precalculus

[golden cairn]

It does

Like you multiply the denominator and numerator by square root 2

Right?

Wait are both sides equal to 0 in the end?

[willow bear]

no, they are not

[golden cairn]

Ok

Can you take stuff up from the numerator like 1 by 1

[willow bear]

??

[golden cairn]

Like I take the fraction up and get the reciprocal

Oops

I meant to say

Denominator

Not numerator

[willow bear]

i don't know what "take the fraction up" means

[golden cairn]

Take the fraction that is in the denominator up to the numerator by taking the reciprocal

Sorry I’m not good at explaining what I am trying to say

I don’t even know

[willow bear]

if you can't explain it then it is likely to be bullshit

[golden cairn]

No it’s not

The teacher keeps doing that though

If something is in the denominator. You have to get the reciprocal of it to bring it to the numerator

[willow bear]

"bringing" is vague and easy to misapply

[golden cairn]

Transport it

Idk

[willow bear]

"transport" is exactly zero improvement.

the first step i would take to simplify $\frac{\frac{1}{\sqrt{2}}}{1 - \frac{1}{\sqrt{2}}}$ is to multiply the num and denom of this fraction by $\sqrt{2}$, like so: $$\frac{\frac{1}{\sqrt{2}} \cdot \sqrt{2}}{\paren{1 - \frac{1}{\sqrt{2}}} \cdot \sqrt{2}}$$

[obsidian monolith]

|Ann⟩

[willow bear]

this turns the fraction into $\frac{1}{\sqrt{2} - 1}$, prior to any further manipulations.

[obsidian monolith]

|Ann⟩

[golden cairn]

Ok

I think I get it now

So that’s the final answer?

[willow bear]

no, we are nowhere close to anything final

i would take one further step to simplify this fraction

[golden cairn]

Rationalize it?

[willow bear]

yes

[tranquil inlet]

is there a specific reason why certain rational functions have stuff in the middle vs just looking like a hyperbola

[proven void]

how to do this: $\lim_{n \to \infty} (3 + \sin n)(0.8)^n$ ?

[obsidian monolith]

milanesa de pollo

[proven void]

its 0

how to do this

[winter comet]

how do you figure?

[proven void]

0.8^n is zero

sin oscilates between -1 and 1

[winter comet]

oh right

sin is restricted so it cant be 0 or infinity

so it aint indeterminate anymore ig

wouldn't that make it undefined though?

i mean

[proven void]

0.8^n is similar as 1/n

its zero

[winter comet]

hmm

dang

i guess its a special kind of undefined

lol

[winter comet]

yea ik

but 0 * undefined isn't defined, although we do have bounds for the undefined number and it works between the bounds i guess

[proven void]

?

[winter comet]

usually when i see undefined but not indeterminate im like nahh

[proven void]

sin oscilates between -1 and 1

[winter comet]

yeah but its still undefined

but yeah ur right im pretty sure

its just still weird to me

[proven void]

,w lim to infinity (3 + sin n)(8/10)^n

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz24

[winter comet]

huh

i see why its right but still

i guess theres different types of undefined lol

[viscid thistle]

I probably need some sleep but can anyone explain how we can factor (2-x) into -(x-2)? I tried proving it and it doesn't seem to work

[winter comet]

2-x = -(-2+x) = -(x-2)

[viscid thistle]

oh my god thank you man

[winter comet]

😂

[viscid thistle]

I didn't even consider that lmfao

[winter comet]

lol

[livid swift]

how do i solve this

[summer ruin]

lhopital

[livid swift]

OH THAT WAS EASY

[arctic tree]

wtf im so bad a math

[proven void]

how do I do f

,, \lim_{n \to \infty} \left( \frac{3n^2 + 2n + 1}{3n^2 -5} \right)^{\frac{n^2 + 2}{2n+1}}

[obsidian monolith]

milanesa de pollo

[proven void]

ah its 1

[agile sparrow]

17

[agile sparrow]

not gonna work bud

[livid swift]

wait it worked for me tho and i got 17

what did you try

[agile sparrow]

u got it by lhospital?

nice ig

[viscid thistle]

All the limits questions should be in #calculus I think

[winter comet]

technically its sumtimes taught in precalc but yeh

most of the limits use calc lol

[hearty bison]

we're about to do limits and i'm excited for them

[tender mist]

Limits were developed for the sake of calculus, but it's difficult to say if that makes them calc or pre-calc

I guess either way it doesn't matter, one way or another you're getting the knowledge anyway

[silver kraken]

do yall know what this is called a < x < b

[winter comet]

that's called an inequality

[silver kraken]

ty

[dense citrus]

Does anyone know how to solve this question

[agile sparrow]

Solve it

[dense citrus]

yeah I already figured it out

the rules dont matter for this one so we can rearrange them based on the vector pattern

[elfin patrol]

Dear god someone help me please

I'm gonna fail my test tomorrow

I've been stuck on one question for decades

Can anyone help?

I cannot for the life of me figure out how to get x = 18

I will literally love whoever helps me for the rest of my life

[winter comet]

there is no 18

[elfin patrol]

Oh wait

Wrong picture one sec lmao

[winter comet]

lol

[elfin patrol]

My bad

18 c)

So basically I got as far as squaring both sides of the = sign

And then I got stuck

Idk if I'm supposed to foil it or what

I can show my work I have so far too

[winter comet]

yeah thats a good idea

[winter comet]

you CAN do that but wouldn't it be better to subtract 5 from both sides first?

