precalculus

[thick ridge]

well i feel a lil more confident bout my math test so ima just do a quick drivers ed review, then head to bed too

[modern lynx]

how solve 😭 . just part ii and iii,
I know how to do ii, its just the answers were different from what i got. thanks in advance for anyone who helps me

[modern lynx]

dont worry about the above question anymore, i got it

[acoustic leaf]

Stop bullying

[whole void]

that’s not bullying. but like actually though what is that

(I’m joking but u should learn how to draw it properly)

[fathom sphinx]

For part d which function on f(x) do i sub f(a)=90? Both or...

[whole void]

This is a poor question on multiple parts.

1. It says the function is defined on all real numbers but g(4) is not defined
2. g(x) is a function

[whole void]

check if either work. see what u find. Remember to check if it satisfies the domain restriction of the piece

[buoyant saddle]

i got

164.5

my friend got 160

which is right

[delicate blade]

Can't you assume that the sphere is instead a cube

and end up with the same ratios

since the linear dimension ratio would be the same either way

alright i tested and it seems to work

[buoyant saddle]

[elfin niche]

When it comes to graphs, I don’t understand really how to plot it when it comes to the pi’s

[raven laurel]

is there anyway to solve systems easier?

[raven laurel]

🤓 its called a period not a cycle

also for tangent period is pi not 2pi

[willow skiff]

Systems of linear equations! Matrices

Row reduction is just solving simultaneously except you don't write x, y, z

But you could also find the inverse matrix of the coefficients of x, y, z and multiply both sides by the inverse matrix

[scarlet wyvern]

if you have to show all your steps matrices become a pain

it takes so long

[willow skiff]

Matrices are a shortcut actually

The problem is that 3x3 takes a long time regardless of your method

Never mind 4x4 and 5x5

Also there's Cramer's rule, maybe you find that easier

[scarlet wyvern]

i havent learned that 😭

i learned gaussian that was about it

[raven laurel]

can u teach me how to do that?

[willow skiff]

Search on YT, org chem tutor

[cyan anvil]

Eddie woo is best tutor of maths on yt imo

[raven laurel]

does this work wwith nonlinear systems?

[sturdy hound]

can someone explain how this is an arithmetic sequence:
log base 3 of x, log base 3 of (x/3), log base 3 of (x/9), where x > 0.

[past meadow]

Usually nonlinear systems can't be solved with matrices unless they can be transformed to a linear system.

[past meadow]

can the second and third terms be written in a different way with log laws?

[sturdy hound]

OHHH
log base 3 of x - log base 3 of 3, log base 3 of x - log base 3 of 9

??

[past meadow]

yep, and then the log_3(9) can also be written as log_3(3^2)=2log_3(3)

[sturdy hound]

oh that makes so much more sense now

[past meadow]

After that rewriting I hope it looks a bit more clear why its arithmetic

[sturdy hound]

yeah

[past meadow]

awesome

[sturdy hound]

tysm

[willow skiff]

Not in general

Specify a type of 'nice' non-linear systems and I might be able to tell you

[raven laurel]

x^2+y^2=9

log (10x)=6y

[willow skiff]

That's just one equation

Well all solutions are given by x = 3 cos t and y = 3 sin t

[inner topaz]

would recommend 3blue1brown and not org chem tutor since he doesnt explain why it works and just gives formulas to memorize

[willow skiff]

,w x^2 + y^2 = 9 and log_10 (10x) = 6y

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[willow skiff]

yeah a lot of equations don't have an analytical solution

everything you have learned so far just happens to be one of the few types of solvable systems of equations

because you can substitute in y = x + constant and get a quadratic in x, and so on

you can only determine that there must be exactly two solutions (WA has plotted this wrong; there is one more intersection where x is positive and very close to 0)

given the shape of a circle and any logarithmic function

[radiant zodiac]

Can someone simplify this?

[inner topaz]

what did you do?

[buoyant saddle]

pls someone hurry

ive done d first part

which is -4.9

my problem is how to compare it to the graph

and how do i compare the tangentto the sope pls someone

slope

[buoyant saddle]

https://tenor.com/view/monkey-confused-gif-15712129875520007531

Someone pls

Someone pls

It's due in 2 hrs

[radiant zodiac]

Wdym

[buoyant saddle]

Someone pls

Anyone pls

[proud trellis]

Hi

I want someone to give me a Precal. equation that is considered simple for me to try and solve

I'm in Alg. 2 but I want a challenge

[winter comet]

precalc is basically supposed to be algebra 2 but with a bit more

[proud trellis]

a bit more ?

[astral apex]

it's mostly a review of algebra but with a few new functions introduced - exponential, log, and trig

there aren't really new types of algebra equations for you to try that don't make use of the new kinds of functions

[whole void]

Precalc is a big waste of a year imo

[muted hinge]

Does f: Z -> R mean a function takes integer input and outputs real number?

[whole void]

especially if u don’t do like trigonometry with complex numbers or basic vectors/matrices

[winter comet]

i agree

or even a semester

💀

i jus skipped it and its fine :l

[astral apex]

yes. Though it could potentially only output rational numbers or integers, and still have codomain R

[main glacier]

in the function f(x)={4x^2+x-5, x<4 | kx^2-6x+7, x>=4}, which value of k makes the function continuous?
not any question i need an answer for, it's just a practice problem

[astral apex]

hint: see what value 4x^2 + x - 5 would have at the "change of definition point" x = 4

then find k to ensure the other expression takes that same value at that point

[ebon tangle]

U did a masters in math?

[astral apex]

I did

[ebon tangle]

From a scale of 1/10 how much harder is it from calc r

4

[astral apex]

how much harder is what, getting a masters in math?

[ebon tangle]

Yes how much harder is getting masters in math

Than doing calc 4

I think in masters u just do proofs so its probably 10/10 harder

[astral apex]

uhh yeah I don't know how to quantify this but it's a lot harder, of course. You're comparing a single class that undergrads take, to a multiple year program where you have to pass a bunch of harder classes and take qual exams

[winter comet]

calc 4 being differential equations?

