagnostic might help with this issue

so bassically do you have like any pre-calc diagnostic reccomendations? (if that's alr with you guys)

uhhm sorry for the long read, thanks for ur patience

[uncut mulch]

khan

a short summary of pre-req knowledge for calc is
basic algebra
functions / polynomials
exponents / logs
geo / trig

[dark niche]

i'm a bit paranoid
thats the logical outcome of learning math

[viscid thistle]

if you had a set of things with something in common, you could describe the relationship as a ratio right? like 3 out of 50 people wearing a blue shirt in a crowd and such, which is also 6% of the people. so what if you had a finite amount of relationships to an infinite amount in the set? what ratio does a number like 3 represent in comparison to all the other numbers that aren't 3 in the set of all integers for example? is 1/infinity? I don't understand

[vapid plaza]

as n approaches infinity, 3/n approaches 0

(in terms of probability, if you were to pick 3 people in a group of infinitely many people, that has a 0% chance of occurring.)

[cosmic girder]

fwiw probability 0 doesn't mean impossible

[bitter bolt]

it means it will not happen? so yes, impossible

[cosmic girder]

no

when randomly picking a number in R every number has probability 0

but they could still be picked

[bitter bolt]

don't you mean the probabilities approach 0? in which that does make sense, they still can be picked but it's such a small chance

[cosmic girder]

no

a more rigorous example

consider a random variable $X$ which is uniformly distributed on the interval $[0, 1]$

[obsidian monolith]

yes yes yes no

[cosmic girder]

let $x \in [0, 1]$. if $\mathbb{P}[X = x] = \varepsilon > 0$ then because $X$ is uniformly distributed we can conclude that $[0, 1]$ contains at most $\frac{1}{\varepsilon}$ points, which is obviously false lol

[bitter bolt]

what in the world is happening

[obsidian monolith]

yes yes yes no

[bitter bolt]

so then what?

[cosmic girder]

epsilon has to be 0

[bitter bolt]

which is undefined

[cosmic girder]

what?

[bitter bolt]

1/0?

[cosmic girder]

?????

do you understand how contradiction proofs work

[bitter bolt]

I'm in grade 11 ap stats idfk\

[cosmic girder]

then don't ackhcually someone when you don't know what you're talking about

[bitter bolt]

I'm just saying from my learning that when a probability of 0 is present, the event simply cannot happen

[cosmic girder]

I just showed you it can

[bitter bolt]

how? you showed me that the variable epsilon must be 0

[cosmic girder]

P[X = x] means probability of X being x

and I showed that it is 0

[bitter bolt]

so if it 0 then what?

then is it all equally possibly or something?

[cosmic girder]

we assumed that X is uniformly distributed

[bitter bolt]

so they are equally likely

but not1

?

[whole hound]

@cosmic girder I would like to ask you to explain like I’m 5 haha

I believe you, It’s just not clicking for me

[cosmic girder]

so imagine you're randomly picking a ball out of an infinite container that has an endless amount of balls in it

the probability of picking a specific one is 0

but it could still happen

[dull aspen]

hello does anyone know the answer to this?

@everyone

[gritty spruce]

It's greater than 5/8

[gritty spruce]

Can you define P(X=x) in a formal way...

[spark wind]

5/sqrt 39

[spark wind]

i mean in theory its 0+....like very small and even if u think practically its still very small....very small

[cosmic girder]

the sum of the probabilities of all sample points in the sample space that are assigned the value x

[cosmic girder]

no... it's 0.

[spark wind]

ur saying 1/infinity is zero?

[cosmic girder]

infinity isn't a number, you can't divide by it. but $\frac{1}{x} \to 0$ as $x \to \infty$

[obsidian monolith]

yes yes yes no

[high zenith]

so this is a very dumb question but if im integrating by parts, and I asign u = x^2, what should du be? 2xdx?

[summer ruin]

yes

[viscid thistle]

0/0 is infinity

0/0 es infinito

[cosmic girder]

[viscid thistle]

bruh

[compact harness]

infinity no is numbor

[burnt hare]

0/0= undefined

0x0=0

divide both sides by 0

0/0=0

[slim steppe]

0/0 is indeterminate

[cosmic girder]

please do your shitposting somewhere else

[burnt hare]

Yes monsieur

[gritty spruce]

This is supposing there is a minimum for P(X=x)... You're not proving anything...

[ionic hemlock]

hey i need some math help

can someone dm me if they can help

[steel smelt]

are you guys familiar with this?

[summer ruin]

without specifying what r, y and x are this table is meaningless

[steel smelt]

it's circular function ...

[light crescent]

i think he means what is o a h in this case

[steel smelt]

yes it's oppo, adja, and hypooo

[ionic hemlock]

Could someone help?

