precalculus

[cloud hinge]

Wolfram Alpha

,w V(x)=400x-x^3/4

[obsidian monolith]

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[cloud hinge]

Look at the local maximum

[viscid thistle]

Yeah I got that

[cloud hinge]

I think thats the answer

[viscid thistle]

But cos you have to calculate the volume I subbed it into 400x-(x'3)/4

And I got a different answer with that than when I fifthed and then square rooted and then cubed the total surface area

[cloud hinge]

,w calculate V(x)=400x-x^3/4 at x=40/sqrt(3)

huh

[viscid thistle]

40/sqrt3

Not 40•sqrt3

[obsidian monolith]

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[cloud hinge]

yep, sorry

[viscid thistle]

Np

So that is when s-d lemme get my calculatir

Whoa that's completely different to what I got when I typed it in the calculator beforehand

Idk what happened

Lemme fix this

Wait nvm

Bodmas forgor

Yeah that's what I got

,w calculate (sqrt(1600/5))^3

[obsidian monolith]

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[viscid thistle]

Yeah

That thing

[cloud hinge]

Hmm

something feel off

I think, its not a cube

[viscid thistle]

Maybe because it's lidless

Yeah

[cloud hinge]

yes

[viscid thistle]

Interesting that

Learn a new thing everyday

[cloud hinge]

1600=x^2+4tx

[viscid thistle]

Thankyou ever so much for your help

[cloud hinge]

yes

t=400/x-x/4

x=40/sqrt(3)

,w calculate t=400/x-x/4 at x=40/sqrt(3)

[obsidian monolith]

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Requested by Joe Mama#8435

[cloud hinge]

ye2

[viscid thistle]

Ok that makes alot more sense

So I'm assuming because it's lidless, the principle of a cube having the lowest surface:volume ratio of any cuboid stops being the case

Bc it's not really a cuboid

Very interesting

[cloud hinge]

yup

[viscid thistle]

That's actually so cool ngl idk why

[cloud hinge]

🙂 agree

[misty briar]

Anyone avaliable to help me with a simple question?

its super easy im just not sure what im doing wrong

[cloud hinge]

just ask

[heady ferry]

all functions continuous on a closed interval have an upper bound yeah?

[tight compass]

Yes.

But wrong place for this.

[willow bear]

a function that is continuous on a closed interval has an upper bound on that interval, yes.

but yeah this is calculus at least

[heady ferry]

oh yeah on that interval i meant

[pallid widget]

how'd they do this?

[crisp palm]

1 is equal to cos(x)/cos(x)

[pallid widget]

🤯

[crisp palm]

so by substituting 1 for cos(x)/cos(x) we get (1/cos(x))-(cos(x)/cos(x))

which is equal to (1-cos(x))/cos(x)

does that help?

[pallid widget]

definetly, now i get the common denominator part for sure

thanks

[crisp palm]

np

[mellow tapir]

by the way this is not the best method of doing things. instead, you should've done this:

$\frac{1-\cos(x)}{\frac{1}{\cos(x)}-1} \cdot \frac{\cos(x)}{\cos(x)}$

[obsidian monolith]

Brontochad (Shuri for honorable)

[mellow tapir]

it does the same thing but is easier to understand + gets you there faster

[hushed sphinx]

But the common denominator is arguably easier to come up with as a local simplification.

[hot reef]

What are some efficient tricks to find limits?

[hushed sphinx]

1. Notice everything is continuous at the relevant points you you can just plug in.

[hot reef]

sorry wrong channel

[viscid thistle]

you don't learn limits in precalculus?

[hushed sphinx]

I think that varies from place to place (if they even have something they call "precalculus").

[crisp palm]

precalc in the us is mostly alg2/trig review

not actual calculus prep

[jolly trout]

How can I transform a polynomial so that its roots are half their original magnitudes (like if I have ax^3 + bx^2 + cx + d, what can I do to this cubic so that its roots are 1/2 of their original value)? Is there even such a thing?

[vapid plaza]

You can replace all the x’s with 2x’s

[willow bear]

if the original polynomial is P(x), the one you're looking for is P(2x)

[vapid plaza]

Then if for example x=10 was originally a root it would become 2x=10 is a root which i assume is what you want

[jolly trout]

ooops why didn't I think of that I'm sorry!

[analog forge]

Is it possible to find the inverse function for a function like this?

f(x) = x^3 + sqrt(x^2+2x)

[vivid void]

i would think no

[finite heart]

,w graph x^3 + sqrt(x^2 + 2x)

[obsidian monolith]

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[finite heart]

the inverse function exists i guess but is unlikely to be expressible in terms of elementary functions

[vivid void]

when the function is discontinuous

[analog forge]

that was just an example I made up anyways

[narrow marsh]

,w inverse function x^3 + sqrt(x^2 + 2x)

[obsidian monolith]

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Requested by Shuri2060#9525

[narrow marsh]

easy peasy

[analog forge]

I was just wondering if there was a way to inverse a function like that

[finite heart]

tf is that

[analog forge]

not helpful at all

[narrow marsh]

I think it is quite helpful

It tells you the task is likely impossible by hand

[analog forge]

that's pretty discouraging, sigh

[finite heart]

ive never seen this notation before

[narrow marsh]

I mean the inverse function exists

if you define the range and codomain properly for the original function

[finite heart]

yeah i know that im just not sure what wolfram is saying

[narrow marsh]

That does not guarantee you can find it in terms of elementary functions.

I think wolfram has defined a 6-piece function maybe, but I have no clue myself

[finite heart]

i guess if you try
y = x^3 + sqrt(x^2 + 2x)

y - x^3 = sqrt(x^2 + 2x)

x^6 - 2yx^3 + y^2 = x^2 + 2x

x^6 - 2yx^3 - x^2 - 2x + y^2 = 0

x as a function of y is a root of that polynomial

[placid folio]

hey guys i need help in a question

which information do you receive with these 3 graphs:
f(x)
f'(x)
f''(x)

what can i say

[rose basin]

So I have this problem that tells me to find the degree, the leading term, and the leading coefficient. What I'm wondering is what is the difference between the leading term and the leading coefficient? Aren't they the same thing or are they two different things?

[hushed sphinx]

A term is the entire thing you add to the other terms, ie including the power of x.

A coefficient is the constant you multiply the power of x by to make the term.

[rose basin]

Alright thanks

[worn seal]

Is anyone available?🙏

[mild swan]

[placid folio]

having some problems trying to find x

can anybody help me

i tried factorising it but it seems impossible

[hushed sphinx]

Are you sure you're supposed to find an exact expression for the root?

One can find one using Cardano's formula, but even then it's not particularly nice.