[astral apex]

probably multivariable calc

[ebon tangle]

No line integrals surface integrals and volume integrals

[winter comet]

oh

[ebon tangle]

Sphirecal integrals

[winter comet]

then whats calc 3?

[ebon tangle]

And cylindreical

[winter comet]

oh i guess they split it into actual multivariable and vector

[ebon tangle]

Series sequence and alittle intergation

Also divergence and cinvergence

[winter comet]

oh what

[winter comet]

what's calc 2 then?

[ebon tangle]

Idk i didnt take calc 2

[winter comet]

💀

[astral apex]

probably the bulk of integration

and applications of that

[winter comet]

interesting

[ebon tangle]

But calc 4 is the hardest math i took so idk how to compare

[winter comet]

how much harder is passing high school than passing algebra

💀

[ebon tangle]

Not much

[astral apex]

I will say, not all classes of a masters program are necessarily harder than all undergrad classes

[ebon tangle]

Just study

Daily

Ur fine

[astral apex]

but it comes down a lot to what you personally find hard

[winter comet]

i meant, thats kinda how your question sounds 😭

except its not probably the same but :l

[ebon tangle]

Oh but i was able to give u an answer

[winter comet]

strange

[ebon tangle]

Makes sense why did u do masters in math btw

For fun

Or

Does it open something

[winter comet]

if someone is getting a degree for fun they must be omega rich and want to dedicate a LOT of time to it 💀

[astral apex]

well, I wanted to get a PhD and become a mathematician, but that plan went seriously wrong. I'm lucky that I happened to complete the requirements for a masters while working toward that

[ebon tangle]

😆

[ebon tangle]

What went wrong

If u dont mind me asking

Also dont phd problems take around 14+ days to solve each

[astral apex]

my self confidence went downhill and I developed a serious substance and gambling problem

[ebon tangle]

That doesnt sound fun

[ebon tangle]

But gambling is just math shouldnt u win every casino u enter

[astral apex]

most casinos games can't be beaten with math

I thought I had an edge in poker

I was sorely wrong

[ebon tangle]

Every probability can be beaten with math

[ebon tangle]

BAHAHAHAHAAHAH

They where better in math then

[winter comet]

😐

[astral apex]

no offense but you don't seem to know what you're talking about

[winter comet]

fr 💀

[ebon tangle]

Theres a story about a person who studied probability alot

And won big

Got banned from las vegas tho

[astral apex]

it's possible to get an edge at counting cards in blackjack. That's pretty much it for casino floor games

without cheating

[ebon tangle]

But yeah in casino they rig the probabilities so u cant really win

[ebon tangle]

What about horse racing

U could win if u do alot of math 😭

Dont gamble tho

[winter comet]

bro is going to mathematically determine how fast one horse is going to run

[ebon tangle]

Lmaooo

No u can determine other factors

The probability of each horse winning

[astral apex]

I vaguely recall hearing a story about someone who actually did make a killing on horse races

[ebon tangle]

Yes its the same dude who got banned from las vegas

[astral apex]

but I wouldn't count on being able to replicate their results

[ebon tangle]

He got a team

[winter comet]

the odds are against you though lol

[ebon tangle]

And started winning multiple horse race bets

[ebon tangle]

Probably yeah gambling as a whole is bad

[terse pebble]

propaganda

[ebon tangle]

💀

[terse pebble]

they just don’t want you to make money bro

[ebon tangle]

Yep

Why would they lol

The point of gambling is to trick people into thinking they can win

[terse pebble]

nah

[ebon tangle]

🙂‍↕️

[terse pebble]

that’s the point of anti gambling sentiment, to trick people into thinking they can’t win

[ebon tangle]

What

Anyways @astral apex what do u work now

[astral apex]

I teach and tutor math

[terse pebble]

14+ days lmao

[ebon tangle]

Ooo tutoring gives alot of money

[terse pebble]

something like that

[ebon tangle]

Yes proofs suck

Well

No we still need nerds to do them

So we can advance

[terse pebble]

you missed the joke

[ebon tangle]

I did

[terse pebble]

it can take like 8 years to get a phd

[ebon tangle]

Dang

Yes thats true

[terse pebble]

not just two weeks

[ebon tangle]

But i meant 1 question takes

14+ days

[astral apex]

it depends on if you mean homework question or research question

[terse pebble]

yea lol

[ebon tangle]

Research questions

Take

6-12months

Lol

U gotta read so many articles and etc etc

Overall only do phd if you absolutely love math otherwise the effort aint worth it D :

[terse pebble]

are you speaking from experience?

[ebon tangle]

My fathers doing a phd so i check his work

Or like

He shows me what he does

[terse pebble]

in what

[ebon tangle]

Idk

But its his

6th year

[terse pebble]

math?

[ebon tangle]

No

Research

[winter comet]

I thought research was an action you do in any subject to get a degree, i didnt know you get a degree in research...

[ebon tangle]

Good point

[winter comet]

💀

[ebon tangle]

Yeah idk even if he told me on whay id forget the next day

[terse pebble]

lol what

[ebon tangle]

But i know

Theres a thesis

That takes

2 years

Or so

[winter comet]

masters thesis?

[terse pebble]

how do you not know what general field it’s in?

