precalculus

[fresh hearth]

Okay I'm looking at symbolab rn right

[proud raven]

its probably a nice number

[fresh hearth]

The step where it says

[proud raven]

,w 7^3

[obsidian monolith]

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[proud raven]

,w 7^4

[obsidian monolith]

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[fresh hearth]

vbut

but how do yuou know to test 4

or use 4

[proud raven]

like without a calc?

[fresh hearth]

oka y wait

lets start over

[proud raven]

sure\

[fresh hearth]

so the question is the question right

We are evaluating the logarithm exactly

So our first step here when given log base and the 2401 (what is this called?)

Is to pretend there is no log and pretend that there is an X

and we are solving for that X which is the exponent

because base of 1/7 is 2401 = x

[proud raven]

argument maybe?

[fresh hearth]

so x would be the exponent because of notation stuff

So it'd be

[proud raven]

well were not pretending

[fresh hearth]

(1/7)^x = 2401

[proud raven]

its more a translation than anything

in the language sense

this is exactly what the log is saying

[fresh hearth]

ahhhhh translation is a better way to think of it

[proud raven]

but yea for notation reasons i guess

log is just saying ilke

[fresh hearth]

I will remember that

[proud raven]

i mean im sure you know

[fresh hearth]

I don't kno w

[proud raven]

"1/7th to what power is 2401?"

[fresh hearth]

my teacher is horrible at explaining things

[proud raven]

so we rewrite

[fresh hearth]

Yeah

[proud raven]

(1/7)^(what power?) = 2401

[fresh hearth]

The book puts it in

7^-x = 2401

[proud raven]

yup

[fresh hearth]

and so we can think of it as 7^x = 2401

[proud raven]

so you can do this in more steps, if youd like

well

7^(-x)=2401

[fresh hearth]

I just am having trouble understanding/following

[proud raven]

err

sorry thats wrong

[fresh hearth]

wat

[proud raven]

lets slow down

[fresh hearth]

Yes

[proud raven]

$( \frac{1}{7} ) ^x = 2401$

[obsidian monolith]

jan Niku

[proud raven]

parens are bad

so we can also write

$\left( \frac{1}{7} \right)^x = \frac{1^x}{7^x} = \frac{1}{7^x}$

[fresh hearth]

waitiwaitiiwa

[obsidian monolith]

jan Niku

[fresh hearth]

so the x applies to both because of exponent rules

[proud raven]

yup

[fresh hearth]

why does it go away in the numerator

[proud raven]

1 multiplied by itself any number of times is just one

and exponentiation is just repeated multiplication

[fresh hearth]

Ooooh

right

Got it got it

[proud raven]

okay, lets do some more manipulation, if that all makes sense

[fresh hearth]

Yes!

[proud raven]

make sense that $\frac{1}{7} = 7^{-1}$?

[obsidian monolith]

jan Niku

[fresh hearth]

Yeah!

[proud raven]

then we can combine

[fresh hearth]

I know why it's 7^-x

[proud raven]

tight

okay

does it make sense why x comes out negative here

i mean not the sign attached to it

but like if we write 7^(-x) = (some number bigger than 7)

why x needs to be negative

alright

[fresh hearth]

Yeah

Because it is a fraction

[proud raven]

well its more like

think a negative exponent is repeated division

[fresh hearth]

So for example if we had like (1/3)^x

we would just have 3^-x

[proud raven]

but like

if you put in any positive number here for x

[fresh hearth]

it's like ^-1 in a sense but X

[proud raven]

3 is just gonna get smaller, right

[fresh hearth]

wat

[proud raven]

,w graph 3^(-x)

[obsidian monolith]

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[proud raven]

its not super important, i just wanted to point it out

[fresh hearth]

repeated division so likea number constantly

so like not the square root

So how exponents are like 4^ 5 = 4x4x4x4x4

but 4^-5 = 4/4/4/4/4

?

[proud raven]

yea

[fresh hearth]

Ooooh I get it

[proud raven]

so if you have 4^(-x) = (some number bigger than 4)

the x has to be negative itself

so the negatives cancel

[fresh hearth]

Yeash

[proud raven]

and 4 can end up being bigger than 4

[fresh hearth]

Yeah!

No!

[proud raven]

its a pedantic point

[fresh hearth]

I'm lost

[proud raven]

you have it 😄

its not important

[fresh hearth]

o

[proud raven]

we can keep going i just suck at explaining

[fresh hearth]

Okay

[proud raven]

you already see it

so the question here mostly boils down to like

7 raised to what power is 2401

its asked in a weird way relating to what i was just saying

[fresh hearth]

Yeah

[proud raven]

you need to be able to factor 2401

which is hard if you dont have a calculator

[fresh hearth]

yeah

so do we do

2401 / 7

until it becomes the lowest whole number that's not a decimal?

so like

[proud raven]

since its so big, id just guess its a nice number

[fresh hearth]

2401 / 7 / 7 / 7 /7

[proud raven]

and try 2401/(7^2) first

if you have a calculator

[fresh hearth]

So

[[[[[[[[[[[[[[[[[[

oops

[proud raven]

i mean for a like

this may not make perfect sense but

imagine 10^x

[fresh hearth]

(7^-x) = 2401 would be like

[proud raven]

every time you put in another higher number for x

you get another digit

so 10, 100, 1000, 10000

so for numbers that are closeish to 10

you can sort of expect this rule to kind of follow for approximation purposes

like 7^1 is one digit

7^2 = 49 is two

7^3 is 343 is 3 digits

make sense?