(What you're showing doesn't even say "solve f(x)=0"; it just defines a function without asking any question about the function).

[placid folio]

well its asking to find x and y

i can show u the ss but its in french

heres the question

[faint pumice]

this doesn't make any sense to me...

what's the question?

[placid folio]

find x and y

then question b

[faint pumice]

y is just f(x)

[placid folio]

asks for the cridical number

[hushed sphinx]

There's no even any y anywhere.

[faint pumice]

yeah....

[placid folio]

i mean find f(0)

[faint pumice]

oh

[placid folio]

yea

sorry

[faint pumice]

then it's just 2

[hushed sphinx]

Just plug in x=0, thn

[placid folio]

exactly

but then

find x

[faint pumice]

0?

[placid folio]

when 0 = the equation

thats the part im stuck in

[faint pumice]

you just gave your self the answer

if f(0) = o

then x is literally x

*0

it's in the equation

[placid folio]

what?

im confused

f(0) = 2

[faint pumice]

yeah 2 lol

sorry

if f(0) = 2

[placid folio]

but im trying to find x

[faint pumice]

then x = 2

[placid folio]

y would x = 0 ?

[faint pumice]

because

4* 0 ^2

is 0

and 6 * 0 ^2 is 0

so 0 + 2 = 2

i keep saying 0 why

[hushed sphinx]

That doesn't make sense.

[faint pumice]

explain

why it doesn't

[placid folio]

im trying to find x when:
0 = -4x^3+6x^2+2

[faint pumice]

yeah

x = 0

wait

x = 2

[hushed sphinx]

Type it into Wolfram Alpha already and see the exact solution in all its dubious glory.

[faint pumice]

WHY DO I KEEP SAYING THAT

[placid folio]

x is not equal to 2 or 0

[faint pumice]

you sure?

[faint pumice]

do this

is this even allowed?

[placid folio]

wth is that

lol

[faint pumice]

wolfram alpha lol

look it up

[placid folio]

ok

[faint pumice]

or desmos

i don't know why i keep saying 0

x = 2

WAI

WAIT NO

[placid folio]

or its like symbolab

[faint pumice]

x = 0

[hushed sphinx]

x=2 is not a root of the plynomial.

[faint pumice]

plynomial?

[placid folio]

exactly

[faint pumice]

i keep getting it confused

the answer to f(0) = 2

and x = 0

that's it

[placid folio]

but how

[faint pumice]

do the math on paper

[placid folio]

if u replace x with 0 it doesnt give u 0

i want an answer of 0

[faint pumice]

f(0) = 2

[placid folio]

0 = -4x^3+6x^2+2è

if u say x =2

[faint pumice]

no no

x = 0

[hushed sphinx]

I still very much doubt you're supposed to find a root of that polynomial, based on the horrible solution. But I don't read French well enough to argue for that based on the text of the question.

@faint pumice do you read French?

[placid folio]

ok lets see

[faint pumice]

yes

please do

[placid folio]

0 = -4x^3+6x^2+2è
0 = -4(0)^3+6(0)^2+2

[faint pumice]

dont forget the +2 at the end..

[placid folio]

0 = 2

which is not correct...

[faint pumice]

what

f(0) =2

[hushed sphinx]

@faint pumice once again, did you see the actual question, and do you understand the language it is written in?

[faint pumice]

he's telling me that the question is to find x.

if f(x) = 2.

[hushed sphinx]

No he's not.

[placid folio]

no

[faint pumice]

what is he telling me?

[placid folio]

if f(x) = 0

[faint pumice]

i don't understand the question

ohhhh

ok

well that makes sense

[hushed sphinx]

If you don't understand the question (I don't either), stop trying to help.

[faint pumice]

i understand the question NOW.

[hushed sphinx]

Have you suddenly learned French?

[faint pumice]

this person is obviously french

and he's translating it to me

f(x) = 2
what is x?

that's the question am i right?

[hushed sphinx]

STOP THAT

[faint pumice]

w?

[placid folio]

f(0) = 2

[hushed sphinx]

There's NOTHING in the question that was posted that can possibly, in any language known to man, have the interpretation you keep instisting it has.

[faint pumice]

sohaib

[hushed sphinx]

I think you haven't even bothered to LOOK at the image of the question that Sohaib posted.

[faint pumice]

i have

lol

[hushed sphinx]

STOP TRYING TO HELP WITH A QUESTION YOU HAVE NO IDEA WHAT IS ABOUT.

[faint pumice]

i don't understand whatever language it's in, but he's told what the question is

so i know it.

what's the problem

why would he lie about the question?

[hushed sphinx]

He has MULTIPLE times tried to tell you that THE QUESTION IS NOT WHAT YOU KEEP SAYING IT IS.

[placid folio]

f(0) = 2
find x

[faint pumice]

if this person is receiving a question in french, he's most likely french

[faint pumice]

yeah lol i keep mistaking it

i don't know why i keep saying f(x) = 2

[hushed sphinx]

Sohaib, it will be better if you stop responding to the troll.

[placid folio]

0 = -4x^3+6x^2+2è
FIND X

[faint pumice]

lol

i'm not a troll

[placid folio]

0 = -4x^3+6x^2+2è
FIND X

0 = -4x^3+6x^2+2è
FIND X

[faint pumice]

got it

just solve for x

let me do that real quick

[placid folio]

ok

[faint pumice]

you wanna try it first?

[placid folio]

i tried

[faint pumice]

im not doing this problem for you

oh ok

well first

[placid folio]

but i cant factorise

ik u do

[faint pumice]

you would substract two on both sides

[placid folio]

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

[faint pumice]

i don't think you should factor it

[placid folio]

then how do u find x

[faint pumice]

hold on

let me see the image

[placid folio]

ok

[hushed sphinx]

FOR FUCK'S SAKE!

[faint pumice]

lol

why look it up

that's the easy way to do it

you'll never improve

if you don't learn

relax.

[hushed sphinx]

DO YOU SE THAT EXPRESSION?

[faint pumice]

lol

why are you so angry

[hushed sphinx]

IT CAN'T POSSIBLY BE THE INTENDED ANSWER TO THE QUESTION

[placid folio]

i didnt look it up lol

its common sense

[hushed sphinx]

BECAUSE YOU FUCKING KEEP LEADINT THE POOR ASKER ASTRAY.,

[faint pumice]

i'm not

[hushed sphinx]

STOP DOING THAT

[faint pumice]

i just didn't understand that question at first

why are you so mad

it's f(x) = 0
find x right?

[hushed sphinx]

You're wasting the asker's time!