[elfin patrol]

Wait hold on

I'm gonna try that

I am actually gonna cry

I have been fighting with this question for almost an HOUR

And it was that easy

[winter comet]

🤣

[elfin patrol]

I'm actually so stupid sometimes

[winter comet]

nah lol we all have those moments

[elfin patrol]

I swear I'm not always this dumb

I had a 98% on my last test

My math teacher would be so disappointed in me rn

[winter comet]

😂

it's probably because the problems before and it seems like possibly after are all squaring first lol

[elfin patrol]

I swear my brain doesn't function right some days

I'm gonna shower before I try the last question on my review

Looking at this next question I may be back because I don't think I've ever tried this kind of question before

[elfin patrol]

Okay I'm back

Yeah 19 a) is confusing as hell

Would I just square both sides first?

[river drift]

yes, you should square both sides

[elfin patrol]

When I square them it would just be the same numbers without the root sign right

[river drift]

but you have to be careful, because that can introduce solutions that don't exist in the original equation. so you have to go back and check you don't get invalid operations (square root of negative number)

[elfin patrol]

That's just the verifying step I think. I would put my answer for x in the original equation to see if it's extraneous or not

[river drift]

yes. it's just good to be aware that squaring does introduce extraneous solutions

[elfin patrol]

Okay I think I may have this figured out

I don't wanna jinx myself

Okay wait no I jinxed myself

For the next question I have:
y-3 = (y-9)(y+9)

What do I do?

I know it was a perfect square of y^2 - 9

[river drift]

if you multiply out the factors, and rearrange terms, it turns into the problem of finding roots of a quadratic

[elfin patrol]

Okay that's what I thought but I wasn't sure

I messed something up

It's supposed to be 3 not 9 for starters

And I'm supposed to end with y=3 and y=4

Neither of which are happening

[willow bear]

y^2 - 9 isnt equal to (y-9)(y+9) tho

[elfin patrol]

I know

[willow bear]

can you show the original problem

[elfin patrol]

Yeah

[willow bear]

cause i personally am confused reading the backlogs

[elfin patrol]

Me too lmao

19 b)

So I figured out what I did wrong

I'm currently trying to fix it

I finally figured it out

I used my thonk tank and it worked

In case you guys couldn't tell, I am garbage at factoring

[hearty bison]

lol that's so real

[elfin patrol]

Guys I'm already stuck on c

😭

I never know what to do after I square both sides

[hearty bison]

what do you have after squaring

[elfin patrol]

I got 7n + 25 = (n+1)^2

Idk what to do with the n side

Do I foil?

[hearty bison]

yeah

foil is ok and more useful for being fast but i feel like punnett squares are more intuitive for me personally for getting an idea of how everything multiplies out

[elfin patrol]

I've never used punnet squares, we were always taught to foil

K wait I'm lost again

[hearty bison]

i was taught foil originally and then my alg 2 teacher introduced me to punnett squares as an alternative method

lol i cannot spell

[elfin patrol]

Now I have 7n + 25 = n^2 + 2n + 1

[willow bear]

yes so now tidy it up

and solve as any other quadratic

[elfin patrol]

So like 5n + 24 = n^2?

[willow bear]

but be mindful that any solutions you get also have to satisfy 7n+25 ≥ 0 (otherwise the root in the original equation becomes undefined), thus you will need to throw away the ones that d onot

[willow bear]

that form is not very helpful

you'd like everything to be on one side

[elfin patrol]

OH WAIT

I'm actually stupid sometimes

[willow bear]

also honestly the FOIL mnemonic is not that great

put a FOIL-pilled student in a situation where one of the brackets contains (gasp) three terms, and they're lost...

[hearty bison]

lol

[elfin patrol]

Sometimes I need to just not be a dumbass

[hearty bison]

don't beat yourself up everyone has lapses in judgement

and honestly calling math mistakes "lapses in judgement" is still being kinda harsh lol you really don't need to worry abt it 😁

[elfin patrol]

If I just thought a little bit harder sometimes it would be so easy

[willow bear]

it is all a matter of practice

everybody makes mistakes, even the best of the best

[elfin patrol]

I almost failed the radicals unit in Foundations & Pre-Calculus 10

So it makes sense

It's like my teacher wants me to fail

I have no idea where to start in d)

[hearty bison]

i've never done this unit so i'm not sure how much help i'd be but i'll try to solve it and if can do it correctly i will try to guide you through it

i think ann would probably be more qualified though lol

[willow bear]

what problem are we doing again?

[elfin patrol]

19 d)

[hearty bison]

i did not do it correctly lol

[elfin patrol]

I'm supposed to get m = 12 but idk how to get there

And m = 12/25 but that's the extraneous root

[willow bear]

i mean, why not square both sides immediately

[elfin patrol]

That's what I did but that's where I'm stuck

I never know when to foil or not

[willow bear]

sounds like you're overthinking the whole concept of "foiling"

[elfin patrol]

I definitely am

[willow bear]

it's never illegal

[elfin patrol]

Factoring is my greatest enemy

[willow bear]

squaring both sides you'll get $8 - \frac{m}{3} = 3m - 8\sqrt{3m} + 16$

[obsidian monolith]

|Ann⟩

[elfin patrol]

Wait where did the 8√3m come from 😭

[willow bear]

$(\sqrt{3m}-4)^2$?

[obsidian monolith]

|Ann⟩

[willow bear]

i expanded this lol

[elfin patrol]

Okay wait would it not be 8 - m/3 = 3m^2 -8√3 + 16?

[willow bear]

no?

$2 \cdot 4 \cdot \sqrt{3m} = 8\sqrt{3m}$, not $8\sqrt{3}$.

[obsidian monolith]

|Ann⟩

[willow bear]

and $(\sqrt{3m})^2 = 3m$, not $3m^2$.

[obsidian monolith]

|Ann⟩

[elfin patrol]

I forgot the m

I'm gonna have a stroke doing this test

Google has been telling me it's squared

Google is dumb

Anyways

[elfin patrol]

Now that I have this, what do I do?

[willow bear]

multiply both sides by 3 and bring all the terms to one side, in either order.

show me what you get and i will tell you what comes next.

