It can be zero
#precalculus
frail lion
Line , y=mx
If zero
gritty roost
Oh right
frail lion
Yes brotato chips
bitter pier
Wait, I think I can see that part in a textbook
what county are you from? your asian right
gritty roost
It just wasn't written as c
bitter pier
perhaps are you Chinese
gritty roost
perhaps are you Chinese
Why do you think I'm Chinese?
frail lion
It just wasn't written as c
Yeah it was for explaination
bitter pier
Why do you think I'm Chinese?
idk initial guess
gritty roost
Yeah it was for explaination
Alright, thanks
frail lion
idk initial guess
Beacuse asian means chinese right ?
gritty roost
idk initial guess
I'm not full Chinese, just part
frail lion
I'm from Asia too bro
gritty roost
I'm from Asia too bro
Are you Chinese?
frail lion
Not a country
No
I'm from "dond dell me what to do "
bitter pier
do you shake your head while explaining?
frail lion
Yeah man it's an indian gene problem
bitter pier
woah
gritty roost
do you shake your head while explaining?
Are you Chinese?
bitter pier
Yeah man it's an indian gene problem
is it true you guys hate pakistan?
fluid sorrel
is it true you guys hate pakistan?
Bro come in #chill
bitter pier
is it true you guys hate pakistan?
wait is political talk allowed
bitter pier
Bro come in <#342850939306246145>
mb
frail lion
is it true you guys hate pakistan?
Bro look honestly I'm not stupid i don't hate
Me hating or loving does not make a god damn difference
gritty roost
is it true you guys hate pakistan?
It's not a universal thing for a country
fluid sorrel
No
I'm from "dond dell me what to do "
Seriously bro
crimson light
i got a question whats the use of mathematical model and use of euler method and why is it even there what perpose does it serve in college they just teach i wanna know why and how did they make it
willow skiff
You from the south?
yes
willow skiff
How do you get the role “very cool people”?
you have to pay for Nitro and boost this server
or if you can get Nitro for free somehow
carmine orbit
Ohhh thanks brotha
frail lion
Oi @willow skiff @carmine orbit guys you interested in trying physics
willow skiff
Oi <@1151031274413228043> <@926400588596518912> guys you interested in trying ph...
no
carmine orbit
Oi <@1151031274413228043> <@926400588596518912> guys you interested in trying ph...
Send if it aint tedious ill do it
frail lion
Send if it aint tedious ill do it
Here
frail lion
No
carmine orbit
Send soln
carmine orbit
carmine orbit
i will try by perimeter of parabola once
Ngl doesnt work
Only thing that works is catenary
And if im not wrong ts is from pathfinder
vivid lintel
what goes for trying, Once i approximated arch of a cycloid by ellipse ( Lame curve to be specific ) lets see what goes with this
lapis sphinx
or you can apply the expansion for ln(1+x)
or you can also use LH rule if you wish
suppose you're given lim x to 0 [ln(1+x)]/x. if you first expand ln(1+x) you need not write the terms after x because their contribution to the sum becomes zero in the limit. so you're left with lim x to 0 x/x which is equal to 1 basically
suppose you're given ln(1+5x)/x lim x to 0 once again expand the series and you're left with lim x to 0 5x/x which equates to 5
hushed sphinx
Yeah, but this is apparently supposed to be done with PRE-calculus tools, which I don't think that series expansion is.
lapis sphinx
if you don't want to dwell in series expansion, you can always opt for l'hospital
hushed sphinx
Not pre-calculus either.
lapis sphinx
if you don't mind me asking, you're not indian right?
hushed sphinx
No. What does that have to do with anything, though?
lapis sphinx
here (in inda), we're mostly taught all of this before college/universities. our system is different from other countries so i am not really familiar with the terms calculus, pre-calculus etc.
series expansion and lh rule are the most recommended ways to solve a limit for our curriculum which is why i suggested those here
hushed sphinx
"Precalculus" is an American term whose precise boundaries I have no good understanding of. But the word only seems to make sense if it excludes things that you need to know about derivatives for.
carmine orbit
Not pre-calculus either.
Nah he is right they are taught series expansion before taylor or maclauren
With PRE calculus
hushed sphinx
Who is "they"?
lapis sphinx
they as in indian students i presume
carmine orbit
Who is "they"?