like if you didnt have a calculator i mean

theyd have to pick nice numbers

[fresh hearth]

I don't get it

[proud raven]

is that too much

lets finish the problem first

[proud raven]

what were you about to ask

[fresh hearth]

How would we algebraically solve that

and then at what point after simplifying it the most with algebra do we use the calculator

[proud raven]

a logarithm

[fresh hearth]

WAT

[proud raven]

unless you know its a nice number

well i mean

if you have a calculator right

the original problem is trivial

you just type it into the calculator

[fresh hearth]

So like

thius is what I mean right

lets say we were given 7x= 2401

We would just divide 7 by both sides

right

but since it's 7^-x = 2401

Wat do we do

like what is happening here

In order to find x

[proud raven]

this is kind of what i was getting at with the negative thing

more broadly like

so through this repeated multiplication that the exponent is giving us

whatever x is

we want 7 to grow, right?

it has to grow, to 2401

[fresh hearth]

yeah

[proud raven]

but if we put a positive x in

were gonna have $7^{-a} = 2401$, where a is positive

[obsidian monolith]

jan Niku

[proud raven]

but then we have $\frac{1}{7} \cdot \frac{1}{7} \cdot \dots$

[obsidian monolith]

jan Niku

[proud raven]

obviously 1/7 times 1/7 times .... is gonna shrink

so we can figure x is gonna be negative

[fresh hearth]

hmm

yeah

[proud raven]

you can do this using as much or as little algebra as you want

sometimes people do a change of variables, youd make a note like

$-x=t$

[obsidian monolith]

jan Niku

[proud raven]

then write $7^t=2401$ instead

[obsidian monolith]

jan Niku

[proud raven]

just making sure to switch back to x at the end

[fresh hearth]

ookay wait

so

[proud raven]

or if you hate that algebra, just remember

[fresh hearth]

I think this will be easier to understnad

How would we put in

7^-x = 2401 into our calculator

How do we make our calculator fin dthat

[proud raven]

if you have a calculator, it boils down to if you can do arbitrary bases

can you put $\log _{\sfrac{1}{7}} (2401)$ into your calc?

[obsidian monolith]

jan Niku

[fresh hearth]

I'm unsure of how to enter subscripts on my TI-84 CE

[proud raven]

because logs are just the way to solve exponent problems like this

hmm

lemme see i might have one here somewhere

[fresh hearth]

I see

[proud raven]

well i have a 84SE

if i hit the MATH button

[fresh hearth]

same thing basically

yeah

[proud raven]

then down to the bottom

theres a command called logBASE(

[fresh hearth]

logBASE?

Oooohj

[proud raven]

yup

[fresh hearth]

OH M G

[proud raven]

make sure you have mathprint enabled

[fresh hearth]

mathprint?

[proud raven]

yea

[fresh hearth]

what would it look like without math print

[proud raven]

bad

[fresh hearth]

I put the question in and I got -4

How would we show our work?

Would we just show us manipulating the equation and then like give the answer

[proud raven]

thats the question, right

to your teacher id say

you can certainly get to this answer by hand

using some approximation

if you assume the answer is nice

its pretty fast

or you can show that you know how to use a calculator

or somewhere between

all of that work we did doesnt really mean anything

if you just put the original question into a calculator

[fresh hearth]

Ohh

but if he did tell us ot show our work

All we would do is like

show him that we're doing

7^-x = 2401

and then write the answer

[proud raven]

i would get to there

[fresh hearth]

x = -4

right?

[proud raven]

reason that x is negative

then take a guess

[fresh hearth]

Okay!

[proud raven]

the guess would be since the answer has 4 digits

4 is a good guess

then you maybe check by approximation

[fresh hearth]

wat

where did u approximation from?

[proud raven]

like i was saying about the 10's

10^2 is 100

10 ^3 is 1000

[fresh hearth]

ahh

OHHHHHHHHHHHHHHHHHHHH

[proud raven]

for each power you raise it by further

you pick up a digit

[fresh hearth]

BECAUSE

[proud raven]

so if you have a number close to 10

and it kinda follows

[fresh hearth]

BECAUSE THERE ARE 4 DIGITS IN 2401, UR GUESSING 4?

BUT NEGATIVE SINCE ITS A FRACTION?

[proud raven]

7^2 has 2

yea

7^3 = 343

[fresh hearth]

OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

[proud raven]

you can then check it

[fresh hearth]

I GET IT

[proud raven]

since 7^4 = 7^2 * 7^2

49*49

[fresh hearth]

YEAH

[proud raven]

you may check this really roughly like

50*50

which is very fast to do by hand

if its around 2401, id call it done

if i didnt have a calculator

[fresh hearth]

Okay!

[proud raven]

and 50*50=2500

[fresh hearth]

I understand more now!

[proud raven]

very close to 2401

[fresh hearth]

ya

[proud raven]

so probably x=-4

[fresh hearth]

Alright

So

okay

Another quesiton

How come Log of 0 is undefined

what does it mean for a log to be 0

Log always has a base of 10

[proud raven]

not always

[fresh hearth]

so 10^x = 0

?

Another questions asks us Log 0

[proud raven]

yea

basically

[fresh hearth]

the answer is undefined

How did we get there

[proud raven]

if you want a really loose interpretation of it

the question is asking "where does the graph of 10^x cross the x axis?"

or alternatively like

say you have 1/10

thats 10^-1

how many times do i have to multiply 1/10 by 1/10 to get to 0

well twice gives 1/100

three times 1/1000

any number of times, it gives me a really, really small number, yea?

but its always 1 over some really really big number

so its a really really really small number

but never 0

thats a really loose way of saying it

you can see it if you look at the graph too

,w graph 10^x from x=-100 to x=-1000

[obsidian monolith]

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[fresh hearth]

wat da hek

[proud raven]

2 times 10 to the -269 haha

maybe better numbers

[fresh hearth]

oooh

0 is an asymptote

[proud raven]

yup

[fresh hearth]

?