[faint pumice]

if i'm going to teach someone something, i'm going to teach them everything

not just have them look it up and explain the answer

step by step

that's how you're supposed to do it

i'm not wasting his time, i'm doing him good.

[hushed sphinx]

You're not going to teach him to solve general cubics.

That's nonensen.

[faint pumice]

"give a man a fish, and he'll eat for a day, teach him to fish, and he'll eat forever"

just teach him it

you don't even know what grade he's in

honestly

[hushed sphinx]

There is NO WAY a question looking like that can be expecting the student to solve a general cubic exactly.

[faint pumice]

i'm pretty sure this is against the rules anyways

#rules

[placid folio]

damn bro theres a big beef rn

[faint pumice]

lol

[hushed sphinx]

Fucking stop wasting the poor guy's time by ENABLING HIS MISUNDERSTANDING OF WHAT HE'S ASKED TO DO.

[faint pumice]

how

ok

lol

i'm sorry for offending you

[hushed sphinx]

I have SHOWN YOU HOW UNLIKELY IT IS that he's actully being asked to find the root of that polynomial.

[faint pumice]

you can go ahead and teach him your self

[hushed sphinx]

Just. Stop.

[faint pumice]

just go ahead and teach him

if you know

[placid folio]

@faint pumice check ur dms

[faint pumice]

honestly, I'm learning math too, so this is a learning process for me too.

you don't want to solve it here?

can't call

[placid folio]

no not that i want to explain u the problem

[faint pumice]

can you send the problem again

[placid folio]

or can u go on vc

8kbps

[faint pumice]

wait i have it right here

[stuck lark]

@faint pumice pls dont mislead others

[faint pumice]

lol what

[stuck lark]

step off if u dont understand the question

[faint pumice]

i haven't given him any steps to the solution yet

i do

just solve for x

[stuck lark]

its written in french. can u read french?

[faint pumice]

he can.

[placid folio]

https://tenor.com/view/john-jonah-jameson-lol-laughing-hysterically-laughing-out-loud-funny-gif-17710543

[faint pumice]

ask him

lmao

[placid folio]

indeed i can

[stuck lark]

has he translated the problem to english yet?

[faint pumice]

why does he need to translate it..

[stuck lark]

bc u cant read french

[faint pumice]

he's french, he can just tell me what it says...

i don't understand that

[placid folio]

@faint pumice plz just check ur dms

[stuck lark]

if u dont know what the question says yet then u cant know how to answer it

[faint pumice]

he told me the problem

[faint pumice]

here

[hushed sphinx]

He told you what he thinks the problem is, but he is wrong.

[faint pumice]

why are you getting so mad anyways

ok

then translate it

please sohaib

[placid folio]

omg

@faint pumice plz call

[stuck lark]

bc u were answering the question BEFORE getting the translation

[faint pumice]

i misunderstood the question.

are you going to help him?

[placid folio]

can u calll????????????

[faint pumice]

no

[placid folio]

ok can u dm

[faint pumice]

yes

[placid folio]

ok anser

[mellow tapir]

What in the world happened here?

[placid folio]

a lot

big beefs between @faint pumice and @stuck lark

there was a war between them

[warm nebula]

XD @placid folio I can help you simplify but not find x.

[placid folio]

its fine @faint pumice did an amazing job helping me

we found the solution

[tardy ridge]

what was the solution.

you should post it here in case it's wrong.

[placid folio]

x = 1,678

[tardy ridge]

lmfao what.

that's the answer to which question?

[old quail]

x=7

lol

[blissful stone]

How does pre calculus differ from actual calculus?

[tight compass]

pre-calc is algebra, trig, plus a few other stuff. Calculus is about limits, continuity, differentiation, integration etc. Doing calculus requires a good understanding of topics in pre-calc.

Most reason people fail calculus is due to a poor understanding of thoses topics in pre-calc.

[bright light]

Hi, What does a prime stand for? I forgot to ask my teacher in class but it's like a 1 but it's a bit tilted and usually in the power spot

example

[civic sierra]

First derivative of y

[blissful stone]

If I understand graphs and algebra, is it enough to begin migrating into pre calculus?

[vivid void]

to my knowledge if you know algebra 2 and trigonometry, you can just start calculus

i’ve heard that precalculus is just review

[blissful stone]

What parts of trigonometry should I know when it comes to calculus?

Is it just cosinus and tangents?

[vivid void]

you should know at least sine and cosine

since everything else can be represented in terms of those two

[blissful stone]

Man only if I had the time to go into my Khan Academy courses

[vivid void]

also the pythagorean theorem, but that itself is just one thing so it’s easy to just memorize

[blissful stone]

Pythagorean theorem is easy as hell to memorize

All that you need to remember is to take square roots out of the sum

[vivid void]

most of the stuff in calculus is just algebraic, but some stuff, like in some of the methods used to compute integrals/antiderivatives, use the pythagorean theorem

[blissful stone]

Antiderivatives? What are those?

[vivid void]

if you don’t know what it is, don’t worry, it’s not important right now

it’s the opposite of a derivative if you know what that is

again, if you don’t, that’s fine, just an example

[blissful stone]

The last semester of middle school is sucking all the energy out

Can’t wait to begin the tech specialized senior high school

There, I will have fun doing maths

[atomic imp]

What grade are u in?

If ur ahead of ur class, I’d suggest doing precalc in ninth or tenth

[blissful stone]

Ninth

[atomic imp]

I’m in ninth doing calc

Cuz luckily there were plenty of courses for me to learn trig and precalc

[atomic imp]

Yea u can start then

[blissful stone]

Swedish school system is simplified

They don’t even teach you trigonometry anymore besides senior high school

[atomic imp]

In my school

They just teach y=mx+b in ninth 💀

[blissful stone]

Same

Unfortunately we have multiples exams all the time on different subjects

And I only wish I could have had more math lessons

I learned a bit of calculus from my swimming teacher

[atomic imp]

Sameee. If you want, I can give you the courses I used from YouTube. I take notes on everything and it covers lots of info

[atomic imp]

Lol

They’re pretty long too

[blissful stone]

He is studying to becoming a civil engineer

[atomic imp]

5-10 hours

[atomic imp]

Wow that is cool

[blissful stone]

Yes please

[atomic imp]

K Is there perms here

Nvm I don’t need perms

K gimme a sec

I’ll do them in the most reasonable order

https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjNoOy_4Nr2AhUik4kEHXb8DyAQwqsBegQIEhAB&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D_F7_zB3BYQ0&usg=AOvVaw1hGzyb1XoKPwZJ7bAig3sF