But yeah it still doenst change the fact
lapis sphinx
another way you could approach this problem i guess is using 1^∞ form of limits
carmine orbit
Who is "they"?
Like they are told to memories series expansion of various functions like sinx e^x
carmine orbit
here (in inda), we're mostly taught all of this before college/universities. our...
The stuff like functions continuity differentiability limits are considered pre calc
lapis sphinx
if i remember correctly this is how you solve it
lapis sphinx
The stuff like functions continuity differentiability limits are considered pre ...
yeah exactly
we were taught inverse trigonometric functions as pre-calculus too
since it pops up a lot in various questions
carmine orbit
And stuff like derivatives integration aod etc are considered calculus
lapis sphinx
@hushed sphinx
carmine orbit
So basically he isnt wrong either since expansion is done in calculus
willow skiff
this is stretching the bounds of 'pre-calculus' but you're right, you can do this without actually understanding calculus
just memorise that specific limit and worry about the derivation later in calculus
carmine orbit
just memorise that specific limit and worry about the derivation later in calcul...
Fr
willow skiff
this is a nice derivation though without calculus
willow skiff
so by variable substitution, $\lim_{bx \to 0} \frac{\ln(1 + bx)}{bx} = 1$ also
and then it follows
lapis sphinx
just memorise that specific limit and worry about the derivation later in calcul...
im like 90% done with calculus so yeah
obsidian monolithBOT
south
lapis sphinx
im like 90% done with calculus so yeah
to be fair you're never really DONE with calculus but there's this exam im preparing for which actually focuses on some specific types of questions so referring to that, i've covered pretty much everything
willow skiff
I hate JEE culture so much, but if that's where your dreams are, then....
hushed sphinx
this is a nice derivation though without calculus
I suppose, if one has defined e as something like the limit of (1+1/n)^n.
I don't understand what is going on in the line with "1^infty", though.
willow skiff
I suppose, if one has defined e as something like the limit of (1+1/n)^n.
I don'...
yeah that should just be removed altogether
or clarified as "1^infinity is undefined, so you need to recognise the specific limit"
carmine orbit
to be fair you're never really DONE with calculus but there's this exam im prepa...
Jee we get it man
carmine orbit
I hate JEE culture so much, but if that's where your dreams are, then....
Bahahahah me too so repetitive
lapis sphinx
Jee we get it man
not if you're not indian no
carmine orbit
What
lapis sphinx
I hate JEE culture so much, but if that's where your dreams are, then....
its not that im fond of it too but we gotta do what we gotta do man
lapis sphinx
or clarified as "1^infinity is undefined, so you need to recognise the specific ...
ok yes
my bad
willow skiff
its not that im fond of it too but we gotta do what we gotta do man
exactly...
lapis sphinx
ok so if this is pre calculus
is there a calculus channel?
#calculus ok yes lets go
frail lion
Send me the solution when youre done
Yeah I have the solution but I don't have it in a vid format and I don't want to see it now because Im not done with the question
And why are you also not trying it
lapis shuttle
guys i'm not wrong right 
my teacher HAD to have typed that in incorrectly or sum cuz i redid it and got the same thing
we will ignore the handwriting ok 😭 😭
raw hill
my teacher HAD to have typed that in incorrectly or sum cuz i redid it and got t...
,w equation of line (2,4306), (7,15071)
obsidian monolithBOT
raw hill
,calc 2153*12
obsidian monolithBOT
Result:
25836
yeah probably a typo
frail lion
fluid sorrel
Answer is 2000?? Or 0... What does that other part say. Is it abt ai
median spear
Answer should be zero
As f(x) has no integers in range
Cuz I'm getting arcos(~1.25), which is not defined
So kinda thinking that function is not defined in any real domain brisky
hidden birch
||2003||?
frail lion
No
hidden birch
oh wait
vivid lintel
0
vivid lintel
technically it sohuld be 2000 + 0 but then the question says to put 0 if no values exist
and since no values exist
answer is 0
frail lion
The answer is not zero damnit
frail lion
final answer ||2001||
No
vivid lintel
its arccos(1.78), but arccos is only valid in the interval [-1,1] right?
so how is the answer not 0\
vivid lintel
yesh send once
west ice
its arccos(1.78), but arccos is only valid in the interval [-1,1] right?