[winter comet]

or is there phd thesis too

[ebon tangle]

Phd thesis

[ebon tangle]

Schools

Maybe

[winter comet]

the heck 💀

[terse pebble]

bro what

[ebon tangle]

I never asked 😭 😭

[terse pebble]

@jovial hare

[ebon tangle]

U will be able to teach in uni with a phd

But

Thats 5 + 5 + 8

18 years

Could be 3 for undergrad

[terse pebble]

bro i have no idea what you’re even saying

[ebon tangle]

Im talking about twaching in universities

The requirment

[winter comet]

oh heavenly mathcord, since you solve all my problems
please tell me where did i misplace my eraser

[ebon tangle]

BAHAHAHAHAHHA

Get a tablet and write digitally

Best upgrade ever

[winter comet]

i doth not mean what i wrote 😔

i cant speak regular english let alone old english

no seriously tho where did my good eraser go

[winter comet]

ur right
lets use the logarithm function to determine where my eraser went

logarithm base eraser

[ebon tangle]

😭

Im bored

I thought id find easier homeworks when i joined

All i see is stuff i dont ever want to see in class

[winter comet]

I FOUND IT

[jovial hare]

Hiii

[terse pebble]

i found your alt bro

[jovial hare]

What happened

Wdym

[terse pebble]

@ebon tangle

[ebon tangle]

Yes

[jovial hare]

What are you implying

[terse pebble]

nothing

[winter comet]

💀

[jovial hare]

Are you bullying me again

[ebon tangle]

I think hes implying ur smart

LOL

[terse pebble]

love this guy

[ebon tangle]

[winter comet]

which guy

oh wait-

[ebon tangle]

Me

Cuz

Other guy

Has

Is it a guy

[jovial hare]

AIDS

[jovial hare]

Thank you. Yes it’s me

[terse pebble]

,av adodo6737

[obsidian monolith]

adodo6737's Avatar

Click here to view the image.

[terse pebble]

goes so hard

[ebon tangle]

Ikr

[jovial hare]

Leave the kid alone wtf 😭

[ebon tangle]

Well

[terse pebble]

we don’t really know

[ebon tangle]

I stopped being a kid 10 years ago

But

[ebon tangle]

😭

[terse pebble]

he took calc 4

[ebon tangle]

A year ago

Now its just physics courses

[winter comet]

i stopped being a kid when i was 7

[terse pebble]

damn bruh

[winter comet]

what major u?

[ebon tangle]

Worth it tho imma need my money up

[ebon tangle]

Electrical engineering

[terse pebble]

barnacle boy

[ebon tangle]

For a uni with 1.2k engineers

Having only 16 electrical engineers

Is weird

[winter comet]

what about LA/ode?

[ebon tangle]

Diffrential equations?

I took that as well

But

That isnt hard

Well none of the courses are u just need to study daily

[winter comet]

💀

[ebon tangle]

Occasionally observe how care free buisness majors are

[scarlet wyvern]

when do i need to check my solutions when im solving trig equations?

[winter comet]

your question is too general

[scarlet wyvern]

like sometimes when i solve trig equations some of my solutions dont work or result in like an undefined answer

but usually most of my solutions work

[winter comet]

you'd want to check your solutions when you do a step that changes the domain/possible solutions

[scarlet wyvern]

would squaring both sides lead to changing the domain

[winter comet]

i say "domain" loosely but yeah it changes the possible values of the squared result (it doesn't change the possible values that go into it though)

like for example,
if you have an equation y = -x
and you square both sides, then you have y^2 = x^2
(x,y) = (1,1) satisfies the second equation but not the first equation, so you could see that squaring both sides of the equation would not have the exact same (x,y) points (it has more in this case)
as an example

[scarlet wyvern]

ah alr that makes sense

wait @winter comet can you show me how to solve this

[winter comet]

so first you'd want to solve for sin(4x) obv ri

[scarlet wyvern]

my answer key said this but im confused on how it would be pi- and 2pi+ cause i thought the arcsin value would be in the fourth quadrant

and also i dont get why it would still be +2pi n

[winter comet]

so you have sin(4x) = -2/3
you know that if sin(u) = -2/3
one value is u = arcsin(-2/3)
since arcsin(x) has range of [-pi/2, pi/2], you know it has to be in the fourth quadrant yes
so you know that the values that satisfies sin(u) = -2/3 would be u = arcsin(-2/3) + 2pi*n for any integer n (since arcsin(-2/3) is a solution, and adding/subtracting factors of 2pi just brings you around the circle to the same place)
but you also have the identity sin(u) = -sin(pi-u), so sin(arcsin(-2/3) + 2pi n) = -sin( pi - [arcsin(-2/3) + 2pi n]),
so another solution to sin(u) = -2/3 is -(pi - [arcsin(-2/3) + 2pi n]) which simplifies to -pi + arcsin(2/3) + 2pi n = pi - arcsin(2/3) + 2pi n
so since u = 4x, x = u/4, so you get
x = (arcsin(-2/3) + 2pi n)/4, (pi - arcsin(2/3) + 2pi n)/4 for all integers n

probably too much idk how to explain, is there something about this that is confusing xD

[scarlet wyvern]

o shoot that makes hella sense actually

[winter comet]

oh kewl

[scarlet wyvern]

yea i see where i went wrong in my thinking

also cause im blind and i didnt realize it was ()/4

[winter comet]

and btw, for each cycle, sin(x) = sin(pi - x) are the only two things you can put into sine and get the same thing...
idk how to say that better 💀

you can see it picturing the unit circle

[winter comet]

oh 😔

[scarlet wyvern]

yea i usually picture unit circle

[scarlet wyvern]

it were in quadrant one then it would be pi-u right

like the arcsin value

[winter comet]

quadrant 3...

[scarlet wyvern]

no like if i had a different arcsin value like arcsin(1/3) then the other answer is still pi-arcsin(1/3) right

[winter comet]

u=arcsin(-2/3) is in quadrant 4, pi - u = pi - arcsin(-2/3) = pi + arcsin(2/3) is in quadrant 3

[winter comet]

yes

[scarlet wyvern]

alr alr

i got it

ty for the help

[winter comet]

and quadrant 3 and 4 are the only quadrants that have angle that satisfies sin(u) = -2/3 so yea

[scarlet wyvern]

@winter comet wait one more thing

for cos and tan

is it also pi- or is it different

[winter comet]

i just realized

its actually sin(pi - u) = - sin(u)

[scarlet wyvern]

o

[winter comet]

cuz cos(pi - u) = cos(u)

[scarlet wyvern]

wait but u is negative in the previous problem so it would turn to pi+u no?