Algebra course

https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=video&cd=&ved=2ahUKEwit_rjU4Nr2AhUVjIkEHbiGCVcQtwJ6BAgQEAI&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D5zi5eG5Ui-Y&usg=AOvVaw1TIy-ZTWGlk6OdXqGaCX2p

Trigonometry course

3. Precalc course #1 (optional)

https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=video&cd=&ved=2ahUKEwjp-8_i4Nr2AhUkLX0KHVazAPMQtwJ6BAgOEAI&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D9IOTI9ViExg&usg=AOvVaw1J15sF-h7tdsuSuV8s0BHL

4. Precalc course #2 (better than the first one IMO)

https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=video&cd=&ved=2ahUKEwjp-8_i4Nr2AhUkLX0KHVazAPMQtwJ6BAgREAI&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DeI4an8aSsgw&usg=AOvVaw2Tob-bu8rFI_QcZOBKHeAJ

5.6.7. Calculus 1/2/3 (I’m on 1 rn)

https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwih77uK4dr2AhW-j4kEHWxSB9QQwqsBegQIAxAB&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DHfACrKJ_Y2w&usg=AOvVaw0rplgT5aPE1T2bOZtq11mG

https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj50-WX4dr2AhVckokEHbj0CAMQwqsBegQICRAB&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D7gigNsz4Oe8&usg=AOvVaw0ztvxjB3oPeOR0O9woEw1i

https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=video&cd=&ved=2ahUKEwiu3Oaq4dr2AhUokYkEHYkGBE8QtwJ6BAgIEAI&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DtaGq6Vusclo&usg=AOvVaw39zxJzY-gjIMaEv1-h0b8q

[blissful stone]

Mhm

I’ll take a look when I have time after school

[atomic imp]

K. I’d suggest simply doing an hour a day

I’ll finish most in like a week or two that way

U will*

[blissful stone]

But right now, it’s 23.20 here and I want to sleep

[atomic imp]

Alr goodnight

[blissful stone]

Thanks

[atomic imp]

Np

[compact tulip]

is this enough for entire pre calculus?

Guys

I just shifted to the US from India

I am currently in the 9th grade and I will go to 10th grade from August

so pls tell me the contents of Pre-Calculus

I really need to complete Pre-Calculus and get into AP Calculus BC

[atomic imp]

Alr I can help

Pre calc should cover algebra, trig, and advanced functions

U should know lots about graphs, quadratics, lines

And about geometry, trig , and even conics to an extent

[atomic imp]

Do both of u want it to be enough. And IMO, all 4 courses I listed before calc 1/2/3 are good for precalc

Doing them all will strengthen ur math by a lot

[compact tulip]

I saw that in khan academy , there are some other concepts like Matrices , Permutations , Combinations , Binomial Theorem and so on

are those necessary?

[atomic imp]

In calc, I don’t think u rlly use permutations, combinations, and the binomial theorem. Calc 3 is about vectors so I think they will teach u matrices in it

But u can search up permutations, combinations, and the binomial theorem on google an a website called “Mathisfun” explains those rlly well

[compact tulip]

okay thx

[atomic imp]

It takes like 30 min to understand

[atomic imp]

Np

[compact tulip]

I know all about them .... I just need to write a full test on Pre-Calculus and pass it to get into AP Calc BC

Im crazy about math

[atomic imp]

Same lol

But I don’t write any exams

I just learn it on my free time

School doesn’t provide me with much unfortunately

But next year I’m taking ap math since that is an option

[compact tulip]

ohhk

[compact tulip]

nice

[atomic imp]

So I get to learn about vectors: )

[atomic imp]

Thx

[compact tulip]

ah nice

vectors are really fun

easy but fun

[atomic imp]

Yeah I learned a lil about them. I plan on mastering them once I’m on calc 3

[compact tulip]

ah nice

[brittle helm]

Hi I am new to discord, can u help me where to go for voice channel so that I can talk and study math?

[tepid cloak]

how do you get the domain and range of this piecewise function

[hushed sphinx]

Try sketching a graph first to get a feel for what you're dealing with.

[tepid cloak]

how do I graph when x is not equal to 2

[hushed sphinx]

Um, I'd have hoped you're able to sketch the graph of a simple linear function ...

[tepid cloak]

idk

[hushed sphinx]

The green dot does not correspond to anything in the specification.

It says f(2)=6, not f(6)=2.

[tepid cloak]

oh didnt notice it

srry

[hushed sphinx]

And then of course you'll need not to have the point (2,4) in the graph.
One usually shows that by interrupting the line by a small circle.

[tepid cloak]

oh wait my graph is wrong

[hushed sphinx]

Yes, but x to the left of this also fall into the x!=2 case.

[tardy ridge]

wtf

8 hours of youtube videos cannot cover an entire semester of math.

if you think you can shrink a 300 page textbook into less than 1/3 of a day then you're missing way too many things.

that's a bad way to learn.

download a book instead.

[atomic imp]

This is for ppl that already have an extensive mathematical knowledge

Ppl good at math don’t rlly need to do 300 pages

Plus those courses are only for the learning

The application can be done by searching up problems

[atomic imp]

And most textbooks don’t teach anything; they are just for practice

[atomic imp]

All the courses add to roughly 50 hours

[atomic imp]

And the amount of math I did this past year contributes to over 600 pages

So I think it is enough

[hallow spear]

what are u guys getting for this pls lmk

[plucky perch]

should i note x^2 +x + 1 as a variable or should I consider doing something else at first?

i was thinking of having that a 6th root of (x^2 + x + 1) and work my way from there but it seems that the x cubed is giving me trouble

[hushed sphinx]

Write the whole thing as x times something.

That should at least get you a candidate p.

How to get all the way to "my candidate p works" without using (or reinventing) calculus I'm not sure though.

(With calculus it can be done by switching variable to y=1/x and recognizing the result as a derivative that can be computed symbolically).

[plucky perch]

well the common factor, as you stated, doesn t help much

i m trying out the switch of variables

i got this

[hushed sphinx]

What do you get with the common factor?

It should be plenty helpful.

[plucky perch]

this looks like a derivative with limit h -> 0

or at least that s what im thinking of when seeing this

[hushed sphinx]

Right. So you have two factors, one of which is x and the other is a sum that clearly goes to 2-p for large x.

In order for the product to have a finite limit, what can you say about the other factor?

The expression with a variable switch does indeed look like a derivative. But it only really matches the form of a derivative if the f(0) term in the numerator f(y)-f(0) has disappeared because f(0)=0 -- and you can use that too to find p.

[plucky perch]

correct, but we just took the limit inside the parantheses, the 1/y * (2-p) is valid?

[hushed sphinx]

My recommendation for finding p is to look at the expression before the variable switch.