That's domain
vivid lintel
That's domain
yes its the domian ,range is 0 to pi
west ice
No range is like the output no?
vivid lintel
No range is like the output no?
Yes but if the domian itself is not satisfied
frail lion
Range is 0 to π
vivid lintel
how can you get the output
west ice
they said the output, and the output is not -1 to 1
hidden birch
last resort, graph it
hidden birch
,w plot f(x)= arccos(√(arcsin(sec(ln((2x²+3x+10)/(x²-3x+2))))))
obsidian monolithBOT
frail lion
Yeah very well
hidden birch
funny graph
vivid lintel
,w plot f(x)= arccos(√(arcsin(sec(log_e((2x²+3x+10)/(x²-3x+2))))))
obsidian monolithBOT
hidden birch
,w plot f(x)= floor(Re(arccos(√(arcsin(sec(ln((2x²+3x+10)/(x²-3x+2)))))))) from -10 to 10
obsidian monolithBOT
hidden birch
0's and 1's
west ice
Glass feels good today and decided to turn on his brain at the weeken for once
hidden birch
ohnoo
maybe it's the tea
i mean I'm not sure of the answer
composite functions' domain and range are my weakness
hidden birch
Damn bro who asked 😂😂😂😂👌👌😂😂
man can we really only say something when someone asks? 
i had to provide the context bro
guess what else no one asked
no I'm not gonna do it
frail lion
man can we really only say something when someone asks? <:sully:6518168201221898...
Ok bro cul i wasnt serious anyway you guys are cul
frail lion
guess what else no one asked
What
hidden birch
Ok bro cul i wasnt serious anyway you guys are cul
i know it's very obvious with the emojis and "Js kidding" you're good
hidden birch
-# I'm not gonna drift further from the math topic cuz it becomes out of topic and mods gonna snipe us
frail lion
You're right
fluid sorrel
The answer is not zero damnit
What's the answer
frail lion
Umm guys guys
median spear
Btw how are ya guys doing it ?
Well I'm not getting the domain in any real interval
frail lion
@hidden birch @fluid sorrel @median spear
median spear
Hmm
frail lion
Hear me out
frail lion
Bro I'm really really sorry I was checking wrong answer
median spear
what's the actual answer
fluid sorrel
Bro I'm really really sorry I was checking wrong answer
Ayee
median spear
which yt channels are you referring to for such questions @frail lion
frail lion
It's 0 guys
frail lion
which yt channels are you referring to for such questions <@1360591290097733642>
Random
I go on search
median spear
It's 0 guys
it's easy actually
median spear
Random
Finna
always check the domain before going for range
Adds on they have Arrowes us to zero thing in question
uncut star
If i remember correctly we had to minimize gpe right
hidden birch
It's 0 guys
so how do u solve it
uncut star
That should give us cosh
frail lion
If i remember correctly we had to minimize gpe right
Hold on 🌍
frail lion
If i remember correctly we had to minimize gpe right
What's gpe?