[mild swan]

I'd try taking a larger picture by zooming in if at all possible

[gritty spruce]

N42°E for 1 mile then ... N132°E for 1/2mile ... Can you draw it on a piece of paper?

Can u figure the coordinates after 1st mile? Then the displacement on the 1/2 mile. ?

Draw it either an app them

Sounds good

Everything is easier with pen and paper.

[mild swan]

Show your work if you can

[gritty spruce]

Can you think of a series that applies here?

[gritty spruce]

I saw your finding earliert can't see it now. I've never used these notation (N42°E etc or 'bearing'), but in finding something that seems 10% of what I think you said you found.
Fell free to DM, but it's midnight here

[cosmic girder]

X is uniformly distributed. what you're saying is nonsense

[spark wind]

@cosmic girder ok dude you gotta chill out and try to talk to people a little nicely?...so what im saying is in our country we are taught that 1/infinity = 0.0000....1 which is a very very small number which tends to be zero but about that ball case since your thinking practically you shouldn't ignore that very small value...even if its negligible cause the chances of picking a single ball out of infinity is also very very very small... equal to negligible

[vapid plaza]

Just because something has a 0% chance of happening doesn’t mean it’s impossible. @spark wind

[lean salmon]

when should i bother analysis on what a limit is

is there even a point?

not looking to become mathematician

we do actually have proof of infinite convergence, right?

[summer ruin]

"proof of infinite convergence"?

[cosmic girder]

define what 0.0000...1 means

[lean salmon]

Yes

Is that not a limit?

[summer ruin]

it's not even clear what you're trying to say there

infinity, convergence, proof, all these terms are only loosely related to the (definition of the) limit

[spark wind]

💀

[spark wind]

0.00000000000000000000......1

It means there are infinite zeroes between .0 and 1

its called 0+

i mean thats what i was taught

[lean salmon]

How do?

How is it not clear

A limit in definition is essentially infinitely converging

[spark wind]

a number just slightly greatet than 0

[lean salmon]

Or is the limit towards it

The limit OF the infinite convergence

[summer ruin]

"infinitely converging" doesn't even make sense

[lean salmon]

How doesn’t it?

Then correct me

[summer ruin]

infinitely isn't a term that's used relative to "convergence"

[lean salmon]

I just read that it is

A limit infinitely close to

Instead of saying I don’t make sense, correct me

[summer ruin]

a sequence a_n is said to be converging to some number A if the limit a_n as n approaches infinity is equal to A

[lean salmon]

Okay, sequences are surely a representation of, but I’m specifically talking about calculus

[summer ruin]

calculus starts with sequences

[lean salmon]

Yes you can describe it as one sure

But I’m talking theoretically

[summer ruin]

the definition of limits of functions is just extention of sequence definition

[lean salmon]

Why can’t you say “infinitely converging”

In common English?

[summer ruin]

that would be like saying it's converging twice or 3 times or infinitely many times

[lean salmon]

Seriously? You know I meant a limit

Whereby it’s never reached but instead is infinitely closer to

[summer ruin]

it’s never reached
no that part is false

take sin(x)/x as x approaches infinity, the limit is zero, but the function also reaches the value zero infinitely many times

[lean salmon]

I’m talking about infinitesimals

[summer ruin]

it is one

you can make that sequence arbitrarily close to zero since it's limit is zero when x -> infinity

[lean salmon]

And degrees?

[summer ruin]

?

[lean salmon]

Btw you gave an example that isn’t exactly what I was talking about

I was referring to not reaching the limit value which is the focus of my learning rn

[summer ruin]

the example I provided does reach the limit value many times, that's the whole point

[lean salmon]

But that’s a cool fact I didn’t take into account from my statement / question

Do we have proof that something can have a limit that it reaches infinitesimally close to?

[summer ruin]

that's the definition of the limit

given any error epsilon > 0, you can choose a number N, such that for all numbers n > N the sequence a_n will be at most epsilon off from it's limit A

[lean salmon]

If we have proof for that why is there no proof for infinity?

[summer ruin]

it's not a proof, it's a definition

and similar definition can be fairly easily obtained from that one for the case when the sequence goes on to infinity

it's just needs to be negated

[lean salmon]

I know I just didn’t want to further argue seeing as how I’ve yet to read any proof for a limit and not definitions

Saying as how you answered proofs with a definition

[cosmic girder]

how can there be an infinite amount of digits if it has a last digit lol?

define it rigorously

[gritty spruce]

Your reasoning by contradiction was nonsense.

[cosmic girder]

how so

[gritty spruce]

You wrote :
let $x \in [0, 1]$. if $\mathbb{P}[X = x] = \varepsilon > 0$ then because $X$ is uniformly distributed we can conclude that $[0, 1]$ contains at most $\frac{1}{\varepsilon}$ points.