[plucky perch]

ohhh, i was using the general formula for derivative

[hushed sphinx]

You cannot find the limit by taking limits of each factor separately -- but what you can do is figure out that you'll be sunk unless 2-p=0. Namely if 2-p is something nonzero then you have a limit of (something that goes to infinity)×(something with a finite nonzero limit), and we know that always diverges.

On the other hand, if 2-p is zero, then we have a limit of (something that goes to infinity)×(something that goes to zero). That is an indeterminate form, which means that taking the limits for each term won't tell us enough about what is happening -- but it is at least possible that the whole thing converges to something finite.
To find out whether it does we need additional cleverness, which is where recognizing the definition of a derivative comes in.

[plucky perch]

ok, i think i get it, writing it down now

so this obviously hints that p=2 is the solution

though, if we were asked to calculate L, what would we do?

[hushed sphinx]

Right. (You can't directly conclude from 2-p=0 that L is finite, only that it might be finite).

[plucky perch]

yeap, clear now

[hushed sphinx]

For getting the whole way, the path I can see is to recognize $$\lim_{y\to 0}\frac{\sqrt{1+y+y^2}+\sqrt[3]{1+y+y^2+y^3}-2}{y}$$ as the definition of the derivative of $$f(y) = \sqrt{1+y+y^2}+\sqrt[3]{1+y+y^2+y^3}$$ at $y=0$, and then differentiate the function symbolically.

[obsidian monolith]

Troposphere

[plucky perch]

alright, thank you

differentiating symbolically is just differentiating as in general, without the knowledge of limit right?

[hushed sphinx]

Also note here that writing "lim x(2-p)" is wrong -- in general it's not valid to replace part of the expression with its limit unless you do that for all parts (and you don't run into one of the indeterminate situations).

[willow bear]

symbolically as in using rules such as power, product, chain etc.

[hushed sphinx]

Yes, I mean "by using rules" rather than "by evaluating the limit".

[plucky perch]

yes, i wanted to explain the judgement, maybe writting infinity * (2-p) is better?

[plucky perch]

oh ok, i wanted to make that clear

[hushed sphinx]

Yes, I'd say writing infinity·(2-p) (without the "lim") is better -- or at least less likely to look to the grader like you're misunderstanding something.

[plucky perch]

ok, thank you

[plucky perch]

this might give in a headache

[plucky perch]

any idea to tackle this?

[hushed sphinx]

Immediately it looks like a job for L'Hospital.

But if so it can't really be "precalculus", I think.

No, wait a moment. Does it mean $\bigl(\log(1+\sin x)\bigr)^{1/\sin x}$ or $\log\bigl((1+\sin x)^{1/\sin x}\bigr)$?

[obsidian monolith]

Troposphere

[plucky perch]

i wasssss

kinda wanting to understand that too hah

[hushed sphinx]

In the former case, the numerator and denominator each goes to 1.

[plucky perch]

true

[hushed sphinx]

Assuming x goes to zero from above only, that is.

[plucky perch]

did you obtain this from l'hopital or another method?

[hushed sphinx]

When x is small sin x behaves like x so log(1+sin x) goes to 0. Meanwhile 1/sin(x) goes to infinity, and a small number to a large power is smaller yet. So (log(1+sin x))^(1/sin x) goes to 0. (That is, still assuming we're considering only x>=0, since for x<0 the power is not even defined at most points).

[plucky perch]

oh ok

is this formal enough to simply write sinx = x for x-> 0 ?

[hushed sphinx]

No, that's abuse of the "=" sign.

The log((1+sin x)^(1/sin x)) interpretation is more interesting, though.

[plucky perch]

true, but i m asking whether or not i need to do more than just saying the numerator and denominator each goes to 1.

[plucky perch]

yeah, but how would that be even achievable tho

[hushed sphinx]

I would give a bit more detail than that. After all, it didn't seem to convince you when I merely asserted it ...

[plucky perch]

i know that sinx and tanx are aproximated as x for tiny angles, it also is the first term in the series expansion, but the problem would seem uncommonly easy if that were the case

[plucky perch]

ie. i think the first case may be what the problem is trying to tell

[hushed sphinx]

It's the more principled understanding of the notation, certainly. Just looks fishy that the other interpretation leads to both numerator and denominator going to 0, which would lead to a more interesting problem.

(Hmm, actually it's not that much more interesting in the second interpretation. Since log((1+x)^(1/x)) = (log(1+x))/x has nonzero first derivative at x=0, the difference between sin and tan doesn't even matter anyway).

[plucky perch]

would the limit still converge into something nice tho?

[hushed sphinx]

Yeah, it just becomes 1 in that case too.

[plucky perch]

oh ok

thank you

[plucky perch]

@hushed sphinx hey, are you still up for one more question?

sorry for bothering so much today

Let there be $f : [0, 1] \rightarrow R$ a continuous, nonconstant function, differentiable on $(0, 1)$ and $f(0)=0$. Show that there is $a, b$ in $(0, 1)$ such that $0 < a < b$ and $b f'(a) < f'(b)$

[obsidian monolith]

Alphara

[plucky perch]

from first sight Lagrange pops up

[hushed sphinx]

How is a question with "differentiable" and derivatives explicitly in it precalculus?

f(x)=-x is a counterexample.

[plucky perch]

hmm, mostly because i do not know where to fit this material

i suppose calculus would be a better fit for this problem

[oak slate]

I have to do a problem of equations that define functions. this is the solution but can someone explain how 5y turned positive and 7 turned negative? also ,why after dividing 5 , did 5 go into the numerator for 7?

[trim hemlock]

adding 5y and subtracting 7 on both sides, or in another way of visualising it, subtracting 3x by "both sides"

and this step is incorrect

[oak slate]

ohhhhh ok i thought i was doing it wrong since i was looking at the answer sheet as reference! thanks

[floral vessel]

I don’t see how this works. Im confused on the domain of g(f(x)) I think it should be (-4, infinity) but I worked it out and got all reals.

wrote the bottom one wrong its ln(-4+4) but my question still stands

[hushed sphinx]

You have g(x) = e^(x-1) and f(x) = ln(x+4).
Then g(f(x)) is indeed only defined for x > -4, but when it is defined, the result equals (x+4)/e. The latter expression is defined for all x -- but of course it can only be equal to g(f(x)) where g(f(x)) exists at all.

The lesson to take home here is that when you simplify an expression, you may end up with an expression that is defined in more situations than the expression you started with is.

This is basically part of what we consider "simplification" to mean -- if we didn't accept that possibility, we couldn't consider the step from e^ln(A) to A to be a valid simplification.