uncut star
Gravitational potential energy
frail lion
What no I don't think so
fluid sorrel
so how do u solve it
Broo
Sec will give all real values except (-1,1)
But sin^-1 domain is [-1,1]
uncut star
Hmmm I need to check as far as my memory goes it was something related to this
fluid sorrel
But sin^-1 domain is [-1,1]
So when sec is 1 is only possible case
Bcz other real numbers arsinx won't accept
fluid sorrel
So arsin1 is π/2
fluid sorrel
i mean i based on the graph wolfram gave as last resort
I didn't check the graph
west ice
hidden birch
Sec will give all real values except (-1,1)
i thought sec's range is from 1 to infinity
west ice
What's happening here
fluid sorrel
i thought sec's range is from 1 to infinity
No no
west ice
,w sec function range
obsidian monolithBOT
west ice
Stupid wolfram
hidden birch
,w plot sec x
obsidian monolithBOT
river drift
i thought sec's range is from 1 to infinity
it's $(-\infty, -1] \cup [1,\infty)$
obsidian monolithBOT
κλαουντ ☁ (cloud)
fluid sorrel
i thought sec's range is from 1 to infinity
It's all real number except (-1,1)
fluid sorrel
oh right i forgot the mirror below
Okkk
fluid sorrel
not really mirror
So
√π/2 is SMTH 1.25
That's not in domain of arcosx
So fx range is 0
hidden birch
sorry i forgot the open interval notation for a bit
fluid sorrel
Answer is 0
hidden birch
ok got it
i actually considered 0 but sam said no at first
after me having 2 mistakes
hidden birch
that's when i used wolfram graph
median spear
But at the end it's easy
hidden birch
so what's wrong with wolfram why it did me dirty by giving that graph
median spear
that's when i used wolfram graph
U can use normal logic
median spear
so what's wrong with wolfram why it did me dirty by giving that graph
Idk
hidden birch
i did
frail lion
I actually was trying to solve it that's why I thought what is this
hidden birch
but sam trolled
median spear
I actually was trying to solve it that's why I thought what is this
alrr
median spear
but sam trolled
Dude chill
hidden birch
for some reason i still trust wolfram
hidden birch
Dude chill
I'm chill
median spear
for some reason i still trust wolfram
Noooooo
frail lion
but sam trolled
Yeah bro chill leave me now
median spear
Trust ur concepts
hidden birch
you chill
median spear
Yeah bro chill leave me now
uncut star
for some reason i still trust wolfram
I suppose the mistake with wolfram was that it was giving the real part of complex range
uncut star
Which is not what we need here
uncut star
?
median spear
hidden birch
I suppose the mistake with wolfram was that it was giving the real part of compl...
it showed two graphs, blue curves as real part and yellow part as imaginary part. but to be fair I can't be sure how to interpret it
frail lion
<:sotrue:826971355542192148>
What are the odds i and triaengle know each other
median spear
What are the odds i and triaengle know each other
1 in trillions
frail lion
It's the one
west ice
fluid sorrel
<:cat_bread:933424847206383637>
Girl has no work
median spear
But for now ,yeah
pretty much unemployed
west ice
frail lion
Girl has no work
Damn
fluid sorrel
I'll have one, I swear <:breadhehe:556700641427456020>
Okayy
vivid lintel
Anyways the graph
And the results were very not simple
Tan of beta is approximately 1
For this
Ok I tried this by perimeter and got a transcendental equation
And radius of curvature is approximately 14.48…
The closest I could get
spiral dawn
ivory fractal
is there any way this can be solved on desmos, or js have to algebraically solve it?
willow skiff
is there any way this can be solved on desmos, or js have to algebraically solve...
you can try on Desmos, but there's an easy way without it
the condition for a slant asymptote is that the numerator has to be 1 degree more than the denominator
so that gives you x^k * x * x has 1 degree more than x^5
willow skiff
the condition for a slant asymptote is that the numerator has to be 1 degree mor...
cause this is how the function behaves like a linear function, when you take the highest terms of the numerator and denominator
neat path
cause this is how the function behaves like a linear function, when you take the...
So you basically need only 1 ‘x’ on the numerator
So that means k+2+’1’ = 5
And thus k is 2?
versed zodiac
we’re using the definition of the derivative to solve B, does anyone know how to solve? (calculus)
amber flint
we’re using the definition of the derivative to solve B, does anyone know how to...
well, start by writing down the limit definition of a derivative
then plug in the function given
also plug in x=3
then just solve the limit?
manic harness
frail lion
For this
Exact answers can be found bro
Tan beta 5/(3√3)
Radius of curvature 52/(3√3 )
0.97 and 10 approximately in decimals
frail lion
And thus k is 2?
Bro the degree above will be k+2 and it should be one more than denominator
K+2=6 ; k=4
alpine vector
is precal hard?
willow skiff
so that gives you x^k * x * x has 1 degree more than x^5
You're forgetting these multiplications @neat path
(k + 2) = 6 instead
Ah, you misinterpreted 1 more: 1 more goes on the right hand side
terse echo
can someone remind me for limit notation, if it says x->2^-, does it mean approaching from the right or the left
i always mix it up
raw hill
can someone remind me for limit notation, if it says x->2^-, does it mean approa...