[elfin patrol]

What I got doesn't feel right

24-m = 9m - 24√3m + 48

[willow bear]

why does it not feel right?

btw word of advice

√3m is ambiguous -- it's impossible to tell if that means sqrt(3m) or sqrt(3)*m [and these are not the same thing]

so write sqrt() and always include those parentheses to tell the two apart

but anyway yeah why does it not feel right?

[elfin patrol]

I just copy and pasted the root sign from google

My answers never feel right lmao

Now I have 0 = 10m - 24 sqrt(3m) + 24

Idk what to do

[willow bear]

where did the 24 multiplying the sqrt(3m) disappear to?

[elfin patrol]

Oops

Typo

[willow bear]

yeah, ok

we can also divide by 2 to make

5m - 12sqrt(3m) + 12 = 0

just to make our lives a little easier

now watch carefully

this is in fact a quadratic equation in disguise

$5 (\sqrt{m})^2 - 12\sqrt{3} \cdot \sqrt{m} + 12 = 0$

[obsidian monolith]

|Ann⟩

[elfin patrol]

Good god

Okay

[willow bear]

we can treat sqrt(m) as our unknown, rather than m itself.

[elfin patrol]

I'm so lost

I'm helpless

[willow bear]

ok wait hold on hold on

first do you understand that sqrt(3m) = sqrt(3)*sqrt(m)

[elfin patrol]

Yes

[willow bear]

right

ok

so we can make this equation look more familiar by making a substitution

x := sqrt(m)

then the equation becomes

5x^2 - 12sqrt(3)*x + 12 = 0

does that make more sense to you now?

[elfin patrol]

Kind of

[willow bear]

what part doesn't make sense?

[elfin patrol]

Well I googled it first and it's going completely different

[willow bear]

they are showing you a different solution path

which is also valid but i am doing something else

[elfin patrol]

Where did the 100 come from?

[willow bear]

by the looks of it, they squared both sides, shuffled some shit around until the sqrt(3x) [our sqrt(3m)] term was on its own, then squared both sides again

omitting like

ten or so steps

so i probably couldn't tell you where the number 100 specifically came from without retracing all of their steps

[elfin patrol]

I think I might just leave that question for tomorrow morning

[willow bear]

up to you

[elfin patrol]

So if I had 0 = 10m -24 sqrt(3m) + 24, would isolating the square root help?

[willow bear]

i mean

you could

i think it's a lot more effort than my way, but you could do that

[elfin patrol]

Making it:
24 sqrt(3m) = 10m + 24

If I did it that way then what would I do

[willow bear]

uh no

sign error

[elfin patrol]

Oops

[willow bear]

24 sqrt(3m) = 10m + 24
would have been correct

[elfin patrol]

Okay so once I have this, would I square it again?

Holy shit I got it

It only took a million steps

Basically

I squared it and then combined like terms then brought everything to one side, then I used the quadratic formula and got my answers

I had one question like this before and had to do the same thing

I hated it

I finally finished and I can go to bed

At 1 am

So proud of myself for using my head

My teacher taught us that if we get massive numbers then we should use quadratic formula instead

There is not a chance in hell I'm taking calculus

[queen shoal]

What am I supposed to find

The function that has that derivative???

[willow bear]

,rccw

[willow bear]

holy shit this is nasty

but yes

essentially you would have to integrate that big ugly fraction

[willow skiff]

,w integrate (16x^3 - 42x^2 + 2x)/(-16x^8 + 112x^4 - 204x^6 + 28x^5 - x^4 + 1)^(1/2)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[willow skiff]

Where is this problem from?

!xy

[tender quest]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[vagrant nymph]

What did i do wrong ans is suppose to be sinx+cosx

[willow skiff]

Actually it's neither

Recall that $\sqrt{u^2} = |u|$ and not $u$ (just try any other negative number for u)

[obsidian monolith]

south

[willow skiff]

So the integral will be -cos x - sin x on some intervals

And cos x + sin x on some other intervals

[vagrant nymph]

I am not great at maths I did not understand this

[willow skiff]

Do you know what the absolute value is?

[vagrant nymph]

But there is a thing I forgot to mention

[willow skiff]

Ah right that is super important

x is in (0, pi/4)

[vagrant nymph]

Yea

But like now what did I do wrong

[willow skiff]

Yep so sin x - cos x (what you got before integrating)

That's negative in this domain

Like sin 0 - cos 0 = 0 - 1 = -1 (technically x can't be 0 but you get the idea)

But then the original function sqrt(1 - sin 2x) is positive cause of the square root

So you need to minus the function to make it positive

$-(-x) = x$

[obsidian monolith]

south

[willow skiff]

https://www.desmos.com/calculator/8l8fc86kil

[vagrant nymph]

Oh okay so because sqrt of a number is positive in this case I have to multiply by -1?

Am I correct?

[willow skiff]

And because sin x - cos x is negative in that domain

[vagrant nymph]

Yep got it thanks

[willow skiff]

No worries

[queen shoal]

ok

[willow skiff]

It can't be integrated according to Wolfram Alpha

Are you sure you have the right question?

[queen shoal]

my class mate sent it to me

[willow skiff]

weird

[willow bear]

reconsider the quality of your classmate as a source of problems

[queen shoal]

i should

[proven void]

I only need two points to be able to deduce slope and the general formula for that line no?