Okay

So

[proud raven]

which you can kinda see like

dividing a number into smaller and smaller pieces

each piece will never be 0 big

they just get smaller and smaller

but its always something

[fresh hearth]

Log 0 is basically Log 10 = 0 which is basically 10^x = 0

[proud raven]

more or less yea

theres a lot of interpretations

[fresh hearth]

I see

[proud raven]

the key point being repeated division will never, ever get you to 0

the only thing you can divide by a number and get 0

[fresh hearth]

Understood

[proud raven]

is if you started with 0

[fresh hearth]

Yes

so Ln 0

is

Ln e =0

[proud raven]

yup

same problem

[fresh hearth]

so also undefined?

it never touches the 0 x axis?

[proud raven]

have you ever seen the change of base formula?

[fresh hearth]

uhhhh

yeah

[proud raven]

its not important to know the specifics

well it is but not right this second

the main point is that base doesnt really matter

different log bases are just constant multiples of each other

[fresh hearth]

LogBASE (b) M - (lnM/lnb)

[proud raven]

similarly the only way to get 0 from multiplication is if you started with 0 here

(you cant multiply by 0 here, since the constant multiple is also a log, which cant be 0, like we just saw)

so you have two logs multiplied by each other relating any two different log bases

and neither one can be 0

aka you never get a 0 out

that one is a bit more involved

but its basically just the original question you asked, applied twice

$\log _a (b) = \frac{1}{\log _c (a)} \cdot \log _c (b)$

[obsidian monolith]

jan Niku

[proud raven]

so for any question you ask about another base, just change it to 10 if you want to

[fresh hearth]

where did c come from

[proud raven]

c is just some other base

[fresh hearth]

hmm

[proud raven]

youd usually see this for like

i mean if you didnt have a fancy calculator

$\log _{1/7} (2401) = \frac{ \ln (2401) }{ \ln (1/7) }$

[obsidian monolith]

jan Niku

[fresh hearth]

I am so lost

[proud raven]

the specifics are not important 😄

you should just know that no log is gonna be equal to 0

[fresh hearth]

ever?

as well as ln?

[proud raven]

yea

[fresh hearth]

Is that just a rule

[proud raven]

i mean it comes from this

you believe it for 10 right?

log base 10

[fresh hearth]

believe what is for 10

Oh yeah

[proud raven]

that we can never get 0

[fresh hearth]

10^x = 0 impossible to reach

[proud raven]

well using that formula i posted

we can change any other base

back into base 10

[fresh hearth]

because u the more u divide by x the number just gets smaller and smaller and never touches the 0

[proud raven]

and its a ratio of logs, neither of which can be 0

is some number thats not 0, divided by another number thats not 0, ever 0?

since any log, of any base, can be written as a fraction with the top and the bottom both being logs of base 10

you should believe neither the top nor the bottom will be 0

like you just said

$\ln (x) = \frac{ \log _{10} (x) }{ \log _{10} (e) }$

[obsidian monolith]

jan Niku

[proud raven]

log _10 x can never be 0

that certainly includes log _10 e

its a logical jump, im more just showing it since you seem curious

i wouldnt worry about it excessively if its not jumping out at you

im also explaining it poorly

[fresh hearth]

Okay

I hope it just clicks

I have a quiz on friday on logarithms

I think it'll just be the notation and changing it and evaluating the expression and equations

[proud raven]

yea, they tend to not murder ppl with these i think

if you understand log 0 undefined for any base

[fresh hearth]

I hope not I iwll cry

will

[proud raven]

how to get from that form to the other

which you seemed just fine with

youll be fine

[fresh hearth]

Okay

Are you in school too?

[proud raven]

yup

uni

[fresh hearth]

me too

[proud raven]

nice

[fresh hearth]

I'm in my first year taking precalc

wat year are u

[proud raven]

senior more or less

[fresh hearth]

Oooh

[proud raven]

fun math classes

[fresh hearth]

can I dm u?

[proud raven]

for math questions 😄

im not always around

[thin dune]

does anyone know?

[restive hound]

@thin dune the directrix would be x

Have you graphed?

Your given is (y-5)^2 = 12(x-2). So the form here is (y-k)^2 = 4p(x-h), so we expect a parabola that opens to the right. The vertex here is (2,5). The directrix is a line and it isn’t inside the parabola, it’s outside of it. Our p is 3 because 4p/4 = 12/4 ➡️ p=3. So that’s our focus, so we move p units to the right of the vertex. In return, to find the directrix, we move p units to the left of the vertex. Therefore, our directrix is x=-1

The purple point is your directrix @thin dune

[swift flume]

why is limit of sin(h)/h as h approaches 0 also one?

[willow bear]

have you seen those memes that go "sin(x)=x"?

[merry sphinx]

You can prove this through a tool called the "squeeze theorem"

[burnt bone]

Hello

I just have a basic question, Ln(ln(x)) = 1

Solving for x will give me e^e?

[jagged glade]

Yea

[burnt bone]

Alright ty

[fresh hearth]

hiiiiiiiiiiiiii

Is anyone available later today to help me with math for a couple of hours

[willow bear]

how much later? @fresh hearth

[fresh hearth]

Like arouuuund

7-8 PM EST

[willow bear]

oh. nevermind then that's night time for me

[fresh hearth]

@willow bear Okay, see u then!