[winter comet]

hmm wait i musta gone wrong smwhere

[scarlet wyvern]

or like

pi-(-u)

wait idek anymore

on unit circle it makes sense

[winter comet]

ok i fixed it

[scarlet wyvern]

wait so is my teachers answer key wrong

[winter comet]

i mean i accidentally had pi + u, because double negative, but it shoulda actually been -pi - u, which if you add 2pi becomes pi - u

[scarlet wyvern]

wait are you sure its -sin(u)

i tried opening sin(pi-u) and it just turned to sinu

[winter comet]

bru i was thinking of sin(u-pi)

you're right i was right the first time

😭

[scarlet wyvern]

😭

[winter comet]

u = arcsin(-2/3) + 2pi n
pi - u = pi - [arcsin(-2/3) + 2pi n]
are solutions

to sin(u) = -2/3

[scarlet wyvern]

alr yea that makes sense

[winter comet]

yea yea

mb bro im so trippy

[scarlet wyvern]

wait so it cos and tan the same pattern

like pi-u = cos etc

[winter comet]

cos(x) = cos(pi - x) = cos(x - pi)

[scarlet wyvern]

o shoot cause its an even function

alr alr

for tan would i just turn it into sin/cos

[winter comet]

yeah you could just divide it

and see tan(x-pi) = tan(x)

[scarlet wyvern]

wait but wouldnt that just turn to sin(x-pi)/cos(x-pi) and sin(x-pi) is negative but cos(x-pi) is positive

which is equal to -tanx

[winter comet]

ive gotta be hard tripping rn

[scarlet wyvern]

wait but tan(x-pi) makes sense cause pi is a period

da fuq

wait @winter comet x-pi is -cos

[winter comet]

cos(x-pi) = cos(pi-x) = cos(x)

tangent...

i was tryna graph on desmos just now and its not helping

[scarlet wyvern]

wait but if you have an angle of x in quadrant one, and then take pi and subtract x, thats in quadrant 2

and then cos is negative

[winter comet]

I think desmos is tripping, or im ultra mega giga tripping

[winter comet]

yeah you're right

💀

mahn my brain

it makes sense now 😭

[scarlet wyvern]

yea i got hella confused too

[winter comet]

cuz of me fr

[scarlet wyvern]

nah youre good

i understand it more now

[jovial hare]

@modern lagoon I’ll help when u need

[jovial hare]

Come back to calculus chat bro

[winter comet]

[modern lagoon]

bro im in geometry/alg 2

[jovial hare]

Sowwy

[jovial hare]

come back

[winter comet]

cool, how did you get in there

[jovial hare]

I forgor

[winter comet]

did you like jump into it or

[winter comet]

[jovial hare]

Now or uh

[modern lagoon]

(ping)

[jovial hare]

A rabid rat will bite u

[winter comet]

failed

[modern lagoon]

here

[jovial hare]

AWA

[winter comet]

owchie

[vivid spade]

im getting 3+4(-2^x) but its wrong and I dont know what im doing wrong lol

[willow skiff]

try writing $3 - 4(2^x)$

[obsidian monolith]

south

[fathom sphinx]

Hi guys for question 12 I'm getting a=3 ( when both completing the square and differentiating). But my textbook says a=11

Is my textbook wrong or is it me ;-;

[limpid pine]

Yeah i think its

3

[fathom sphinx]

Ah alright thx Inco!

[arctic dagger]

what does one-to-one mean

does it mean something like the inverse of the function?

[river drift]

one-to-one means injective

[arctic dagger]

,w injective

oh so for example y=x is injective, but not y=sin x

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by lkjsfkjsiu

[arctic dagger]

so in the example,
\[ f(x)=x^2-6x+20 \]
and
\[ f(y)=3\pm\sqrt{y-11} \]

[obsidian monolith]

0_א

[arctic dagger]

ok so for that quadratic function to be injective, the domain must start from the vertex to either side of the parabola

[astral apex]

yes, and other domains work (subsets of that one), like finite segments on one side that avoid the vertex

you could even have some segments from both sides of the vertex, as long as they have no y values in common on the parabola

[arctic dagger]

i see

[arctic dagger]

so what's the answer here, 3 or 11?

,w plot y=x²-6x+20, from 3 to infinity

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by lkjsfkjsiu

[arctic dagger]

imma do it in desmos

[astral apex]

the answer to what question?

btw if you enter your equation to desmos with {3 <= x} after it, it'll only graph it on that domain

[arctic dagger]

the question in number 12

[willow skiff]

yeah because $y \ge 11$

[obsidian monolith]

south

[willow skiff]

your textbook messed up

[fathom sphinx]

Thanks south!

[warped shuttle]

how to solve 2^x = x^2 using algebra ?

[willow skiff]

unfortunately there's not really a way

https://en.wikipedia.org/wiki/Lambert_W_function

we define a special function to solve equations with exponentials and polynomials

https://math.stackexchange.com/questions/2605114/intersection-points-of-2x-and-x2

it's pretty nasty

there's another real value of x that is not 2 nor 4

[warped shuttle]

Range of the function y = 2^(x^2+2x-1)-2^(x^2+2x+1) with Domain of [-2, 1]
Explain all the details to understand, anyone can help ?

[wispy yarrow]

Hello, any resource for dominating the factorization? I've seen many methods of factorization in my last class but some of those results are a bit large and unnecessary, I want to learn one fast method that helps me in any problem

[scarlet wyvern]

x method

and intuition

its the easiest and fastest imo

if you cant factor tho then youre just gonna have to use the quadratic equation or completing the square if you can

[whole void]

wdym “dominating” the factorization? And what r u looking to factorize

[whole void]

there’s a lot more than just quadratics

[elfin niche]

Is the reason why I got the range for number 1 wrong because I didn’t apply the transformations to it?

[terse aspen]

Can some explain how this is orthogonal

#81

[winter comet]

orthogonal vectors have a dot product of 0

[terse aspen]

Yea but dumb question how is that 0

Wait

Im actually a dumbass

[viscid thistle]

Whats the dot product?

[terse aspen]

I genuinely stupid

[viscid thistle]

Nah ur good

[spring kettle]

Anyone know how to get domain of trig function 😭

[astral apex]

sine and cosine: all real numbers. Other ones: anywhere their denominator doesn't equal 0

[wispy yarrow]

Maybe all the algebra of baldor?