[floral vessel]

Got ya. Would it be right to assume that x < -4 would be considered extraneous solutions similar to the ones for rational functions, and when should I check for these cases, is it only when I simplify?

[hushed sphinx]

Yes, you could think of it that way.

A better way, however, would be that when you're considering "what is the domain of this expression?" you need to consider all of the problematic operations in it (divisions, logarithms, square roots, tangents, etc.) one by one before you simplify anything. Take the subexpression that the problematic operation is applied to and write down the condition for that being defined. Then you can start simplifying the condition rather than the entire original expressions.

[floral vessel]

Okay I got it. Thanks for the explanation.

[river oasis]

Go to #calculus

[shut folio]

<@&286206848099549185>

[velvet star]

Hello! I'm having a hard time understanding continuity but I really want to get it. Can someone please explain to me how to know if the function is continuous at x=0, 1, and 2? Thank you so much.

[calm locust]

Welp

[supple owl]

separate the limits

[obsidian hinge]

what?

that's not a plus sign

wdym by "separate"

[supple owl]

he should do root of x+5 / x alont and root5 * 1/x alone

[obsidian hinge]

he can't do that though

since it's a multiplication sign

[supple owl]

ik what i am saying

its will be esier

[calm locust]

Ok and then what?

After separation

[supple owl]

you will see that in the limit you will get root5 multiplied by 1/infinity

so

root5*0

oh wait

[calm locust]

Ok so?

[calm locust]

Ok, anyone else that know how to solve that?

[obsidian hinge]

can you tell me the form of that when you just plug infinity in?

[calm locust]

Wdym?

[agile gazelle]

continuous at x=a (where 'a' is any number) sorta means that the graph doesn't break at that point

I think it'd be easier if you saw an example of discontinuity

look at the graph you sent when x=5

[agile gazelle]

see how the graph "disconnects" at that point?

if you were to draw that graph with a pen, when you reach x=1 or x=5 you'd have to lift your pen

the moment you lift your pen, the graph is broken (i.e. the function is discontinued)

hope that helps

[obsidian hinge]

have you been taught abt indeterminate forms

[slate reef]

you should factor x^2 out of the squareroot

then you can cancel the x in numerator and denominator

and you can substitute x for infinity to find answer

[obsidian hinge]

what?

??

[delicate crown]

basically you make it sqrt(x+5)=sqrt(x^2*(1/x+5/x^2))=xsqrt(1/x+5/x^2), so you can cancel the x.

[obsidian hinge]

that gives you infinity times 0

so you get nowhere

[delicate crown]

no but the x cancels out with the x in the denominator

[obsidian hinge]

ohhh facts

[delicate crown]

yeah then its pretty easy

cos 1/x and 5/x^2 go to 0...

[obsidian hinge]

i thought you mean $x\sqrt{\frac{1}{x} + \frac{5}{x^2}}$ and i was so confused

[obsidian monolith]

valley

[delicate crown]

oh lol

[golden parrot]

||o||

[meager cairn]

Idk if its calculus question or not, can someone help me to find lower value of function given.

I know highest value can be 1 at x= pi/2

[junior saddle]

Find 1nd derivative and set it equal to 0 but I dont think that will make anything easier.

hmm let me think about it

[meager cairn]

Man that’s really a tough job

[fair cloud]

Yeah, doesn't seem to have a way around it. I got D

First derivative isn't so bad, deriving the second derivative to prove it's the lowest point is pretty bad

[fair cloud]

Writing $y=\sin(x)^{\sin(x)}$ as $y = e^{\sin(x) \ln (\sin(x))}$ you get $$y' = e^{\sin(x) \ln(\sin(x))} \cdot (\cos(x) (\ln(\sin(x))+1)$$ and $$\begin{aligned} y'' & = e^{\sin(x) \ln(\sin(x))} \left( \cos(x) \left( \ln(\sin(x))+1 \right) \right)^2 \ & \quad + e^{\sin(x) \ln(\sin(x))} \left( - \sin(x) \left( \ln(\sin(x)) +1 \right) + \dfrac{\cos^2(x)}{\sin(x)} \right) \end{aligned}$$

[obsidian monolith]

EvilSonidow

[fair cloud]

Setting $y'=0$ yields $x=\dfrac{\pi}{2}$ and $\sin(x) = e^{-1}$. Substituting these into $y''$ yield the former as maximum and latter as minimum

[obsidian monolith]

EvilSonidow

[haughty idol]

anyone here?

[zinc plaza]

can soemone help

An airplane is travelling at 500 mph. A wind is blowing 135 degrees from east at 75 mpg. The airplane aims 20 degrees from east. What is the plane's ground speed and angle?

[vital holly]

can someone help me with my precal homework

i need help finding zeros of a polynomial

[willow bear]

@vital holly do you still need help with your problem that you didn't post?

[fast oxide]

You can factor the polynomial, use the PQ-formula or the quadratic formula.

Are you familiar with those methods?

[daring bane]

hey pals what the hell is a linear combination

more specifically i need to find the linear combination of the vector $(\frac{5\sqrt{26}}{26},\frac{\sqrt{26}}{26})$

[obsidian monolith]

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

[willow bear]

"the linear combination of the vector <...>" does not make any sense

@daring bane can you perhaps post the problem exactly as it appears in your textbook/webassign/whatever?

[daring bane]

sure

[willow bear]

so this is poor wording to say "write this vector as a linear combination of i and j"

or rather, it's poor wording when ripped out of context like you did.

[daring bane]

possibly

[willow bear]

you know what the letters i and j mean here, right?

[daring bane]

im just confused

because i looked up linear combinations and all i found were multivariable equations

[willow bear]

.

yes or no

[daring bane]

all i really know is that they have a hat on them and hat tends to mean approximator

or at least in stats it does

[willow bear]

no

[daring bane]

also sorry my internet went out for a sec

[willow bear]

nothing to do with approximators or anything like that

[daring bane]

alright

[willow bear]

this is linear algebra

so you don't know that i and j are the vectors in R^2 which have length 1 and point along the x- and y-axes respectively?

and you don't know that together they form what is called the standard basis of R^2?

[daring bane]

i mean i know that a vector in R^2 with length 1 is a unit vector

didnt know i and j notate that though

so there do i still just put 5sqrt(26)/26 and all that with their respective letters here?

because i already found the unit vector

[willow bear]

kind of weird that you would make it through some sort of vector algebra course, go on to learn some statistics, and never learn such basics as this.

but yes, just put the x- and y- coordinates as coefficients on i and j respectively...