- is left, + is right
terse echo
thank you 🙏
raw hill
thank you 🙏
vivid lintel
Exact answers can be found bro
As I said earlier I used alternative method
vivid lintel
So it’s just an approximation
neat path
Bro the degree above will be k+2 and it should be one more than denominator
K+2...
No, we need numerator 1 more and so k+2=4
willow skiff
For example, 11 is 1 more than 10
neat path
@willow skiff
Do you need any other extra training as a high schooler
I know most things you learn in grade 11
frail lion
No, we need numerator 1 more and so k+2=4
Bro wot
frail lion
Ok
neat path
And a linear function gives a slant line
frail lion
Yes generally
frail lion
As I said earlier I used alternative method
But what about answer bro the second one was a lil wrong
frail lion
Yk one more thing
When ya divide these both polynomials by long division, the quotient you'll get will be your asymptote
willow skiff
Do you need any other extra training as a high schooler
bro I'm at uni
west ice
frail lion
bro I'm at uni
I think he is asking
vivid lintel
But what about answer bro the second one was a lil wrong
I will look into that because it required transcendental equation to be solved
frail lion
Ok
carmine orbit
<:opencry:586078614865444865>
will you change your name toi fionna the employed once you get a job?
shell bobcat
Hi everyone,
I'm about to start my first year as a business major and need to take MATH 108: Introductory Calculus with Business Applications. I've always struggled with math and am concerned about keeping up. I want to prepare myself and improve before classes begin.
What are the best strategies, resources, or study routines to build confidence and succeed in this course? Any advice or tips would be greatly appreciated!
Thanks in advance!
deft jetty
considering it sounds like this course probably isnt very rigorous id advice simply brushing up on computation involving basic algebra (up to quadratics, rational expressions) and arithmetic (exponentiation rules, being confident at handling fractions), those are some major things that ppl can trip up on anyways
id also recommend getting comfortable with reading graphs and learning to see how a graph will look based on the function and vice versa
as for resources i think something like khan academy would be useful but its also an idea to find any worksheets or such that u can as volume is a p important factor in building these skills
i cant personally give any recommendations but #book-recommendations surely has relevant information
carmine orbit
thomas calc or aops works fine
delicate wedge
what is pre calc?
timid jackal
calc is short for calculator guys
worldly blaze
what us precolc
worldly blaze
thomas calc or aops works fine
ri gore?
scenic lance
Calc is short for calculus goofy goober
vital swift
Calc is short for calculus goofy goober
nah its calculator
scenic lance
Calc-ulus
bold carbon
x -> -2^- means that we want to figure out the behavior of the function as the x value moves towards -2, from the right. what's the behavior of the function near -2?
median spear
See the graph
As x tends to -2^-
That is js behind -2, check the value of graph
(it tends to ♾️)
fluid sorrel
Infinity as -2^- is a number just on the left side of -2... So see the graph from the left side of-2.. as x tends to-2 y tends to infinity.
carmine orbit
Calc is short for calculus goofy goober
lol
carmine orbit
ri gore?
https://tenor.com/view/pat-patrick-bateman-patrick-spongebob-meme-spongebob-gif-12593993314823291186
median spear
https://tenor.com/view/pat-patrick-bateman-patrick-spongebob-meme-spongebob-gif-...
Dude use #chill
void scaffold
Hopefully this is the right channel since idk I don't do math en English but
How do you calculate a linear function when you know two points like f(-1)=4 and f(2)=-5
I mean I tried to take some guesses but there's gotta be a way to calculate it right?
echo sinew
Do you know the general form of a linear function (also known as line)?
It is y = ...
clear berry
y=mx+b
y=kx+b
y=mx+c
y=kx+c
pick one
trim shard
clear berry
nah general form is clearly ax+by+c=0
echo sinew
Indeed
But let's start with the explicit, I guess
Hopefully it should be a little easier, in my opinion
clear berry
Hopefully this is the right channel since idk I don't do math en English but
How...
yes
frail lion
fluid sorrel
It's continuous at x=0 so we can apply lim x to 0 and simplify to just get the terms of n?