[tame pike]

How do I convert ax^2+bx+c to the quadratic formula?

[winter comet]

complete the square

[tame pike]

Ok

What do I do first?

This is a confusing question

[whole void]

Nah

[whole void]

any ideas?

[arctic dagger]

completing the square means to manipulate the equation such that part of it becomes a square of a binomial

,,(a\pm b)^2=a^2\pm2ab+b^2

[obsidian monolith]

0_א

[tame pike]

Parentheses for (ax^2+bx)

[whole void]

why?

[tame pike]

That’s the way to complete the square

[whole void]

adding parenthesis doesn’t do anything in itself, but ok. so try to complete the square

[viscid thistle]

yall

im taking geometry and algebra II rightg now is precalc rly hard

im gonna be taking it as a sophomore

[whole void]

not rlly I don’t think so

precalc kinda seems like a waste of a year imo

[viscid thistle]

im taking ap stats and precalc concurrently then calc ab then calc bc

[whole void]

I thought u said u r doing geometry and alg ii

[viscid thistle]

No i meant next year

this year

geometry and algebra II

next year pre calc and ap stats

[viscid thistle]

what year r u

[whole void]

Junior

[viscid thistle]

what math

[whole void]

ap calc bc

[viscid thistle]

bvr

as a junior???

[whole void]

yeah

[viscid thistle]

how??

[whole void]

what does that mean

[viscid thistle]

i kmeant bro

[whole void]

My school offers it

[viscid thistle]

what did u take freshman year

[whole void]

geometry

[viscid thistle]

then how in the world

are youtaking calc bc

what did u take sophomore year

[winter comet]

you don't really need precalc. . .

[viscid thistle]

where i live

[winter comet]

and you def dont need ab for bc

[viscid thistle]

its a prerequisite

[whole void]

ap calc is rlly not that hard like the ap makes things very easy im being honest. that’s not to say of course that some things in calc aren’t hard of course but the ap is easy

[viscid thistle]

broi what

r u talknig abouit

[winter comet]

i meant like

content-wise

[whole void]

algebra

[viscid thistle]

algebra II right

[winter comet]

calc bc repeats the concepts in calc ab

[whole void]

yeah

[viscid thistle]

so can you please explain to me

how in the hell

[winter comet]

in some places

[viscid thistle]

you went from algebra Ii

to calc bc

inone year

[winter comet]

cuz he doesnt have more prequisites 😔

[viscid thistle]

where does he live bro

i have to take pre calcthen ap calc ab

[winter comet]

i feel like many places don't require it

[viscid thistle]

MINBE DOES WT

F

\

[winter comet]

😔

[jolly raven]

ab is not a prereq to bc

but it often is considered that way

[viscid thistle]

BRO

WHERE

[winter comet]

it is for him apparently

[viscid thistle]

DOES IT SAY THAT

[winter comet]

i think some schools do

[viscid thistle]

WHAT KIND OF SCHOOLS YLALO BE GOING TO BROP

[winter comet]

did you actually read for sure that ab is prereq to bc?

[jolly raven]

my school made ab be a prereq

but

[winter comet]

bro the first semester of bc is just ab

[jolly raven]

calc bc is basically what it would look like for you to take calc 1 and 2 in college

[whole void]

I don’t think ap calc bc does like hard integration at all

[viscid thistle]

AP calculus ab Prerequisite pre-calculus it says

[winter comet]

yea

[jolly raven]

ab is one whole year of calc 1

[winter comet]

😔

[viscid thistle]

and calc ab for bc

[winter comet]

it isn't usually but ig it is at your school :l

i mean you get more math experience lol

[jolly raven]

uhh idk about that

[whole void]

minus all of the proofs/intuition for things

[jolly raven]

you get more differentiation experience

[jolly raven]

calc 1 and 2 in college doesnt have proofs or intuition either

if you want proofs concerning calculus topics, take analysis later on

[viscid thistle]

so after calc ab and bc wgat ckases r thgere

[jolly raven]

like for math in college?

[viscid thistle]

yea

[jolly raven]

depends on ur major

what do u wanna do

[winter comet]

multivariable, diff eq, linear algebra, discrete...

[whole void]

bruh. calc 1 and 2 are rlly something a middle schooler could do then if that’s the case

[winter comet]

i guess real analysis in there too

[jolly raven]

yeah these are the last four "easy" math classes

[winter comet]

after bc yeah

[jolly raven]

nah analysis and algebra are their own things

[winter comet]

i was tryna list things that only have prereq of calc 2

[jolly raven]

i see

[winter comet]

which ig real analysis does

prob not complex analysis tho

[jolly raven]

not generally true

[winter comet]

cuz contour integrals are line integrals lol

[jolly raven]

but a smarter kid could i guess

[jolly raven]

RA has calc 3 as a prereq

[winter comet]

they could but they usually don't lol

[jolly raven]

or well

[winter comet]

oh

[jolly raven]

its not called real analysis in college usually

[winter comet]

i wouldnt know its not offered here XD

[jolly raven]

lol fair enough

[whole void]

just memorize the basic integration rules, the derivative rules, etc

[jolly raven]

usually its just analysis 1 and 2

then you take real analysis 1 in graduate school

[winter comet]

ahh

[jolly raven]

im doing complex before real analysis actually

because of annoying scheduling stuff

[winter comet]

so calc is like meh not rigoruos, analysis is like pretty rigorous and then real analysis is like ultra gigachad rigorous?