[daring bane]

we are starting out on it

cool thank you

[willow bear]

but how are you learning stats before vector algebra

thats what makes no sense to me

or how have you learned stats before vector algebra, i mean

[daring bane]

im in precalculus

i just took stats this year bc why not

[willow bear]

okay so you took a version of stats that presumably does not require any calculus or vector math

[daring bane]

yes

primarily bc im a sophomore in high school

its mainly just the terminology tripping me up here

we just went thru the trig unit so now we are learning applications of trig

[red plume]

pls help do this one

done everything else except this

dont know where im going wrong

[hushed sphinx]

Neither do we, since you're not showing any reasoning for your answer.

[obsidian hinge]

^

[devout wren]

where does the -pi/6 come from for multiplying the coordinates?

[merry scarab]

A car braking is represented by this function

Is the car gonna stop before it reaches the stop sign

The stop sign is at 62 km

I found -2 as the position when the car stops what does that mean

Nvm i found the answer

[timid pivot]

Hi guys

I have a test based on an exercise that we have to do as an assignement

and I am really lost

I have to calculate these limits using l'Hôpital's

Can someone help me ?

[viscid thistle]

Find the derivative of the following functions:

[valid parrot]

what is precalculus to be clear ? cause i don't feel like derivatives are early university

[hushed sphinx]

The channel naming follows typical US progressions, even though several other countries teach derivatives by default in the STEM tracks of their high school analogues.

[tawdry urchin]

hey

i need some help

can someone help me

can i cancel the four so the equation would be x2+32-32 ?

[knotty garden]

really? Im not from the US and where im from everybody "takes" (or rather is taught) Calculus in high school, irregardless of how good they are. Its part of the curriculum

[knotty garden]

non

i mean you can get rid of the 4 yes, but not like that

[tawdry urchin]

what can i do?

please guide me

[obsidian monolith]

Pebble

[tawdry urchin]

i need to delete all the oether number and leave x literally bi itself

but i would have to dive the 32 right

[knotty garden]

yes

[tawdry urchin]

Look, I’ve done all of them I’m just missing that step

[fast oar]

this is the maximum you can simplify

[tawdry urchin]

oh well, I tried man, i will tell my teacher that

Thanks

[olive ingot]

1+5=55343232432432423443554445-fhifhr83r8244872832948293842948

-2>-10000

ez

lol

https://tenor.com/view/when-your-bored-of-maths-maths-op-who-tf-told-that-maths-is-difficult-math-is-easy-maths-is-not-difficult-gif-21408663

https://tenor.com/view/resolvendo-matematica-rio-fazendo-a-questao-equacao-problema-de-matematica-gif-18352312

[viscid thistle]

IMAGIGINE

YALL ARE NERDS LOL

[rose basin]

So I have a question about Cauchy's bound. It tells me to use Cauchy's Bound to find an interval containing all real zeros for this equation that I have. I'm wondering how do you use Cauchy's bound to find the desired answer.

[obsidian hinge]

for anyone else who doesn't know wtf cauchy's bound is here it is

[obsidian hinge]

this seems to follow naturally from the formula i listed below

sooooooo

just do that

[rose basin]

Yeah I got it now thanks

[obsidian hinge]

yw

[mental steeple]

Anyone know how b= 3?

I’m confused

For the period

<@&286206848099549185>

[narrow oxide]

There are 3 complete periods from 0 to $2\pi$, so the period is $\frac{2\pi}{3}$.

Oh woops, bot is down. I mean there are 3 periods in the part from 0 to 2pi, so the period is 2pi/3.

[mental steeple]

Can I do that with other problems

Wait and where did you get the 2pi in 2pi/3? @narrow oxide

[narrow oxide]

From 0 to 2pi (within this red region), there are 3 complete waves, hence there is 1 complete wave in 2pi/3.

@mental steeple

[narrow oxide]

Yes.

[mental steeple]

Wait so how about this

Can I do the same thing for the last problem

There are 1.5 complete periods

[narrow oxide]

I mean, it's obvious here that there is 1 wave from 0 to pi, so the period is just pi.

[narrow oxide]

You only need to do this when you can't read directly from the graph.

[mental steeple]

For cos is this a full period

?

The red

[narrow oxide]

No.

[mental steeple]

O

[narrow oxide]

A wave always starts and ends at the same height.

[mental steeple]

So there are 2 waves

Right

[narrow oxide]

Huh?

I don't get what you're trying to do. You can tell from the picture the period is pi.

[mental steeple]

Nvm

im wrong yes sorry

Wait so can you help me with sketching now

[narrow oxide]

For this, you couldn't read from the graph, so you had to use the fact that 3 periods is 2pi.

[mental steeple]

Like with a given function

This was my work but I had some mistwkes

[narrow oxide]

Uh, I needa go do my practice problems. Maybe someone else can help.

[mental steeple]

oh

[normal vault]

k so

[supple owl]

you need math to get better playing minecraft boy

[fast oar]

this is a sin because it starts at the centre and does the kind of sideways s shape that repeats every pi
cos starts at the top and makes a valley kind of thing, returning to the top

they key to finding the period is looking at where the function starts repeating itself exactly as it is

so like here the red part is the period because the blue parts are exact copies of it to the right and to the left

if you notice, this doesnt necessarily have to be a sin function

you can also make it a cos function with a horizontal displacement

its just easier to call it sin because you dont have to deal with the displacement then

[mental steeple]

It’s actually a cos graph

[fast oar]

it's not really a cos graph but you can call it that if you want by starting the period at a different point

[mental steeple]

lol my teacher said it was

It says to create

A cos function

@fast oar

[fast oar]

Oh ok

Then it's a cos function with a horizontal displacement

[narrow marsh]

<@&268886789983436800>

[daring drum]

Ty

[obsidian hinge]

ryc forgot to say b&?

[sly osprey]

i have a simple question, in a fraction like this only one number is actually negative right, so is it the denominator negative, or the numerator?

im finding trig ratios so cos is x/r, so would my x value be neg or pos

[obsidian hinge]

trig ratios?

you mean like in a triangle?

[sly osprey]

like this

[obsidian hinge]

that's a length

it's a distance

it'll always be positive

[sly osprey]

this is my actual question

am i going about it right?

[fast oar]

so this is how it looks

theta will be equal to pi radians (or 180 degrees) minus arccos(2/3)

idk if you use degrees or radians

[fast oar]

so to answer this, it's the x that would be negative here, not the r because r is a radius and it always has to be positive while x can be a negative value

[sly osprey]

i never thought r would be negative i was thinking whether y would be negative or x

[fast oar]

ic

[fast oar]

well the question is cos(theta) = -2/3 and as you said before cos is equal to x/r

so in this case it's x

if that's what youre asking

[static gale]

can someone dm me and help me

[tardy ridge]

no

[proven flax]

Can anyone here assist me with this? I know to multiply by the conjugate and use pythag ID but I'm not able to simplify enough to get credit.