U did it in 18s 🗿
carmine orbit
U did it in 18s 🗿
probably knew answer before hand
west ice
probably knew answer before hand
He just has a good gaming chair
frail lion
U did it in 18s 🗿
Bro i left it in 18 s
I knew i couldn't move this mountain
So i left it
frail lion
I knew i couldn't move this mountain
Or i should say could try other questions
fluid sorrel
Bro i left it in 18 s
Did u try what i told
Like tried it
Bcz that's the only reason they said continuous at x=0
fluid sorrel
I mean I obviously will
Send me if u get answer 
frail lion
Ok bro 👌
frail lion
Yeah man very comfy 100 percent suggested
carmine orbit
it looks like i can sit on that for hours
fluid sorrel
Bro it's actually a genius decision coz
I am getting f0 as 4lambda
The only problem is how to find lambda
south mural
Can someone help me w 1 and 2
proud tangle
The increacing intervals would be the upper right, and the decreasing would be the bottom left (for question 1) and the increasing for question 2 would be the middle part, and the decreasing woud be the extremities (I think)
worldly scarab
Guys I struggle with limits and always make mistakes
What should I do to get better?
winged wigeon
Guys I struggle with limits and always make mistakes
How come? Most of the time it’s just direct substituting or if it’s graphed it’s mostly eyeballing
fluid sorrel
fluid sorrel
I am getting f0 as 4lambda
...
worldly scarab
How come? Most of the time it’s just direct substituting or if it’s graphed it’s...
Idk what limits you have but it’s def not just replacing or substituting
I have to use tons of trigonometric identity and I musnt make a single mistake to not ruin everything
winged wigeon
Not these?
worldly scarab
No 😂 I saw those, those are so es
Ez
I have to sleep tho it’s late for me ill tell u more later
winged wigeon
Alright cuz I’m curious why you considered those limits to be hard😭
fluid sorrel
Does anyone know how to solve this??? I have typed my work above
fluid sorrel
Alright cuz I’m curious why you considered those limits to be hard😭
Solve this bro
fluid sorrel
..
bold carbon
Does anyone know how to solve this??? I have typed my work above
compute the limit as x -> 0 from the left and from the right
from the left, (x+1) < 1 and nearby, this means (x+1)^n -> 0 as n -> infinity
so the limit is just the lambda sine thing / x, as x -> 0 which i think you found to be 4 lambda
from the right, (x + 1) > 1, so (x+1)^n dominates, and the limit becomes
(1 - cos(1 - tan(pi/4 - x)))/x^2 as x -> 0
that comes out to 2
to be continuous, we need the left and right limits equal, so 4 lambda = 2 -> lambda = 1/2
then f(0) + 2 lambda = 2 + 2 * 1/2 = 3
the sine / x thing is easy to find the limit of, the trig composition thing is a lot more annoying, but you can use taylor expansions to simplify
tan(pi/4 - x) centered at pi/4 is about 1 - 2x, so then we have (1 - cos(1 - (1 - 2x)))/x^2
= (1 - cos(2x))/x^2
and thats a lot easier to find the limit for
fluid sorrel
compute the limit as x -> 0 from the left and from the right
from the left, (x+...
Of i was just not sure abt the right side
Got it now
Thanks
lavish ferry
I really need help, I skipped algebra 2 so I could take pre calc and I’m strongly regretting it, I spend three hours outside of school a week with tutors for me just to keep failing test and for my tutors to just tell me my math skills are weak and I’m probably not going to get a good grade in the class. I don’t know what to do I can’t switch out, I’m working on maybe something for my test anxiety, but I’m willing to put in the work to get the grade I want. I just don’t know how to do it and I would love some guidance!
worldly scarab
I really need help, I skipped algebra 2 so I could take pre calc and I’m strongl...
Do you know exactly what you’re struggling with?
lavish ferry
Not exactly l guess just algebra in general which has like transferred over into my pre calc causing me to not do good
worldly blaze
Not exactly l guess just algebra in general which has like transferred over into...
practice fundamentals
Since you skipped algebra 2 you kinda skipped the “other part” of algebra
precalc is basically just a review of both algebra classes so you should practice fundamentals msybe go over a textbook
lavish ferry
What textbook would you recommend? Or online resources? What are exactly are the fundamentals?
worldly blaze
What textbook would you recommend? Or online resources? What are exactly are th...
i guess a textbook i would recommend would be Stewart’s precalc. It covers fundamentals in the 1st unit. If you do all the problems you might be set.