Say for example I am given that f is a lineal function

And im being told f(1) = 5 and f(-3) = 2

This is a limear system of equations

[river drift]

yes

you can extend that line of thinking to higher order polynomials, as well

[proven void]

How to find b

Waaat

Ahh i cannot use same slope for both formulas

[river drift]

your slope formula is incorrect

[proven void]

Yeah

One sec

Its the same slope

I believe

[river drift]

that looks correct, you can check your work by making sure the equation holds for the given points

[proven void]

Oki, thanks

[solemn notch]

guys does anyone know about graph transformation

Im confused about something

you know when its vertical, y+1 would make it go up, y-1 would make it go down in a function but for (x-2) it would make it go right not left, and (x+2) it would make it go left not right

right

in a function

( y-1=f(x-2) )

[obsidian monolith]

Dari

[solemn notch]

for this

It goes right by 2 points

but shouldn't it go DOWN by 1 point?

I dont get why in this equations its going up by 1 for y

cause in text book it said it goes up when we do minus for vertical

BROO this makes no sense how does that equation make 3,4 to 5,5

[summer ruin]

what did it say exactly

[solemn notch]

The example I remember was:
F(x)+k = Shift Up
F(x)-k = Shift Down

F(x+k) = Shift Left
F(x-k) = Shift Right

I just watched the The Organic Chemistry Tutor about this and hes showing the same rules so Im so confused

Using this logic I tried to figure a problem out which I got stuck at: I thought it would be B)

[summer ruin]

y = f(x-2) + 1, so of course it is shifted up

[solemn notch]

wouldnt it be B?

yes

thats what Im saying

I think

yes

Im saying its

B

[summer ruin]

you're saying the opposite

[solemn notch]

oh

[summer ruin]

you think it should go down

[solemn notch]

but doesn't y + 1 = f(x-2) mean up

because y+1?

[summer ruin]

y = f(x-2) - 1

[solemn notch]

wait why are the signs switching

[summer ruin]

I moved 1 to the other side

[solemn notch]

we have to isolate?

[summer ruin]

you don't have to, but you're misunderstanding the statement otherwise

[solemn notch]

man I still dont understand 😭

[summer ruin]

the graphs (x, f(x)) and (x, f(x)+k) are different in that the second one is shifted up by k (if k is positive)

but you for some reason decide that you're supposed to write "upwards shift" as y + k = f(x), which was not what was stated

[solemn notch]

so is it A

[summer ruin]

have you checked whether the point (3,4) indeed goes to (5,5) under this function?

[solemn notch]

nO

no

it goes to D

D)

y-1 = f(x-2)
+1 +1

y = f(x-2)+1

so I had to isolate Y to actually understand the

[solemn notch]

proper shift

[solemn notch]

so when I was doing B) I was basically doing
y+1 = f(x-2)
-1 -1

y = f(x-2) -1

ok

[solemn notch]

so my only issue was I wasnt isolating it

[solemn notch]

yes\

[proven void]

how to find image

also my exercises are called problems instead of exercises which is mildly annoying

even though they are exercises

[summer ruin]

find maximum and minimum, analyze derivative sign

[proven void]

i need to differentiate then?

mmm

what does central value say

idk how to say in english

central value theorem?

mmm

,w first derivative f(x) = 2sqrt(9x^2 + 84) - 9/10x^2

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz24

[proven void]

,w simplify 18x/(sqrt(9x^2 + 84)) -(9x)/5

it becomes zero when we plug zero to the first derivative

[summer ruin]

where else is it zero

[proven void]

thats what I wanted to ask you

[summer ruin]

just solve the equation

[proven void]

true

,w solve 18x/(sqrt(9x^2 + 84)) -(9x)/5

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz24

[proven void]

so?

[summer ruin]

find maximums and minimums, then analyze sign of derivative

[proven void]

do I need to plug in first derivative of f this roots?

[summer ruin]

do you know how to find local extrema?

[proven void]

i mean this derivative test is always confusing

I guess not?

[strong epoch]

I need help

I think I got everything else

I’m just not sure what the limit is at - and positive inf

Would it be dne for both

?

[summer ruin]

https://www.youtube.com/watch?v=aFXBZArOX4M

[summer ruin]

it's positive infinity

[strong epoch]

For both ?

For these too

[fierce fossil]

is it one or two and i need surface area

[willow bear]

are you gonna try to ask for answers again now

[fierce fossil]

no i actually need help

[willow bear]

ok alright

so let's start with choosing the right net

do you know in general what a pyramid is? Y/N

@fierce fossil

[fierce fossil]

no

i dont understand nothing

[willow bear]

😵‍💫

well, it would have been nice to see "I don't know what a pyramid is" upfront.

[fierce fossil]

i never said i dont know what a pyramid is i said i dont know what the net is

[willow bear]

...

[fierce fossil]

now i feel like ur bein rude

[willow bear]

i asked you:

do you know in general what a pyramid is? Y/N
you answered:
no

[fierce fossil]

u ask me and i say idk

[willow bear]

i didn't mean for you to immediately come up with the right answer for which diagram is the net

i meant for you to answer my guiding question

the first of a bunch that im planning to ask you, taking you through the reasoning for this problem

so let's try again:

do you know what a pyramid is?

[fierce fossil]

ye

[willow bear]

ok. right.

how many faces should a triangular pyramid have?

[fierce fossil]

3

right

[willow bear]

are you sure?

(i would have asked this regardless of if you got it right or not)

[fierce fossil]

4

[willow bear]

are you sure?

[fierce fossil]

ONG

OMG*

ok let me think ok

include bottom?

5

[willow bear]

again, my asking you "are you sure?" is not an indication of whether you're right now.

the more guesses you throw into the air, the longer we will spend on this one step

[fierce fossil]

okay

[willow bear]

if you want, i can explain to you how to count the faces of a pyramid.

[fierce fossil]

i just need this hw done by 5:30 its 4:30 im in stress that y i came here

we can save for another time

[willow bear]

bruh.

no. im not going to just give you answers.

failure to plan on your part does not make an emergency on our part.

to construct a pyramid, you start with a polygon (called the base) and a point that isn't in its plane (called the apex -- the tip of the pyramid).

each vertex of the base is connected to the apex with an edge. and with these edges, every side of the base gives rise to a triangular face (with the apex being its third vertex)

so you have as many faces as the base has sides, plus 1 for the base itself.

does this make sense to you, or is your stress clouding your thinking too much?