[echo wagon]

[willow bear]

[silk mulch]

What would be the best way/mindset to approach the chapter "functions"?

[tidal ferry]

how would I solve this inequality?

this is the answer, I just want to know how to solve it

[viscid thistle]

Im assuming x can be any real number?

[tidal ferry]

doesn't say so yes

[viscid thistle]

consider cases where x>=0 and x<0

[tidal ferry]

right wait I think I've seen this

hm

i don't remember how to write it correctly

the cases I mean

[viscid thistle]

first we know from the fraction that x!=1 and we can manipulate the inequality to get $\frac{1}{x-1}\leq{x-1}$

[obsidian monolith]

jswatj

[tidal ferry]

o

[viscid thistle]

Yeah consider cases where x<1 and x>=1*

if x<1 then x-1<0

[tidal ferry]

wait what's 1*

[viscid thistle]

correction

[tidal ferry]

idk what x* is but I think I know what u mean but I forgot the word for it

it's where x=0 right

[viscid thistle]

• just means correction

[tidal ferry]

what's that?

[viscid thistle]

nothing mathematical

when you make a mistake

[tidal ferry]

AHA

lol oops yeah

okokok wait

ik that's the wrong way to write it but yeye

what do I do now?

[viscid thistle]

so we look at x>1 and x<1 since x!=1 yes

manipulate the inequality

[viscid thistle]

.

[tidal ferry]

x! means where x=0 then?

[viscid thistle]

No

$x\neq{1}$

[obsidian monolith]

jswatj

[tidal ferry]

o.o

idk where that's to be used but maybe I'll see

yes ok so 1/(x-1)=x-1

[viscid thistle]

You cant divide by 0

[tidal ferry]

Oh

YES RIGHT

[viscid thistle]

if x=1 then you'll get 1/0

[tidal ferry]

okokokok so that's for which x's it's not allowed?

[viscid thistle]

yes

[tidal ferry]

aight i'm caught up yes

1/(x-1)=x-1, x!=1

what do I do now with the cases? Ik there's like a scheme for it

OHHH

[viscid thistle]

<= you mean

[tidal ferry]

I'll try!

[viscid thistle]

multiplying by x-1 changes the inequality sign

whether it is larger or smaller than 0

[tidal ferry]

wait where did I do that

I just switched sides on +1

so I didn't multiply anything yet

I'll try to draw the scheme

[viscid thistle]

multiply the x-1 on the other side

and change it if its negative

from <= to >=

[tidal ferry]

o.o

oh

hmmm

ok, (x/x-1)*(x-1)>=0

there

[cursive imp]

can someone help me solve q.22?

[fervent barn]

use synthetic long division

[cursive imp]

wouldn’t i need the values of m & n for that?

[uncut hollow]

I'd use factor theorem

(as it tells you what the polynomial evaluates to at x = 1 and x =2)

[autumn holly]

@fervent barn He can't just do synthetic or long division like that. I am sure there is a formula or smth.

[willow bear]

you could do it in terms of m and n

or you could use the remainder theorem and talk about the values of your polynomial at x=1 and x=2

[bold zinc]

Is this equation correct: $g=\dfrac{v}{t}=\dfrac{2s}{t^{2}}=\dfrac{2\left( vt-s\right) }{t^{2}}=\dfrac{v^{2}}{2s}=9.8ms^{-2}$?

[obsidian monolith]

Huzaifa

[uncut hollow]

Well it depends, lol

For an object being accelerated in a gravitational field from 0 velocity, er, yeah i guess?

[jovial token]

How do you simplify the inverse of f(x) = x/(x-2)?

[harsh smelt]

solve y = x/(x-2) for x

[jovial token]

I put it through a calculator but I don't know how to get there by hand

The inverse was (2x)/(x-1)

[serene tiger]

hi

so um

actually idk if this is precalc stuff but i guess i'll just put it here and you can tell me if it isn't

so i found these 2 functions

top one is reciprocal of the gamma function (i think?)

and when you look at the graphs

its kinda cool because they intersect really close to pi, but not exactly at pi

and neither of them have any decimal stuff going on its just square roots, x, and integers

so i found it kinda weird that they intersect in a point so close to pi but not at pi

are there any other functions like this?

[full pagoda]

not gonna lie to you chief i think it's just a coincidence that they intersect at a point close to pi

[serene tiger]

yeah that's probably it

but its still kinda cool i guess

[plucky rampart]

it's just a thing of algebra...

i mean to get the inverse

[south summit]

Why is precalculus important

[uneven cobalt]

im looking for someone to help me with pre calc questions, im willing to pay beacause its important, please dm me if you are interested

[dreamy siren]

Just post problems you need help with

@uneven cobalt so how do you think you should begin this problem? I see it’s #3 so did you do others like it already?

[uneven cobalt]

yeah i only have like 8 left to fo

[dreamy siren]

So how far did you get on this one?

[uneven cobalt]

not far, started getting confused on with root zeros

[undone girder]

Omgggg

I neeeeddd help with mathhh

[high patrol]

Hi guys I need help with an equation

So far I have a and e done

[cursive imp]

can someone solve this question?

[late mica]

Try this as an equation with the domain for t being 0<t<=12

[late mica]

S(t) = 15,000(1.5*t)

[late mica]

Hopefully that's enough to get you started.