For online resources maybe khan academy and prof leonard’s college algebra. If you want lectures that covers the book prof william would be good too.
other textbooks could suffice, i do heavily recommend using khan academy though because it’s pretty good for lower mathematics
halcyon prawn
Its about the limsup
proud tangle
If log 3+7=x+log3+1, then do I cancel everything out as usual, and then do the same with the logarithms if they are both the same? (x = 6 then right?)
manic trench
Yeah
log 3 is still a value after you calculate it
So it works out the same as any other number/term
proud tangle
So it is the same as a variable if I am canceling things out then right?
willow skiff
So it is the same as a variable if I am canceling things out then right?
yes
$u + 7 = x + u + 1$: subtract $u$ on both sides, $7 = x + 1$
obsidian monolithBOT
south
willow skiff
$\log 3 + 7 = x + \log 3 + 1$: subtract $\log 3$ on both sides, $7 = x + 1$
obsidian monolithBOT
south
worldly scarab
i guess a textbook i would recommend would be Stewart’s precalc. It covers funda...
Id have to agree with leona here
Stewart precalc is good
It’s also available in many languages if you need it to be translated
frail lion
Guys I was somewhere out so i wasnt active for some time 😅
But yeah no problemo see this
frail lion
Guys I was somewhere out so i wasnt active for some time 😅
By guys i mean my only friend @fluid sorrel
fluid sorrel
Options????
fluid sorrel
By guys i mean my only friend <@1247446254938624121>
Broo
Btw that limits question
Did u check the answer
A dude replied when I reposted with my work
We just had to check f0+ and f0- when n tends to infinity how it affects (x+1)^n
frail lion
Options????
Hold on
J-i
-i-j
I+j
I-j
Cap cap cap cap
Include cap in all
I aint typin all those caps
frail lion
I+j ???
I + j is far asf bro
Like far asf
Any one else wanna try can try too
I mean who's stopping you guys
frail lion
Ok ok tell me how i-j
You're taking centrifugal force right ?
Opposing that is friction?
I suppose you did this
fluid sorrel
Ok ok tell me how i-j
Ahhhh 😃
Ok so r vector is perpendicular to v
And it makes 45^° with + axis
So it's roughly proportional to i+j
But it's perpendicular to v
And by figure and data we can say that v is 90° ahead of r
So it's proportional to -i+j
Which we can see from figure
And friction is in the opposite direction of v
So -(-i+j)
i-j
frail lion
So it's roughly proportional to i+j
Man what how
fluid sorrel
First i forgot the fact that v is ahead by 90° and it's obvious by figure that it's going to be -i+j
frail lion
And friction is in the opposite direction of v
Friction will oppose v or force?
What more what less?
Opposes both doesn't it ?
fluid sorrel
R vector is j-i
Confusion
fluid sorrel
Opposes both doesn't it ?
Yeppp
frail lion
frail lion
Ru sure with the answer it's i-j??
No answer is not
This
Matter of fact it is given but
It's conceptually wrong
frail lion
No
fluid sorrel
Then
fluid sorrel
It's that we can't
Which book is it
frail lion
No bro I did the worng answer
I mean I knew how the paper setter had
Thought
Centrifugal
And did d
fluid sorrel
You're telling?
Asking
frail lion
Centrifugal radially outward thats what I thought
But problem is that
Some friction will oppose velocity too
This is who I discussed ts with
And we reached here
fluid sorrel
Bro
In static state
fs acts in direction of Fc
It's given in book
To prevent this outward sliding, the static friction force fs must push the particle back inward, towards the center, thereby opposing the tendency to slide out.