😂

[jolly raven]

analysis is very rigorous

RA isnt necessarily more rigorous

it just looks at more stuff

[winter comet]

ahh

[jolly raven]

like measure theory

[winter comet]

ah

is clusters not an analysis thing

[jolly raven]

idk what those are

[viscid thistle]

is says on colllege board website calc ab is equi`valent to a first semester college calc course in differential and integral calc and that calc bc is equivalent to a firts semeseter college calc course and subsequent single variable calc course

[winter comet]

oh

[whole void]

why is analysis not just calc

[winter comet]

i remember reading abt it somewhere 💀

[jolly raven]

yes exactly

[winter comet]

for analysis of some sort

[jolly raven]

which is why ab is not a prereq

ab is a slower version of bc

that covers half as much

[jolly raven]

yeah ive never heard

[winter comet]

calc bc is jus normal pace

ish

[jolly raven]

it is

as i said its like calc 1 and 2 in college

[whole void]

what year are u

[winter comet]

heres what a.i. said it was, used for limits 💀

[winter comet]

11

[jolly raven]

i see

[whole void]

oh

[winter comet]

i think they used cluster points to define a limit of a sequence maybe? or something idk

its what it seems like to me but idk what im talking about

[fathom sphinx]

Vicious aren't you a math major-

The more questions I ask the more questions I shall have.

[winter comet]

no, where'd you get that idea from

[winter comet]

fr

[fathom sphinx]

You know so much-

Meths

Maths*

[winter comet]

dang i do know a lot of meths frfr

😭

[fathom sphinx]

And you have the undergraduate role 😭

[winter comet]

thats cuz the math i study is considered undergraduate math by this server 😔

and they said take the role of what you studyin or whatever

[fathom sphinx]

Omg this pic is so crispy

[winter comet]

anyway uh

[fathom sphinx]

Fr

[fathom sphinx]

when i saw this it reminded me of this vid ☠️

https://youtu.be/wPSnOqOJYM4?feature=shared

[dull terrace]

yo from these topics, what should i focus on the most for calculus ???

[astral apex]

all of them

but especially the first 4

or 5

radical expressions are somewhat less commonly needed

[dull terrace]

ok thanks 🙂

[lyric cradle]

so in my first ( and only) calculus class my teacher told us that we shouldnt treat (d/dx) as a fraction but as a function. So how is this allowed

[fading monolith]

Is not rigorous but a convenience. Here you should integrate respect x on both sides of df/dx=g so int df/dx dx is just f(x) by Fundamental theorem of calculus

[willow skiff]

technically d/dx is not a fraction, but it behaves like one through the rigorous proofs mathematicians have come up with

you actualy have dx/dy = 1/(dy/dx) and so on

dy/dx * dx/dt = dy/dt, well these are applications of the chain rule

[fathom sphinx]

Hi here with question 6 the Inductive step is it necessary for me to factor out what I got?
Or can I just leave it the way it is.

[elfin niche]

excuse me what website is that?

[winter comet]

you showed that your result equals the expected result (from induction), even though you didn't explicitly write the correlation...

like i would try to make it even more obvious but the logic is there so. . .

[viscid thistle]

I mean you could just for the sake of making the point clear, but the induction here is pretty much done (although if you're writing it as a proof you'd need to show things better)

[dull terrace]

Aleks

[terse aspen]

Why is 53 discontinuous at x=2

[river drift]

,rccw

[river drift]

what is the value of the function at x = 2? what is the value of the limit as x approaches 2?

[terse aspen]

2, approaches from diff values

Dne

[river drift]

so if the limit does not exist, what does that say about whether the function is continuous?

[terse aspen]

Discontinutyt at 2

[river drift]

yes, it is discontinuous

[terse aspen]

Whole thing right? Except intersection?

[river drift]

wdym by "whole thing except intersection"?

[terse aspen]

Wait nvm on that

I was buggin

What abiut this numma 67

[river drift]

,rccw

[terse aspen]

Yea I am just confused how to get a and b here I know how to do for ex 63

[river drift]

you are trying to find a and b to make it continuous?

[terse aspen]

Yes

[river drift]

so think about where it might be discontinuous

[terse aspen]

Ok

[silent raft]

Hey Im bored of highschool grade 9.

[silent raft]

Polynomials and Exponents.

Because you need algebra and trignometry.

[sturdy hound]

can someone check if i got the right answer?

answers i got:
T_A_ = 4217.8269 lbs
T_B_ = 2108.9117 lbs

[dull terrace]

thank you

[fierce nexus]

how much do i really need to know about rations fractions and percentages to be ready for calculus?

these have always been my weakness

[viscid thistle]

How would I go about finding the maximum and minimum value of something like
7sinA + 24cosA

[willow skiff]

Divide by 25 (then remember to multiply by 25) first

[willow skiff]

Now can you find a theta such that cos theta = 7/25 and sin theta = 24/25?

[fathom sphinx]

Oh I see thanks Viper! ( I'll just expand the expected result. )

[winged peak]

AYO ANYONE UP I NEED HELP

[halcyon yew]

yeah?

[ancient zinc]

guys i need to compute the 3 ans for the cube root of -27i

So I thought that I would try to use the method of polar form In order to compute this cubic root

But I'm having a small problem

When I try to compute the theta

I'm using the formula theta = arctan(y/x)

hence it gives arctan(0)

this gives the theta as 0

but after looking at this solution the theta should be -pi/2 in order to give the correct answer

[halcyon yew]

what the yap

it's literally just 3i

[ancient zinc]

wait i should have specified my q

i need 3 different ans

of the cube root

otherwise yea i would have done 3i directly XD

@halcyon yew

[halcyon yew]

ok

the polar form

27 e^(ipi/2)

cube root is

[willow skiff]

because the period of tan(x) is pi radians

[ancient zinc]

how pi/2

[halcyon yew]

3e^(ipi/6), 3e^(3ipi/6), and 3e^(5ipi/6)

[willow skiff]

your answer will only be correct to the nearest multiple of pi

[halcyon yew]

because i = e^(ipi/2)

[willow skiff]

just use your brain, the argument of real number * -i is 3pi/2

[ancient zinc]

This is all of the working I have done till now

[willow skiff]

and -27/0 is not 0

it's undefined

[ancient zinc]

welp yea you are right

[willow skiff]

undefined means either pi/2 or 3pi/2

[ancient zinc]

and tan is undefined at pi/2 and -pi/2

thx @willow skiff @halcyon yew

[willow skiff]

no worries

now give me my rep even though that doesn't exist on this server

[ancient zinc]

yea this server doesnt have rep iirc

[ancient zinc]

how did you get.