[viscid thistle]

can someone explain what inverse trig functions are in simple words?

[mild swan]

It's just an inverse to a trig function (being sin x, cos x, etc.)

An inverse function is one that "undoes" another function

[narrow oxide]

Trig functions let you find the sides of a triangle using the angle. Inverse trig functions let you find the angles of a triangle using the sides. They have the opposite effect.

[viscid thistle]

thank you

[viscid thistle]

thanks

[bold marsh]

Does anyone have any exponent law big word problems or simplifying radical exponents word problems any one of em gr9

[minor forge]

Bruh I’m going inverses tomorrow in trig

[jade coral]

Can somebody solve this?

[full nacelle]

Can anyone help me with 2+2 please I've been stuck on it for like an hour

[hushed sphinx]

Hint: work modulo 1; it then reduces to 0+0.

[vernal anchor]

such memes have no place on this server

[viscid thistle]

Leave the server, you'll become intelligent then and can answer it on your own.

[violet widget]

how do u find the range of x^2+x? I know its [-1/4, inf) but I dont get how they found the -1/4

any idea?

[vapid plaza]

Write the quadratic in vertex form

That makes it very obvious what the minimum/maximum value would be

[violet widget]

Wdym by that

How to write it in vertex form

[uncut mulch]

completing the square

[wind shale]

can someone send me the answers to this

i already did question 1 but the rest i’m confused on

[hushed sphinx]

No, we're not going to do your homework for you.

If you can explain your confusion in more detail, we can try to un-confuse you.

[warm nebula]

@split rock you still need help?

[neon latch]

Wassup

How can i find the min and max values of trig functions?

[hushed sphinx]

-1 and 1.

[neon latch]

The problem is asking me this

On |x| ≤ π/2

Find the max and min of sin x + cos x

[twin palm]

could it be asking it in radians?

[supple owl]

guys do how i can make a series converge ?

like making the terms smaler

[tight compass]

What do you mean by this?

[supple owl]

like making a divergent series converge

[tight compass]

If the sequence of term is positive and decreasing and converge to 0 you can apply alternating series test.

[supple owl]

what is it this ?

[supple owl]

thx

[tight compass]

Looking at this more clearly than before, what you said does not make sense. If a series is divergent you can’t make it converge.

I interpreted it as something else.

Unless your clear what you mean by “make it converge”.

[supple owl]

yup

they want us to prove the alternating series of ln2 and see if its all positive is will be a harmonic series wich it deverge

[hushed sphinx]

You can define a different series that may or may not diverge.

How your new series relates to the original seems (for the time being) only to be limited by your imagination ...

[supple owl]

its just a homework and i am just tired$

i can do better if i was in morning

[hushed sphinx]

Or in other words, "show that it doesn't converge absolutely".

[supple owl]

yeaaaa

that what they said to us

[hushed sphinx]

That's not quite something that ought to be described by "making a series converge", though.
So I'm still unsure what the actual roadblock you're hitting is.

[supple owl]

just making a series that converge diverge by changing its terms

or vise versa

[hushed sphinx]

Sorry, that still makes very little sense to me. If every kind of "changing its terms" is allowed, then changing every term to 7 will produce a series that diverges.

Can you show the exact text of the problem you're trying to solve?

[supple owl]

i dont have the book they gave them a homework and they told me that

i think i am wrong or i just forget other stuff

[tardy ridge]

The solution to this problem is sketchy. Don't I have to apply absolute value every single time I use logarithm laws in order to not lose solutions?

for example here

they used log(x^2) = 2log(x)

how do I apply log laws without losing solutions constantly

[uncut mulch]

considering the initial bases of the logs

5x + 9 and x+3 must be greater than 0

(and not equal to 1)

[tardy ridge]

thakns

[hybrid pewter]

wouldnt you still need to do it by cases then since x can still be negative

log(x^2) = 2log(x) when x is positive and 2log(-x) when x is negative

[tardy ridge]

no.

there's no x^2.

[viscid thistle]

can someone help me with this problem please

is this right

[willow bear]

it's good enough

[viscid thistle]

thanks ann

[drowsy elm]

I would make the further statement that, the reason 10^x = 0 cannot be solved, is because 10^x is always strictly positive. (Mainly to show why you know it can't be balanced, as opposed to simply saying it.)

[brazen barn]

Why does deltax turn into 6deltax and (deltax)^2 here? Second step

[drowsy elm]

Because you squared (3 + Δx)

It's just the identity

(a+b)² = a² + 2ab + b²

with a = 3, b = Δx

[young hollow]

Can someone help me verify the equation? I know that sin^2x = 1 - cos^2x, that secx = 1/cosx, and that is need to use (a+b)(a-b) = a^2 - b^2, but aside from that, I don't really know where to start and then eventually end.

Now that I think about it, I probably should have asked in trigonometry, but I'm taking this in pre calc so I just figured why not post it here...

Secondly, I don't know if I should start on the Left hand side or right hand side.

[tight compass]

@young hollow Simply the right side to 1 -1/sec(x).

Which is equal to 1-cos(x).

Now, for the lhs, what do you think we should try?

[young hollow]

For the LHS so far I have (1-cos(x))(1+cos(x)) / 1 + cos(x)

I'm guess cross out like terms? But then I end up getting rid of the denominator

[tight compass]

That is right.

You end up with 1-cos(x).

Which is what you want.

[young hollow]

right

OH

Thank you so much lol

I understand now

I forgot I could simplify both sides

thought I could only do one for some odd reaspn

reason*

[tame axle]

Hi! I need help with this problem..

[tight compass]

Observe we have -3 + s6 = 15 implies s = 6.

So how can we use that result to find c?

[tame axle]

ohhhhh

OH

so then 10 + s2 = c

and 9 + s0 = 9

we can solve for s first

then once you have s just solve for c with that equation/

?

[tight compass]

Yes.

[mental steeple]

I’m confused with b

[tame axle]

Thank you so much!

[viscid thistle]

What's confusing

what have you tried

[mental steeple]

I figured it out

[minor forge]

Inverses am I right

Can someone explain what they are please

[tranquil haven]

I don't understand the step where he gets rid of log

[willow bear]

the one where he ends up at $\lim_{n \to +\infty} \exp\paren{\frac{\frac{3}{3n+1} - \frac{3}{3n-1}}{-\frac{1}{n^2}}}$?

[obsidian monolith]

Ann

[tranquil haven]

Yes

[willow bear]

sounds to me like he applied l'hôpital's rule

a little bit dodgy