[valid aurora]

it's a singular 3-simplex

[willow bear]

yes congratulations you know how to describe it with $10 words

for us this is supremely unhelpful @valid aurora

[valid aurora]

oh I understand you ened to understand thethraehodn because of cauchy tetrahedon

[willow bear]

you are not helping.

[valid aurora]

so that you derive stress tensor

[willow bear]

cease this at once.

[valid aurora]

ok sorry

[fierce fossil]

huh

[willow bear]

@fierce fossil ignore that guy

he is basically just trying to be disruptive on purpose and nothing else

[willow bear]

do you understand what i wrote here?

[strong epoch]

Anyone know precalc limits

And graphs

Confused on 2 small problems

They’d problem take a second I just don’t get it

Sorry for repost

[fierce fossil]

ima just give up

i dont understand

[willow bear]

up to you...

thought i could at least try

so you have as many faces as the base has sides, plus 1 for the base itself.

thought this might have been clear

but probably not so if your thinking is clouded by stress.

[fierce fossil]

so i add 13x4 + 20

[willow bear]

😵‍💫

why are you jumping ahead

(and where did you even get those numbers from lmao)

[proven void]

what answer did you got for the surface area

[young gazelle]

Any 1 here know how to simplify -4/2√ 13

[winter comet]

is the sqrt(13) on the bottom or top

[white rapids]

,w 4/2√13

Oh crap

[surreal crescent]

I would think that as x goes to negative infinity, y would approach positive, and the other one does not exists because x does not go to positive infinity

[strong epoch]

Hmmmm

Sounds like it would work

Everything else looks right ?

Like limit approaching 0 from left and right

[strong epoch]

Thanks for helping tho

I can kind of visualize it like you said

[surreal crescent]

Well, ig it would actually be indefinite not infinite

Everything else looks correct

It took me too long to relize infinity mean not finite

[white rapids]

Uh would polynomial graphs belong here

[fiery creek]

sure lil bro

[strong epoch]

I have a question

What would the dimensions of the rectangle be

Is it just x by y

Yeah I missed that

I missed 2 on it

[viscid thistle]

Hint: It’s not y

[strong epoch]

OWWWWW

MY KNEE

It just popped

[strong epoch]

Is it related to x

Does it rhyme with x

[winter comet]

doesnt this belong in calc

[winter comet]

ouch

[strong epoch]

I’m in precalc

[winter comet]

how did you get the answer?

[strong epoch]

Which answer x by y?

[winter comet]

the maximum area being 81 when x = 9

did you just know it a square?

bc thats usually max in this case?

[strong epoch]

Nah here

[strong epoch]

Well

I got the max

Because I put it in a table

[winter comet]

oh

-b/2a

?

[strong epoch]

What.

[winter comet]

a...calc?

[strong epoch]

I put x(18-x)

In a table

[winter comet]

like a calculator table?

[strong epoch]

Yea

[winter comet]

how did you know the max tho

[strong epoch]

Well it’s usually low and the table is auto so it puts like 20 values 1-20 x value

And the max is the highest it gets

Out of the values

Because when it hits the max it dips

After

[winter comet]

...huh

ok

[strong epoch]

I’ll send a picture

[winter comet]

this is literally a calc problem just without calculus 💀

[strong epoch]

See where it dips

[winter comet]

ahh

yea ok that makes sense

[strong epoch]

Yea I saw some stuff on yt with more steps but my teacher just said to use the table

More steps to find the max^ x

[winter comet]

yeah cuz you dont actually know for a fact the max is 9 by the table

but yeh

for the class ur in he prob said that cuz hes not throwing any loops or nothin

lol

[strong epoch]

Loops

?

[winter comet]

tricks

the max could be like 9.1 or smthn XD

[strong epoch]

Oh

Oh nah

😂

[winter comet]

and if you wanted the exact you'd do calculus

or -b/2a

i guess

-b/2a is just the vertex of a parabola

like

[strong epoch]

We’re doing more algebraic stuff now

[winter comet]

-b/2a, f(-b/2a)

[strong epoch]

Like review from algebra using it for limits in calculus

Precalc*

[winter comet]

☠️

[strong epoch]

Like this

It’s synthetic division

[winter comet]

yea

[strong epoch]

I hate math

But I tolerate it

Lowkey it’s not even that bad

Just has to snap

[winter comet]

lol

i feel like i have holes in weird places :l

[strong epoch]

We have a new grading system that makes it

Almost impossible

To get an A

[winter comet]

bruh

[winter comet]

how is it?

[strong epoch]

At least for the average Joe like me who misses 1 -2 questions

On a test

And gets a c

[winter comet]

wait what ☠️

[strong epoch]

It’s called standards based it goes 1 2 3 4, 1 is a 60, 2 is a 70, 3 is a 90, 4 is 100

In order to get a 4 you have to get the level 4 question right which is like a challenge question

[winter comet]

oh bruh

[strong epoch]

If you get every question right even the challenge question and make a mistake like miss a negative sign

It goes from a 4 to a 2

So one tiny mistake gets you a 70

But we get to retake which I honestly don’t take full advantage of

Chilling with a B right now

Also retaking it requires remediation

So like all practices done and an extra review

[winter comet]

bruh 💀

[strong epoch]

I miss when it was 9/10 = 90 and not 70

[viscid thistle]

Yes

[strong epoch]

Difference of cubes is so easy

Hopefully I don’t jinx it

Talking big game hopefully don’t get an f

[winter comet]

😭

[strong epoch]

I am doing all my homework

Gotten 2 assignments done today

3rd one

Let’s get it

[strong epoch]

Is it just x

[runic patrol]

Yo

Got a hard/ good one

[fiery creek]

,rotate

[fiery creek]

you can factor out a three

you would get $\sin^2(x) + \cos^2(x) + \tan^2(x) + \cot^2(x) + \sec^2(x) + \csc^2(x) = \frac{29}{3}$

[obsidian monolith]

aguaman

[fiery creek]

but I assume the last term is csc

because it looks kinda weird

but you notice at the beginning with have a sin^2(x) + cos^2(x)

which is 1

so we have

$1 + tan^2(x) + cot^2(x) + sec^2(x) + csc^2(x) = 29/3$

[obsidian monolith]

aguaman

[fiery creek]

but there's another sneaky simplification you can do @runic patrol

do you know?