[high patrol]

wouldn’t it be y=1.5x + 15,000

[late mica]

For that equation, try it out at year 1 - if you plug in 1 for x, your output is 15,000+1.5, which is just 15001.5. This is not a 50% raise, which is why it hinted to multiply by 1.5.

[mighty forum]

help me with the prolem b)

[tawdry condor]

1+1=3?

[slate shale]

Yes

[small orchid]

15000(1.5)^(n-1) where n is the year

It’s just like a compound interest equation, it’s exponential

I’ll go write it on some paper to help explain

[small orchid]

And actually it should be 15000*1.5^x because it says the first year is “year zero” in the problem

[small orchid]

This is incorrect

[wicked tendon]

Any one know a good resource to learn this? I can't find what its called or find anything related to it and my professor hasn't given any notes or anything on it .

[small orchid]

From my understanding you would say x != M

Because the denominator can’t be equal to zero, so there should be 2 values that x can’t be equal to

[potent nest]

one of those values is 3

[small orchid]

No

The numerator can be 0, the denominator can’t because you can’t divide by 0

[potent nest]

ahhhh

i am big dumb but i have my own brain melting things to deal with

[small orchid]

Well there’s situations where you’ll have a function and x has to be positive or negative

But in this case x just can’t equal 2 values

It’s a strange question in my opinion

[potent nest]

so therefore, wouldn't x not be equal to m?

[small orchid]

Yes

And M is the answer to:

x^2 + 6x + 5 = 0

[potent nest]

therefore

solve for x?

[small orchid]

Yes

[potent nest]

x²+6x=-5

[small orchid]

And those will be the two values that it’s impossible for x to be

[potent nest]

in this case a x=±#

[small orchid]

No

[potent nest]

oh wait i just did the exact thing i shouldn't do

[small orchid]

(x+1)(x+5) = 0

Therefore x cannot equal -1 or -5

[potent nest]

our greater than or equal to value would be...

also, my version of brain melting things:

the stuff i've struggled with for the past 3 years

[wicked tendon]

Do you have any links that helped you get that answer or the knowledge to answer this question?

[small orchid]

The only knowledge you need for that question is that you can NEVER divide by 0

[viscid thistle]

in multiplication of matrix should the row and column of 2 different matrices be equal or vice versa ,so that its defined ?? can anyone help me ??

[willow bear]

the number of columns in the first matrix and the number of rows in the second matrix have to be equal.

i.e. you can only multiply $m \times n$ matrices by $n \times k$ matrices

[obsidian monolith]

Ann

[viscid thistle]

Thanks

[obsidian solar]

How do I do this?

[dusk elm]

How are arcsin and sin related? If you know that the problem should become very easy 🙂

[obsidian solar]

They are the inverse, but I’m still stuck

[dusk elm]

Ok so they are inverses of each other. So if I took sin(x) then took arcsin of that, what would you get?

[night pier]

What do you guys think i should do if i have already finished my precalculus course on khan academy

[obsidian solar]

D: -1 to 1 and R is -Pi/2 to pi/2

For arc sin

Wait is number one saying arcsin = sin (x-2 Pi) ?

[pine marsh]

When your solving inequality’s how do you know when to use infinity and when not to use it

[dusk elm]

Try substituting x-2pi into the first problem. Notice that a function multiplied by it inverse cancel each other out

[dusk elm]

What do you mean by using infinity?

[obsidian solar]

Wait why? LOL

[dusk elm]

why do functions and their inverses cancel out or why substitute?

[sick steppe]

definition of inverses...?

[dusk elm]

^

[south summit]

What does inverse look like, the opposite of it's origin? so a parabola opens up, the inverse of that would be opens down?

Does that sum up inverse well?

I'm not sure what you mean by opening to the side

is this an inverse?

with a 90 degree rotation it seems

[nocturne jacinth]

Ok. Simple explanation is that an inverse graphically is the function being reflected over the line y=x

[south summit]

I can see that's what the graph says on the left hand yes.

[halcyon granite]

im tasked to find the oblique asymptote of f(x)=x+(1/x-1)+(1/x+1). but i can't simply use long division for this, so how can i find it?

[nocturne jacinth]

And the ordered pairs switch

So if (5,8) is on the curve, (8,5) is on the inverse

[south summit]

ahhh

what if one of them are negatives?

[nocturne jacinth]

Not all functions have inverses btw

They must be one to one

[south summit]

It looks like you can do something with the conjugates

you're trying to simplify it right? the LCD should be (x-1)(x+1)

[halcyon granite]

i tried simplifying now lol, i got it, now i can long divide

[south summit]

what did chu do

[pine marsh]

Like -infinity positive infinity

[dusk elm]

Are you just trying to express your answer in interval notation?

[pine marsh]

Yeah I was wondering why some questions use infinity and some don’t

[dusk elm]

Sure so some questions use infinity to express all the possible numbers that can be a solution to an inequality. For example, x>0 would be (0, ♾) in interval notation while 3>x>0 would be (0,3) in interval notation

The first one uses infinity because any positive number can be a solution

[pine marsh]

Could you give an example We’re using I finite would be wrong

*infinity

[sharp hollow]

I'm not sure how to do these

transforming a parent equation, 3x-6

especially c)

I got y=1/2x +1 but i'm not sure if its right

[proud raven]

d-did u get it

@sharp hollow

im hesitant to ping 4 hours later

[visual brook]

is this true or nah

[hasty vale]

i think this is true? i’m not sure about the case where $lim_{x \to a} g(x)$ DNE because idk how $h$ could even approach a value that doesn’t exist (could definitely be wrong), but in all other scenarios it seems fine

[obsidian monolith]

yatfiw

[frigid holly]

Do indeterminate forms of limits necessarily imply that there is a limit? Or when one sees an indeterminate form, it merely shows that the question on whether there's a limit is still unanswered?

afaik the first interpretation is the right one, but I'm not entirely sure 😄

[uncut mulch]

the latter

when your have an indeterminate form, you'd need to do more work

consider
$$\lim_{x \to 0} \frac{x}{x^2}$$

[obsidian monolith]

ℝamonov

[uncut mulch]

@frigid holly

[frigid holly]

ah true

[empty bronze]

Pedro and Amelia share a common investment goal and once they reach their goals, they will withdraw their money.