(3ipi/6), and (5ipi/6)

[halcyon yew]

because

uhh because I did something wrong

i = e^(ipi/2) = e^(ipi/2 + 2ipi) = e^(ipi/2 + 4ipi)

so it should be

5/6 and 9/6

[halcyon yew]

implicit differentiation

you've differentiated the expression with respect to x, which involves treating y as a function of x

[paper oriole]

ohh tyy

[sleek dome]

Hello guys

Could someone help me find the derivative of (x-1)/x²

Pls explain too

Idk why I'm not able to do it

😔😔😔

[dusty sigil]

just split the fraction and it should be easier

[turbid bloom]

,iamnot dy

[obsidian monolith]

Removed the studying! role from you.

[viscid thistle]

@sleek dome
Rewrite the fraction as multiplication.

E.g., (1/x^2) = x^(-2)

[sleek dome]

Oh shit

It was that easy

Omfg

How did I not see that

I'm so fucking sorry guys

Sorry

😔😔😔

[sleek dome]

Thanks tho

Guys I'm so dumb

I might kms

How did I not see that

Bye

😔😔😔

[viscid thistle]

Anyway, this is my solution to @sleek dome's problem.

[sleek dome]

Thank you bro

I'm so dumb

[sleek dome]

I thank you for opening my eyes

Idk how my brain decided to commit suicide

[viscid thistle]

Does anyone know why B is wrong? (Also ik that the derivative of option A is wrong but its still 1>0 in the correct ver)

[terse pebble]

,rotate

[terse pebble]

you’ve just said it was undefined

[viscid thistle]

I mean if 2nd deriv equals to 0 or undefined wouldnt it mean it has no local extrema?

Like the answer key says only C is correct but im just asking about what makes B wrong? Because from what i know if second deriv has a positive or negative number as a result then it has a local extrema

[terse pebble]

it means the second derivative test is inconclusive

[terse pebble]

sure but division by zero isn’t defined and thus since the second derivative doesn’t exist it’s not a positive or negative number

[bitter eagle]

Hey does anyone offer one on one tutoring? I’m doing pre calculus as a pre requisite for an engineering program and struggle with most of the concepts

I’m doing it online with Khan Academy and through my university

[astral apex]

I think soliciting and advertising paid tutoring is against the rules here

[terse pebble]

dawg

[winter comet]

nobody said paid...

[fathom sphinx]

For question 9a can the range be worked out like this?

x>-3
x+3>0
(x+3)^3-1>-1
qp(x)>-1

[muted hinge]

Does qp mean multuply them

[willow bear]

no, it means composition

it's short for q(p(x))

[willow bear]

yeah that tracks

[muted hinge]

Oh

[tranquil oriole]

Hey guys

can u help me solve
∫(lnx)/(cosx) dx

[willow bear]

!status

[tender quest]

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

[willow bear]

uh wait actually

where did you get that integral? looks quite ugly and potentially not even doable in an elementary fashion LMAO

[winter comet]

ayyy ann is back

[willow bear]

that i am indeed

[tranquil oriole]

my classmate once asked me👀

[winter comet]

your classmate wanted you to suffer

💀

[tranquil oriole]

i tried hard,but couldn't find the solution 😦

[willow bear]

yeah i dont think thats your fault then

i threw it into WA and it tried to give me some kind of infinite series thats not even a power series in anything

which you know is a bad sign ☠️

[winter comet]

💀

[halcyon yew]

,w integrate lnx/cosx

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by diamondpanda16

[tranquil oriole]

bro,can u solve it?

[halcyon yew]

there's literally no elementary solution

how am i supposed to solve it

[tranquil oriole]

yeah,

[fathom sphinx]

ah alright thx so much Ann

[fathom sphinx]

viper where is ur pfp from it looks familiar...

[winter comet]

one piece

[fathom sphinx]

WAT

no way-

[winter comet]

yes way :>

[fathom sphinx]

☠️

[winter comet]

💀

[fathom sphinx]

i got some catching up to do

[winter comet]

well

maybe

its a guys stomach

side character

[fathom sphinx]

lol

[winter comet]

wouldn't expect it to be recognized 💀

[fathom sphinx]

bro frrr

whatt arc even-

[winter comet]

skypiea

[fathom sphinx]

you know what let me stop questioning

[winter comet]

js trust frfr

[fathom sphinx]

I thought it was frommm the new arc

omg

[winter comet]

naw

[fathom sphinx]

hopefully one piece can run for another 1k episodes its too short

fr

[winter comet]

i wish bro

[willow bear]

!redir

[tender quest]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[rough mortar]

yo is anyone awake

pls help me

im suffering

[muted hinge]

Sigma bot

[ember crag]

how u do this slope and equation of the tangent line

[echo sinew]

Does the word "derivative" ring you any bell?

[ember crag]

nopee, our teacher ain't even mention that

[echo sinew]

Ok alright

So you'll be forced to use the formula you sent in the other chat

[ember crag]

so there is other formulas to solve this equation?

[echo sinew]

Yes, the derivative

[viscid thistle]

Can someone check if this is correct?

Interval of convex: ]1, postive infinity[

Interval of concave: ]negative infinity, 1[

[willow bear]

i think you have them exactly backwards

ie you have the words "concave" and "convex" switched around

[fathom sphinx]

For 11b is g(x) both y=4x+12 and y=-1/2x+12 ?

i'm perplexed-

[willow bear]

g would be a piecewise function

$g(x) = \begin{cases} 4x+12 & -5 \leq x \leq 0 \ -\tfrac12 x + 12 & 0 < x \leq 14\end{cases}$

[obsidian monolith]

ann.in.a.teacup

[fathom sphinx]

oh thanks @willow bear

[viscid thistle]

I dont know but my book says its like this wait lrt me show you;

Are the intervals that i sent correct tho

[willow bear]

thats... odd actually

[kind glade]

Is it possible to memorize the Unit circle

[cursive ocean]

yes , it is possible
I had to remember and memorize it when I was in high school because my teacher didn’t allow us to use the unit circle diagram as reference during tests

From my experience, understanding the graph of the unit circle as a whole (ex: which angles have both positive x and y points? Which angles have both negative x and y points?, etc.) and knowing how the values look like (ex: the angles and how they are placed in the graph ) made the memorization way less complicated than it looks

For example: when you know what 45 degrees look like and you also know that it’s in the 1st quadrant of the graph, then it will also come to mind that its x and y values are both positive

[willow bear]

possible? yes. worth it? not really, imo.