I wasn’t thinking of that

I was thinking 1 + tan^2

[willow bear]

variables

[proven void]

,w Solve[1 + Tan[x]^2 + Cot[x]^2 + Sec[x]^2 + Csc[x]^2 == 29/3 && 0 <= x <= 2 Pi, x]

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz24

[proven void]

,w Solve[1 + Tan[x]^2 + 1/Tan[x]^2 == 26/6 && 0 <= x <= 2 Pi, x]

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz24

[proven void]

,w Solve[1 + u + 1/u == 26/6, u]

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz24

[proven void]

,w Solve[Tan[x]^2 == 3 && 0 <= x <= 2 Pi, x]

,w Solve[Tan[x]^2 == 1/3 && 0 <= x <= 2 Pi, x]

[willow bear]

#bots ...

[proven void]

sorry I fell into the rabbit hole

really nice trigonometric equation

[proven void]

https://youtu.be/T4vNtcP0D5E?si=-kaWessU-QUA2U60

[willow bear]

this is strictly against the rules!!!

<@&268886789983436800> we got a test payment solicitor

[agile sparrow]

What's that

[white rapids]

Can somebody help me with this, i watched a lot of videos behind this, but i just cant seem to understand

I appreciate it if someone helped me go over this ty 🙏

[river drift]

f consists of a bunch of different linear factors multiplied together. find the sign of each factor on the interval, and multiply them together to get the sign of the whole function

[white rapids]

Uh

[white rapids]

How do i start finding the sign for each factor

Is it like setting up inequalities somewhat

[river drift]

find where each factor is 0, then it has a particular sign on one side of when its 0 and the opposite sign on the other side

so then you just need to plug in a test value and find the sign on whichever side your interval is on

[white rapids]

So what ever x equals, I plug in the set of factors?

[river drift]

the factors can only change sign when they're zero. so as long as know each factor isn't zero somewhere in the interval, then the function must be the same sign on that interval. if that's the case, you can find the sign by plugging in a value of x somewhere in the interval

[white rapids]

Oh alright

[white rapids]

Uh Im a little lost right now

Is it just 1 value within the interval that I have to plug in to prove whether it's negative or positive

Because I tried that

[river drift]

the value isn't 1 on the entire interval

but if it's never 0 or undefined on the interval, then the sign is the same

[white rapids]

Can you provide an example

[hearty bison]

if you think about this problem graphically it is basically just asking whether the y value of the graph is above or below 0 within a given range of values. so to find that you can just plug in a value in that range (normally it's most convenient to just use an integer since it makes the computations easier) and then you just need to see if the end result is positive or negative

there are some shortcuts you can use too where instead of bothering to write the number out you just write a + or - and then depending on how things divide and multiply out you don't actually have to compute anything but addition can sometimes mess that up so i wouldn't worry about that until you get the hang of it more

for example in this graph you can see that on the interval -3 < x < -2 the sign of f would be positive but on the interval 0 < x < 1 it would be negative

and if you plugged a value between those intervals into that equation then the sign of your result would reflect what you see on the graph

[hearty bison]

this specific graph has a bit of an ugly equation lol i just found it by searching "graph" on google

[hearty bison]

for the purposes of this problem though you don't need to make an actual graph

if you just sketch out a number line and plot each of those zeros on it then you know that at each of those the sign will either change as the graph dips below the x axis or it will remain the same as it bounces off of it

so you just need to find what the sign of each of those regions is by plugging in easy values into the equation

[white rapids]

I guess that works

But

I get confused when you have to split a given interval into 2

Because of the zeros

So it's like I dont know what specific value I have to use especially with fractions if im doing it mentally

[hearty bison]

before doing anything else you will want to draw out the number line and plot out the zeros. normally the intervals will just be within two of those zeros but if they aren't then you can find the signs of the regions the interval is a part of and if they match then that is the sign of the interval. if they don't then it will sometimes be positive and sometimes be negative

[hearty bison]

the fractions are annoying but converting them to decimal can help to get a more intuitive feel for where they lie on the number line

[white rapids]

Ye

[hearty bison]

is there anything that still doesn't make sense? i might be forgetting something

[white rapids]

I think that's it

Maybe I just need a little more practice

[hearty bison]

practice definitely helps with these

they can get a bit repetitive but if you practice them a bunch then eventually they become really easy to do

[white rapids]

👍 Sounds good

[proven void]

,, \int e^{x^2} dx

[obsidian monolith]

milanesa de pollo

[proven void]

how to integrate

[willow bear]

are you /srs or /j

[indigo dew]

f(x) = ∣x∣ + ∣x-1∣
this function range will be [1, infinity)

[proven void]

i tried u subbing x^2

can i do by parts?

how to tackle this?

[willow bear]

are you serious or joking

[indigo dew]

is this correct?

[proven void]

why joking

[mossy quiver]

this is not precalc at all lol

[willow bear]

$e^{x^2}$ is one of those functions that \textit{famously} don't have an elementary antiderivative

[obsidian monolith]

|Ann⟩

[willow bear]

yet you are posting it as if it was a homework assignment.

i do not believe that your professor is that much of a sadist.