Amelia starts out with twice as much money as Pedro and it takes Pedro 6 times longer than Amelia to reach this goal.

They both use the same bank that provides a 4% annual interest rate compounded quarterly.

Work out how long it takes Pedro to reach his investment goal.

Give your answer to the nearest year.

[teal matrix]

can someone help me that’s wrong

[uncut mulch]

you gave the explicit formula instead of recursive

[teal matrix]

hmm

[uncut mulch]

express a_n In terms of a_(n-1)

if you were given any term in this sequence, how would you obtain the term after it?

[simple glade]

How I can solve this? and in what category does it go under?
Complex Numbers??

[simple glade]

<@&286206848099549185>

[modest coral]

wheres the physics #

[sharp hollow]

mm i'm not confident in my answer

[proud raven]

can u post again

[sharp hollow]

sure

[proud raven]

how'd you check it

what makes you think its wrong?

[sharp hollow]

mm'

maybe through mapping notation

so random original point 2, 0 should become 5,0

[proud raven]

let me try graphing 😄

[sharp hollow]

kk!

[proud raven]

just to be sure youre asking about b?

[sharp hollow]

ah a)

but c) is probably the one i'm most unsure

[proud raven]

i always remember how much i hated these questions when i try to help with them lol

[sharp hollow]

lmao

also quick question

is invarient points only for on the axis

[proud raven]

invariant?

[sharp hollow]

because for a question, the reflection over the y axis doesn;t change the graph at all!

[proud raven]

like points that dont get mapped to a different value?

[sharp hollow]

invarient are points that dont change when transformed

what if all the points are flipped to other side

but graph doesnt change at all

[proud raven]

[sharp hollow]

ah nvm lol

[proud raven]

lemme think of one at a time

[sharp hollow]

its hard to explain without the question

[proud raven]

so its hard to say like

and this is why i hated these questions

"a vertical compression by a factor of 1/3"

[sharp hollow]

ye i see

[proud raven]

to me sounds like two things at once

compression usually means youd be squished inwards right

[sharp hollow]

x +3, 1/3y

is what the points all change by

[proud raven]

y=3x-6 would become y=x-2

or it should be y=9x-18 maybe, if you interpret it normally

then y=9(x+3)-18

or y=9x+27-18

y=9x+9

[sharp hollow]

huh

[proud raven]

oops

[sharp hollow]

thats

weird?

[proud raven]

to the right

so y=9(x-3)-18

this looks more right i think

[sharp hollow]

y = x-5 is what i got

[proud raven]

,w graph 3x-6 and 9x-45

[obsidian monolith]

Results provided by WolframAlpha

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Requested by jan Niku#2119

[sharp hollow]

what bout c

?

[proud raven]

again i hate the language 😄 it sounds to me like itd be

$y=3(\sfrac{x}{6}+4)-6+5$

[obsidian monolith]

jan Niku

[proud raven]

,w graph 3x-6 and (x/2)+12-6+5

[obsidian monolith]

Results provided by WolframAlpha

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Requested by jan Niku#2119

[proud raven]

not a super helpful graph

[sharp fiber]

can someone explain why its 9v^2 instead of 3v^2

[full pagoda]

explain why $(3v)^2=9v^2$ and not $3v^2$?

[obsidian monolith]

a disappointing son

[sharp fiber]

wait i understand now

its cause you distribute

[full pagoda]

yes

[sharp fiber]

makes sense

[visual brook]

is this true or nah

[obsidian monolith]

Disorganized

[tired axle]

@visual brook (apparently TeX eats mentions even when they are outside the delimiters)

[visual brook]

I agree

[undone girder]

Helppp me pleased

[proud raven]

w what

[sharp atlas]

Can someone help me find gog? 🙂

[uncut mulch]

where are you stuck

[sharp atlas]

I got fog and gof but I’m stuck trying to figure out how to find gog

I found gog for the bottom and top problems just can’t find gog for the middle

[uncut mulch]

what did you do for gog in the top and bottom

[uncut mulch]

you ignored the cube when plugging in g(x)

[sharp atlas]

How so

[uncut mulch]

g(x) is x^3 + 2 right?

what happens when you replace all the x in that with (x^3 + 2)

[sharp atlas]

Ohhh. Okay got it. Appreciate it 💯💪🏼

[gray silo]

I know its really difficult to read

but I was trying integration by substitution

and I cant seem to find the right answer

apparently its supposed to be 500 and something/3

[copper vigil]

integralization

u = 4x+1, x = (u-1)/4, du = 4 dx, dx = du/4
1/2 * integral of (u-1)/sqrt(u) du

= 1/2(integral of sqrt(u) - integral of 1/sqrt(u)

x=5, u = 21
x=9, u = 37

,w integrate 1/2(sqrt(u) - 1/sqrt(u)) from 21 to 37

[obsidian monolith]

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Requested by EndTimes#8053

[copper vigil]

,w integrate 8x/(sqrt(4x+1)) from 5 to 9

[obsidian monolith]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by EndTimes#8053

[copper vigil]

you forgot to divide by 4. also, if u^2 = 4x+1, then x = (u^2-1)/4

and you also forgot to adjust the bounds

you made a lot of errors

it's hard to find just one

[restive hound]

Hello, this is about solving for trigonometric equations. This is an example from a video I watched on YouTube, I was wondering what does 2πn in the general solutions, which are x = π/3 +2πn and 5π/3 + 2πn, mean. I understand that you can find cosx = 1/2 in π/3 and in 5π/3. I’m confused on why there’s a 2πn. He said that n could be any integer and whatever integer it is you’ll end back at π/3 and 5π/3. Is it 2πn because one whole rotation on the unit circle is 2π?