[frail ember]

I'm watching this, I dont understand how y = e^x looks and is described like it is at this timestamp: https://youtu.be/JrWJnwCMlP0?list=PL0o_zxa4K1BU5sTWZ2YxFhpXwsnMfMke7&t=735

Cant e and x be anything? if e is 0 and x is -1, it would be 0, but apparently not...

[inner topaz]

e is a constant

it is around 2.7

just like pi 3.14

whenever you are raising to the power of something a positive number it can never get negative

e^-100 for example would just be rewritten as 1/e^100

which is a very small number close to 0

but not quite

if you go very very far back you can say that the lim as x approaches -inf is 0

whereas if exponent gets bigger it gets big wayy faster

bigger the exponent way bigger the number gets

[frail ember]

okay, so e is a known constant with a set value like PI? then it makes sense why it doesnt yield a negative number that way.

but could you explain why a negative exponent cant yield a negative result? ofc. i understand that ex. 2^3 is 2 * 2 * 2, but how would this be written with 2^-3?

[inner topaz]

the negative in the exponent makes it a fraction

[frail ember]

cause it cant be -2 * -2 * -2 ofc

[inner topaz]

2^-3 makes it 1/(2^3) for example

so 1/8

2^-6 makes it 1/(2^6)

[frail ember]

but why? i get its a rule, but could you explain the rule?

[inner topaz]

try doing 2^2 divided by 2^3

you subtract the exponents

2^(-1)

[inner topaz]

if you were to do it normally it would yield to 1/2

using quotient rule btw

or whatever it is called

[frail ember]

what did you get 2^2 from?

[inner topaz]

just a random example

[frail ember]

yeah, but what does this have to do with a negative exponent?

[inner topaz]

lets say b is greater than a

lets make b = 5 and a = 3 for example

2^3 / 2^5

[frail ember]

ah then we get a negative exp

[inner topaz]

it can be rewritten as 2^(-2)

yes

but if you were not using the rule

[frail ember]

okay, let me think for a sec

[inner topaz]

and just using simplification

(222)/(22222)

holy

[frail ember]

yeah * sucks

i get what u mean

[inner topaz]

yea thats that

[frail ember]

ok lemme think if i really understand this

[inner topaz]

let bro cook

[frail ember]

yeah i see, if you follow the quotinent rule and have this:

x^-3

Then to get that, you can use any 2 numbers which would yield that ex:

x^(3-6)

you could rewrite that to this using the rule:

(2^3) / (2^6)

which would yield the same result as x^-3

I now see how it works.

But now i just gotta wrap my head around it more and figure out why this is, if you get why i mean. Like, why is the rule like it is... how did someone figure it out

embarassing how i dont know this stuff but work with 3d rendering and use vector/matrix math every week lol

trying to learn calculus, but i have so much stuff to learn before lol

[inner topaz]

not at all embarassing

people assume true some of the fundamental stuff

yet when someone asks to explain it they are perplexed

like the delta epsilon definition of limit i doubt everyone understood it properly and just memorized instead of comprehending the logic behind it

[frail ember]

could you explain the quotinent rule a bit more? like how i could understand it? all examples when i google seems to explain it using derivatives which i dont know

[inner topaz]

are you talking about the exponent thing or derivative?

[frail ember]

the one you posted

[inner topaz]

in the end it's basically a simplification

you could write it out entirely 2^5 and 2^2

simplify top and bottom and you get the "answer"

happens because the number on the exponent represents how many 2s there are

so whenever you simplify the number goes down

[frail ember]

hm, english isnt my first language, what do you mean by simplifieng the top and bottom?

[frail ember]

you mean that the -3 exponent is a simplification?

[inner topaz]

(2*2)/2 for example

you can cancel out one two on top and one on the bottom

(2)/1

(this was (2^2)/(2^1)

we removed 1 two on top and one on the bottom

(2^1)/(2^0)

the exponent represents how many 2s there are

[frail ember]

ive always had a problem understanding how that works. i guess i just have to start thinking of division as ratios instead of just an expression?

[inner topaz]

hmmm think about let's say 1/2

it's the same thing as saying 2/4

or 4/8

[frail ember]

yeah exactly

[inner topaz]

or 8/16

[frail ember]

it makes much more sense than just looking at the numbers themselves

[inner topaz]

we generally want a simplified answer

so hmm lemme think not too sure how to explain it

[frail ember]

hm could you explain this? isnt x/2^0 undefined?

[inner topaz]

2^0 is equal to 1

[frail ember]

oh

okay

i guess we'll have to go down that rabbit hole too? XD

[inner topaz]

think about 2/2

[frail ember]

i have a bunch of courses on khans academy i plan to go through, but it just feels like idk where to begin to learn the stuff for the next course

[inner topaz]

(2^1)/(2^1) is just 1

2^(1-1) = 2^0 = 1

[frail ember]

ah, you got 2^1-1 using the quotinent law?

[inner topaz]

yea

or if you want you could also use the product one

2^1 * 2^(-1) = 2^0

[frail ember]

what did you get 2^-1 from?

[inner topaz]

just a random example to make it 0

in the product we sum the exponents

2^(1-1)

very similar to quotient

[frail ember]

and with the quotinent law we subtract?

okay, i see how you get 2^0 then.

[inner topaz]

yes

[frail ember]

but how does this explain the laws?

maybe im looking for the mathematical proof?

[inner topaz]

let's use another example

2^2 * 2^5

expanding it

2 x 2 x 2 x 2 x 2 x 2 x 2

we have 7 2s

so 2^7

the exponent tells how many 2s we have

[frail ember]

yeah then we add

i follow so far

[inner topaz]

at the end we have 7 2s