[proven void]

that’s relative

[proven void]

i just asked how to integrate i didnt said it was my homework

[proven void]

why doe

if its derivative exist can we represent it as an approximation using taylor expansion

I mean you dont have to answer since this is not my homework, but I wanted to know aswell

[viscid thistle]

That’s full blown calculus wym relative

[willow bear]

i mean you can write out the taylor series for e^(x^2) and integrate it termwise if thats what you want

there just wont be any closed form expression for the result

[proven void]

,w taylor expansion e^(x^2)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz.24

[proven night]

Hi

What is the hardest and last topic in precalculus?

[uncut mulch]

difference quotients and limits

[shut dust]

A simple integration question. Can a limit from a number to the same number in negative and still give a value that’s not 0?

I always thought it did and today I found out I’m wrong

[willow bear]

...do you mean to ask: Can it happen that $\int_{-a}^a f(x) \dd{x} \neq 0$?

[obsidian monolith]

|Ann⟩

[shut dust]

Yeah

[willow bear]

yes, it can.

[shut dust]

Let’s say when it’s a cos X graph

Cuz I thought when ur finding areas in different quadrants it cancels out

[willow bear]

$f(x) = \cos(x)$? cool. $\int_{-\pi/2}^{\pi/2} \cos(x) \dd{x} = 2$.

[obsidian monolith]

|Ann⟩

[shut dust]

Guess I’m being dumb

😭

[proven void]

,, \lim_{x \to 0} \frac{\cos(6x) - 1}{\ln(6x+1)}

[obsidian monolith]

milanesa de pollo

[valid aurora]

ez

[winter comet]

wait is the answer just 0

[proven void]

,w lim x to 0 (cos(6x) - 1)/(ln(6x+1))

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz.24

[winter comet]

les goooooo

i did uh

ln(e^numerator)

then used l'hop ;-;

i might have overclmplicated that wait a min ute 💀

[uncut mulch]

if you're going to LH why not LH directly

[winter comet]

yea...

💀

i was tryna do something fancy and it didnt work so then i went back but

yeah that was overcomplicating it

could just take l'hop from beginning 💀

idk how to do it without tho

[willow bear]

first off you can get rid of the sixes by substituting t := 6x

so you get (cos(t) - 1)/log(t+1)

then perhaps you might remember the special limits of (cos(t)-1)/t and log(t+1)/t

[proven void]

special limits?

[willow bear]

yeah a bunch of simple limits that you prove once and reuse forever

[proven void]

I knew only the first one.

[willow bear]

horrible typesetting and a notational blunder committed 3 times

and also incomplete

i mean ok like

i guess log(1+x)/x at 0 could be seen as a modification of #3 there

but still

also the first = sign in each of those lines should be erased

[proven void]

I just noticed they wrote lim =

That’s hilarious

[desert void]

clopencry

the fucking cursive lim is making my eyes bleed

and why are the numbers RED

[proven void]

how to find absolute extrema of a function on a closed interval

[willow bear]

assuming your function is differentiable and the interval is called [a, b]:

1. find all points where f'(x) = 0
2. filter the points in step 1 to only those that fall in [a, b]
3. evaluate f at all points from step 2, and also evaluate f(a) and f(b)
4. take the lowest and/or the highest value from the list in step 3 according to need

[coarse surge]

You also can narrow it down more by putting the values of 2 lets say one of them is called x and finding what f''(x) is. If its positive its a minimum, if its negative its a maximum. Then just do step 3 with those.

[proven void]

Thanks

Both

[winter comet]

because your eyes are bleeding

[proven void]

Let ( f ) : ( \left(-\frac{1}{2}, +\infty\right) \to \mathbb{R} ):
[
f(x) =
\begin{cases}
\frac{\ln(2x+1) + \cos(x^2) - 2x -1}{x} & \text{if } x \neq 0, \
0 & \text{if } x = 0.
\end{cases}
]
Find, if it exists, ( f'(0) ).

[obsidian monolith]

milanesa de pollo

[summer ruin]

use definition of derivative at 0

[proven void]

dont I need to check continuity first?

before applying the definition of derivative as a limit at x = 0?

I mean, dont I need to check lim x to 0 for both sides to check continuity (they both should be equal)

[summer ruin]

if it's differentiable then it's continuous at that point

[proven void]

alright

I dont get it what do I need to do?

[summer ruin]

differentiability at $x_0$ says that $f(x_0+h) - f(x_0) = f'(x_0)h + \alpha (h)h$, so if $f'(x_0)$ exists then taking limit as $h \to 0$ you get $\lim{h \to 0} (f(x_0+h) -f(x_0) = f'(x_0) \cdot 0 + 0 = 0$

[obsidian monolith]

Transparent Elemental

[summer ruin]

use definition of derivative at 0

[summer ruin]

yes, a = 0

[proven void]

one second

f(x) is known

f(0) is known?

[summer ruin]

yes

[proven void]

oh we need to evaluate both sides

one sec

ln(1) = 0
cos(0) = 0

[summer ruin]

you already given value of f at 0

[proven void]

ah true

sorry

that is zero

f(0) = 0

,, \lim_{x \to 0} \frac{f(x) - f(0)}{x - 0} = \lim_{x \to 0} \frac{f(x)}{x}

[obsidian monolith]

milanesa de pollo

[proven void]

,, \lim_{x \to 0} \frac{ln(2x+1) + cos(x^2) -2x -1)}{x^2}

[obsidian monolith]

milanesa de pollo

[proven void]

how do I save this limit?

lhopital?

twice?