[vapid plaza]

Yep!

[blazing snow]

yea basically the period is 2pi

So you use 2 pi

i hope

[vapid plaza]

2pi(n) are a whole number of rotations

So doesn’t change cos

[blazing snow]

You seem like an intellectual being

[vapid plaza]

[blazing snow]

I think i am going to be an inclined plane wrapped helically around an axis if i don't study in 30 mins

[restive hound]

Woah okay, thanks. I have another question 😅 let’s say I already found the value for cos, sin, or tan when solving trigonometric equations. When writing the general solution, is the operation always used is addition? And how will I know what number I’ll write after the value and the plus sign? What I mean by this is for example π/6 + πn. Why is it πn? How will I know its πn? I’m a little confused lol

[vapid plaza]

For the addition thing, did you mean we could also use subtraction?

[restive hound]

Oh I don’t know 😅

I’m really confused on how I’ll know what to write after the value and the plus sign

[vapid plaza]

You could use subtraction cuz integers include negative numbers
But the convention is to use addition

[vapid plaza]

It should be the period of the function

sin and cos has period 2pi
Tan has period pi

[restive hound]

Oh okay, what do you mean by “the period of the function”?

[vapid plaza]

That is, how long does it take for the function to “repeat”

[restive hound]

To repeat until it end back at the value?

[vapid plaza]

You can see, the graph for tan repeats

(And they repeat every pi)

So adding a whole number of pi’s in the input doesn’t change the tan value

Similar deductions can be done for sin and cos

[restive hound]

Ahhh okay, I don’t remember learning this at school 😅 When writing the period of the function, is it only either π and 2π?

[vapid plaza]

If tangent, the period is pi

If sine or cosine, the period is 2pi

[restive hound]

Oh ok but I have an example here and the final answer was cosx = +- sqrt 3/2 and the general solution are x= π/6 + πn and 5π/6 + πn. If the period for sine or cosine is 2π, why is it π here in this example?

[vapid plaza]

Hmm, this is interesting

You can draw a graph of cosine to help understand it

[restive hound]

Ahh but I do not know how to graph a cosine 😕 from what I remember, I didn’t learn it at school

It’s an example from Mario’s math tutoring that one ^^

[vapid plaza]

I’ll draw one rn
Meanwhile, try to search for a graph of cosine function

[restive hound]

Okay, thank you

[vapid plaza]

Give me some time lol

[restive hound]

It’s okay, I’m watching a video of graphing sine and cosine

Thank you very much for the help

[blazing snow]

Watch khan academy

Its like the best of the best

[vapid plaza]

Hopefully this clears out sth

[blazing snow]

okay yes confirmed @vapid plaza is a highly intelligent being

which do you use?

[vapid plaza]

Notability

[blazing snow]

i used goodreads for my notes

@vapid plaza whats your education?

[vapid plaza]

I’m the equivalent of 10th grade I think

But I learn math for fun

[blazing snow]

hmm so you are 15?

[vapid plaza]

Ye

[blazing snow]

You must be an asian?

[restive hound]

my gooodness

[blazing snow]

lmfao

Asians connect

Anyways

[vapid plaza]

Bruh
but yes

[blazing snow]

Can someone tell me an easy way to diffrentiate under modulus?

[blazing snow]

indian?

[vapid plaza]

Uhm
Not telling u

[blazing snow]

so you are indian

Hmm

[restive hound]

Elon mass I’ll just type for a while wait haha

[blazing snow]

@vapid plaza can thy make me understand how to differentiate under a mod function?

Your younger brother asks you

[vapid plaza]

Bruh is that calculus

[blazing snow]

so?

[vapid plaza]

Well
I’m not very good at calculus and don’t know that you meant lol

[blazing snow]

You have

dissapointed

Me

[vapid plaza]

[blazing snow]

Anyone good in physics here?

[vapid plaza]

There’s a dc server for physics if you want that

[blazing snow]

Yes please

[vapid plaza]

#old-network

[blazing snow]

thank you

I have some resnick halliday questions

The nerve to provide half the solutions only.

[restive hound]

@vapid plaza I almost understand everything already but why is it 2pin? It’s supposed to be pin, from the example 😅 though I quite understand what you meant about filling the gaps. So I’ll just basically multiply any integer from pi?

Why did it italicized XD

[vapid plaza]

You have a “arithmetic sequence” right?

[restive hound]

Ohhhh nope 😅

[vapid plaza]

Hmm

I mean, each element differs a distance of pi from the next

So, we can set one element as the “pivot”
And locate all the other elements with it

So if you have pi/6 + 2pi n
You have

…
pi/6 -3pi
pi/6 -2pi
pi/6 -pi
pi/6
pi/6+pi
pi/6+2pi
pi/6+3pi
…

Which is exactly what we want

[restive hound]

Okay, thank you very much for the help. In any case, I really appreciate it. Makes me understand more

[vapid plaza]

Have a nice day

[restive hound]

Thank you, you too!