What you mean is:
Suppose P(X) has a minimum epsilon...
But you have not prove that epsilon exists.
There your reasoning by contradiction does not hold at all.

[obsidian monolith]

bigkafka

[willow bear]

What you mean is: Suppose P(X) has a minimum epsilon
no, no such supposition was ever made.

they said, "Supposed P[X=x] is positive. Call this positive value epsilon."

[vapid plaza]

• since the distribution is uniform, all the possibilities have the same probabilities. That's what they called epsilon. (correct me if i'm wrong)

[lean salmon]

https://archive.org/details/methodoffluxions00newt/page/68/mode/2up

has anyone read it?

[viscid thistle]

Is there a youtube channel that explains precalc well?

Or is there a website for it?

[cosmic girder]

what topic

[viscid thistle]

All of precalc, I had a rough go since the start of the semester and want to get a better understanding

[cosmic girder]

use khanacademy

[viscid thistle]

Alright any other places?

[viscid thistle]

Do you have any notes for precalc

[slim steppe]

Organic Chemistry

[sullen bone]

Is this wrong 😭

[burnt hare]

only God knows

[brisk pasture]

How do I write this?

How would I write this? As a piece function

[lean salmon]

does anyone know how sin and cosine actually work? why are numbers allowed to behave weirdly with them? how can f(0) be 1 for cosine?

cos90 = 0

whats the actual function/ transformation that allows these?

do degrees have special properties?

and how can you treat them like non numbers

this has to be limit related surely?

or is this only working for triangles/unit circle?

[summer ruin]

the definition of sine and cosine?

[lean salmon]

why does the cosine rule even work?

all i see is repeated formula and rules to memorise that help people work things out but never a reason why

so the trig functions were derived from triangles in circles and plotted with such knowledge, its not like you can just make a function that can do that

i first started thinking about this from this:

something which you mentioned yesterday

feels counter intuitive

theres no way sin0/0 is 1, it has to be zero

they say it is not defined unless you define it? lmao?

[cosmic girder]

,, \lim_{x \to 0} \frac{\sin{x}}{x} = 1

[obsidian monolith]

yes yes yes no

[lean salmon]

See screenshot

so you are saying that 0.000000001 = x, you will get 0.99999999, but when you get 0 it will not work

there is still a point on the curve at x=0

or does it skip

[summer ruin]

technically writing sin(0)/0 is incorrect

[lean salmon]

it becomes undefined is there a infinitesimallly small gap between the line?

this is hard to imagine

[summer ruin]

shouldn't be too hard to imagine a single point where the function is undefined

[lean salmon]

when its infinitely small it is

i literally cannot imagine it

so a single point here you just imagine it as x=0

as a... point

thats helpful

Yeah makes things easier to think about

[summer ruin]

was it hard to imagine that 1/x is undefined for x=0?

or square root being undefined for an entire half of the real line

[lean salmon]

because a point is a point but an undefined gap being a point is weird and hard to imagine

[lean salmon]

is this relavent?

[summer ruin]

yes

[lean salmon]

having never done analysis i wouldnt understand any of this properly

maybe i shud just accept it and not try

[coarse kernel]

a limit tells you what value of the function should be there depending on the surrounding points in a way

[worn sequoia]

Help plz

[fiery flare]

-pi/3

[candid hearth]

got a precalc exam coming up. weve just been doing trig so far. any tips on studying?

[dark girder]

does this sequence converge to zero?

if not do we have a name for the constant?

[worn sequoia]

Hm.

[fiery flare]

yes they all work im not gonna list them all out

[cosmic girder]

,, H_n - \ln{n} \xrightarrow[n \to \infty]{} \gamma

gamma is the euler mascheroni constant

[obsidian monolith]

yes yes yes no

[dark girder]

is there a name for Hn?

[cosmic girder]

nth harmonic number

$H_n = \sum_{k = 1}^n \frac{1}{k}$

[obsidian monolith]

yes yes yes no

[calm locust]

Having some hard time understanding limit definitions, any suggestions to understand them better?

Whats the whole point

[summer ruin]

the point is that no matter how small (but positive) error epsilon you choose, starting from some (large, but finite) number n the error between the sequence and it's limit will be always less than the epsilon of your choice

[slim steppe]

Practice the theorems, get an understanding of how the unit circle works, make up your own problems or find problems that you can solve

[burnt hare]

unit circle was fun lmao

1/2,sqrt2/2,sqrt3/2

[burnt hare]

love your name. i know it’s fake

thawne.

[slim steppe]

😉

[burnt hare]

when i first watched the show it was so fucking epic

the suspense

[slim steppe]

Yeah, it sure was. It's a bit emotional that the next season is the last one, but its time has come

[radiant kite]

yea im trying to solve

its just sectors of circle area

answer: 314