[summer ruin]

once will be enough

[proven void]

no

wdym once

look denominator

[summer ruin]

applying lhopital once will be enough

[proven void]

okay

,w differentiate ln(2x+1) + cos(x^2) -2x -1

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz.24

[proven void]

ah thats why you meant that

,, \frac{-2x\sin(x^2) - \frac{4x}{2x+1}}{2x} = \frac{-2x(\sin(x^2) + \frac{2}{2x+1})}{2x} = -\sin(x^2) - \frac{2}{2x+1})

,w -sin(0) + 2

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz.24

[summer ruin]

you got the sign wrong when factoring x

[obsidian monolith]

milanesa de pollo

[proven void]

$f'(0) = -2$

[obsidian monolith]

milanesa de pollo

[proven void]

wait was that it?

or did I missed something in the middle

[summer ruin]

that's it

[proven void]

thanks

How do I find domain and image of $f(x) = \frac{e^{x/3}}{x-1}$

[obsidian monolith]

milanesa de pollo

[cedar juniper]

ok so idk what image is but for domain i would just say x belongs to all real numbers, x cannot equal to one? bc the denominator cant be 0

[hexed minnow]

Hii can someone help me with this

[winter comet]

what is gf(x)

g(f(x))?

[hexed minnow]

Yes

[winter comet]

hmm

i think i know how to get the answer

but

idk the actual conventional way

[winter comet]

what progress have u made?

[hexed minnow]

I actually got the answer but I’m not sure about it because I can’t find the marking scheme for it

I got 8

[winter comet]

you might be right but i got 5 💀

what did you do to get 8

[white rapids]

Can someone tell me what I did wrong, im currently self teaching this so im a little confused

With the log_9(8) I just expanded it do log_9(2^3) then moved it to 3log_9(2)

[uncut mulch]

z not 2

and missing () in several places
that's all I could catch due to image quality

[white rapids]

Oh crap lol

[white rapids]

Alr ty my bad

I did not see that wow

[uncut mulch]

power of 6 applies to the whole (zx), not just the x

[white rapids]

Ye

[silent oasis]

Why is it not like -4≤x≤-2 for the decreasing part?

[arctic sundial]

Is the midline 2 or 0

It’s 2 right

Bc (22-18)/2 =2

So the bank isn’t the midline?

So point g is (2,2)

?

[viscid thistle]

just simplify it using the laws of logarithms

or identities whatever it is called

@white rapids

[past dune]

decreasing means the function has downward slope like a slide

[silent oasis]

so why is -2 not included?

[proven void]

yeah domain is R - {1} correct

how to get range of f doe

i tried first derivative test

[proven night]

Hello

I found the solution for this equation and i am wondering whether i should leave the answer like that, or maybe do smth with that

The right pic is the solution

Photomath shows answer in another form, simpler form, but it does much more calculations throughout the solution

[wicked shore]

what is it

[proven night]

One moment

[willow skiff]

Btw using log laws this is ln(7/4) / ln(4^3 * 7)

= ln(7/4) / ln(448)

[wicked shore]

use Change of base formula to that

[willow skiff]

Yes

Ahhhh then yeah

[proven night]

But

[proven night]

Is it necessary?

[willow skiff]

Also ln(7/4) = ln((7/4)^(-1)) = -ln(4/7)

[willow skiff]

No

The other form is totally fine and simplified already

[proven night]

Okay, your answer is compressed, opposed to mine. But is mine still correct?

[willow skiff]

It's more important to be able to see how you might get to that answer, which (ln 7 - ln 4)/(3 ln 4 + ln 7) does

Then it is to have a random number like 448 imo

[willow skiff]

,w 7^(1 - x) = 4^(3x + 1)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[willow skiff]

Jesus

Anyway yes it's correct

Since I can manipulate what you have into the answers Photomath and WA are getting

[proven night]

Okay, thanks you guys a lot

[willow skiff]

No worries

[proven night]

I just started learning calculus, but i noticed i have small troubles with some precalculus topics like exponential equations

Also i'd like to ask what "solve algebraically" mean? I often hear smth kind of "algebraic way of solving"

[hushed sphinx]

Usually it just means to solve whatever-it-is by doing algebraic manipulations. Do you have more context? That could help us explain what (if anything) the author meant it in contrast to.

[proven void]

Do you have an example?

Maybe you mean like solve this limit using limit algebra instead of differentiating numerator and denominator (if in indeterminate form)

[proven night]

Okay, thanks

No i dont have an example but i understood you

Also, i would like to ask

What logarithm base should i use when i want to take logarithm of both sides?

For example, here i took logarithm with base 3

[uncut mulch]

depends

[uncut mulch]

usually one of the bases of the exponents

[proven night]

Okay

But i often see log10 or ln when there is no 10 or e in the equation

[uncut mulch]

doesn't really matter when there are multiple exponents as long as the base is valid

[proven night]

Okay

Can i take ln of negative number?

Probably no

[uncut mulch]

no

[proven night]

Okay

Can you explain why BASE cannot be negative?

[hushed sphinx]

You can't raise a negative number to a non-integer power in general.

[shadow summit]

Try rewriting 9^x as 3^2x

[uncut mulch]

lowercase g not capital G

[proven void]

is this an exam?

[uncut mulch]

look at the praph where x=5

[willow bear]

do you know how to read function graphs in general?

reading graphs is more of an algebra 2 thing than precalc tho.

[proven void]

try plugging x = 5 to the graph

[willow bear]

https://youtu.be/kvU9sOzT2mk?feature=shared

try this

https://youtu.be/1BfRY7jcjxc?feature=shared

this might also be good

[proven night]

What do i have to do here

Do i have to equate f(x) to x?

[proven void]

find x and y intercepts basically mean find when x = 0 when y = 0, imo

[proven night]

Got it

Okay

[winter comet]

Help with what

do you know how to plug in x = 3?

You have f(x) = -72/x + 1

When you have f(3) you gotta replace x with 3

So in -72/x +1, where is x?