[warm crescent]

Is this correct?

[willow bear]

,calc 364 * 363 * 362/365^3

[obsidian monolith]

Result:

0.98364408753345

[willow bear]

seems ok

[warm crescent]

Thanks I was confused a little

[gray silo]

thanks!, the derviative was the problem, I did adjust the bounds though, just alot earlier than normal

,w integrate 8x/(sqrt(4x+1)) from 6 to 20

[obsidian monolith]

Results provided by WolframAlpha

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Requested by FatGuy#8519

[gray silo]

yep, I just did it weirdly sorry lmao im self taught

[viscid thistle]

that should go in #calculus

[gray silo]

this isnt pre-calc?

sorry, Im not in uni yet so I used this one

[viscid thistle]

you learn about integrals in calculus not precalculus

[gray silo]

ok, ty

[copper vigil]

i find it helpful to make a chart when doing a u sub:
u = (an expression in x), so x = (an expression in u)
du = (derivative of that expression of x) dx, so dx = du/(derivative of that expression in x)
and then adjust the bounds and substitute accordingly

[gray silo]

yeah. ive sort of learnt to do that now, tysm

[copper vigil]

😎

[wary laurel]

Help?

[fleet yew]

If f(x)=ax^2+bx+c

Then f'(x)=?

@wary laurel

[wary laurel]

idk thats all it gives

what are you askikng? @fleet yew

[fleet yew]

Take the derivative

[wary laurel]

I got it

[green kernel]

Would the amplitude be 0 or -1?

[wary laurel]

i tthink 1

[green kernel]

Well yeah, I meant one cause it's always absolute.

I'll try 1 and see

It was 1, thanks.

[copper vigil]

[river moth]

Would someone here possibly have a pdf copy of Stewart/redlin/Watson precalculus book 7th edition?…

[steel venture]

might be against TOS

[willow bear]

think about that for a moment

i mean really think about what you said

what would it mean for a function to have zero amplitude?

[green kernel]

Straight line

[willow bear]

i would've expected a complete sentence rather than just a word blurted out

but yes, such a function would be constant

which yours decidedly isn't

[green kernel]

lol

[viscid thistle]

is this correctly done

[echo wagon]

The last line of part 4 is nonsense

And basically you want to restructure part 4 completely

You should not assume |4x+1+3| < e at the start

You only assume |x+1| < delta, and then you show that |4x+4| < e

[viscid thistle]

alright, thanks

[viscid thistle]

does this check out then

[mild robin]

So my teacher gave me this correction but im not sure why x became 150 since its 150 ft away from the tower

Am i doing something wrong here? (My teacher's answer is the one written in green)

[lilac swift]

to prove this shouldn't you substitute x with the value it approaches to (-1)?

[viscid thistle]

no

i just have to prove for any e>0 i can find a d>|x+1|

[lilac swift]

oh I see now

but I don't understand why you'd need to prove that

xD

[lilac swift]

I think this one is correct then

[echo wagon]

The proof is fine noe, but the last line is still nonsense

Why are you saying e > |4x+4|

That's not what you are doing at all?

[viscid thistle]

what do you mean

e>|4x+4| is the same as |4x+4|<e

hey

is this channel free

i just want an answer to a quick qn

is 0*0=0 or indeterminate?

[viscid thistle]

0*0=0

ok thanks bro

[echo wagon]

@viscid thistle but it's not about all e > |4x+4|

It is for all e > 0, there exists a d > 0 such that if |x+1| < d then |x+4| < e

The way you are writing it is not the same

[viscid thistle]

ah

thanks man

[viscid thistle]

yo

is it cool if i ask a question here ?

[viscid thistle]

3

[warm forum]

Ok

[viscid thistle]

can u solve

[warm forum]

I just came here

So lemme think

[viscid thistle]

ok take your time

gimme the idea alone ill try to capitalise on it

hello?

[warm forum]

2f(sinx)+sqrt2 f(cosx)=tanx
Probably try substituting x with (pi/2 - x)

And you’ll get another equation

From those two equations you can solve for f(sinx) and f(cosx)

[viscid thistle]

yeah ill try now wait

yeah done

what now

[warm forum]

What’s f(sinx)

The one that you got

[viscid thistle]

tanx - 1/(tanx*sqrt(2))

[warm forum]

Yeah right

Okay

Now do the limit

Substitute x with sin x or sin y

It’s up to u

[viscid thistle]

do which limit?

the limit asked in the question?

[warm forum]

$\lim_{x\to1}\sqrt{1-x}f(x)\
\text{Let }x=\sin{y}\
x\to1\
\
y\to\frac{\pi}{2}\
\
\lim_{y\to\frac{\pi}{2}}\sqrt{1-\sin{y}}f(\sin{y})$

[warm forum]

Yeah

Then just change f(sin y)

And solve the trig limit

[obsidian monolith]

Muzan Jackson

[viscid thistle]

good method but i have 1 doubt

[warm forum]

Okay

[viscid thistle]

f(siny) is just what i said but replacing x by y

[warm forum]

Yeah

[viscid thistle]

so if y tends to pi/2

tan y would be indeterminate right

[warm forum]

That’s why you have to simplify the function first

It’s limit

[viscid thistle]

i mean ur right

ok

[warm forum]

And see what you can do with the sqrt(1-siny)

[viscid thistle]

i will simplify further

[warm forum]

Okay

[viscid thistle]

ill try tom im gonna sleep today