This
frail lion
Yes this defines the d option I agree cro
This is the centrifugal force concept man what
Exactly what I said
Which book tho
fluid sorrel
Which book tho
Module
So now I understand how we were supposed to get this approach
If u remember the core concept of banking of road
There we used this concept in derivation of formulas
frail lion
Yeah
ivory fractal
how does synthetic division work?
ivory fractal
What do i do next
frail lion
X-3=0
X=3 ok right
1 -1 2 ok right
Bring down 1 multiply by 3
Ok right
3×2 6 ok right
ivory fractal
howd u get x+2 as the quotient
frail lion
You've got 1 and 2 in last
Not multiply the 1 by the degree you would get after subtractingthe upper max degree by lower max degree
Which Is , in this case , x
So 1×x
And then multiply 2 by one less degree , which is x^0 , which is 1
So 2×1
This is your quotient
X+2
ivory fractal
the remainder is 8 tho
frail lion
It's nothing bro
It has no specific integer value because it'll change as x changes
Why ? Coz the degree after Subtracting is zero which is some constant
Which is changing as x changes
So its nothing
green trail
What do i do next
Send the question
ivory fractal
Send the question
thats the questions. use synthetic division to solve that expression
worldly blaze
Don't learn that shi
it’s faster than normal polynomial division in some cases, i do get where you’re coming from though because it’s a big time-waster
frail lion
If synthetic division is taught first and only that is taught , then one can't do anything he'll have to learn it but it's of no profit to learn it after proper long division
Like i did
uncut star
Yk how is it i-j??
We translate the central force vector to the origin
That gives us i-k
J
I-j
fluid sorrel
We translate the central force vector to the origin
Got it
It's fs
Acting in direction of Fc
uncut star
Some friction will oppose velocity too
Probably not since at is taken to be 0 acc to options
frail lion
We're actually not given this information
Ok see assume there is some a tangential
Centrifugal radially outward
Tangential force direction of tangent
Angle between both is 90 degrees
but we don't know the mass and allat to use the tangential acceleration
Of force hence friction
Now if youre assuming that there is no tangential acceleration which the invigilator thought we would assume gives option d
That's why I did d but
I am just saying that actually assuming this is not conceptually sound
last rose
derivatives are precalc right?
need to ask a derivative question
why can we use derivatives to find the biggest area of a shape / volume
sonic hill
why can we use derivatives to find the biggest area of a shape / volume
Because you can use derivatives to find the maximum of a function and so if you have a function that represents area or volume you can find the maximum of it.
last rose
Because you can use derivatives to find the maximum of a function and so if you ...
i figured out the question i was abt to ask you as i was writing it, my bad if you were waiting for me to type it
sonic hill
No worries
frail lion
Wym physics cup solution
frail lion
Oh ok bro
hushed sphinx
As distinct from the mathematics mug, or the chemistry chalice.
green trail
thats the questions. use synthetic division to solve that expression
You can also solve it by Wavy Curve Method
green trail
Why did you put Denominator equals to zero ? @ivory fractal
ivory fractal
Why did you put Denominator equals to zero ? <@1132146139177685042>
So i could find the value of the root
green trail
So i could find the value of the root
Denominator doesn't equal zero
If then the function will be not defined
In that question, what do you have to find the value of x or just synthetic division to find quotient and remainder ?
@ivory fractal
ivory fractal
In that question, what do you have to find the value of x or just synthetic divi...
yeah its just the synthetic division
green trail
yeah its just the synthetic division
I solved it, I got x+2 as a quotient and 8 as a remainder, is that the correct answer?
ivory fractal
yes
green trail
some other dude said it was x+12 or x+10
😭
short olive
the fuck is calc
ivory fractal
what i got was
green trail
what i got was
?
ivory fractal
green trail
It's correct
ivory fractal
Oh ok thx
frail lion
the fuck is calc
Calculus deals with some type of continuous change
Like rates of change ,area under curves
worldly blaze
Calculus deals with some type of continuous change
Like rates of change ,area u...
acshually calc is short for calculator STOP giving out DISinformation 🙄
hidden leaf
what is this diddyblud doing on the calculator
frail lion
what is this diddyblud doing on the calculator
Brainrot ahh
spring jolt
How do you learn solving logarithmic equations and exponential. My brain is wired to find one way/formula to solve all of the same types of questions, but these vary so much it’s hard.
median spear
How do you learn solving logarithmic equations and exponential. My brain is wire...
Do feel free to share your doubts
Questions will help you understand concepts in better way
spring jolt
Because all of pre calc up to this has been pretty like
Do these steps, and i’ve mastered it all
But this one has stumped me
ivory fractal
Since im learning polynomial division/synthetic division, thats how i’d verify for part a?
raw hill
Since im learning polynomial division/synthetic division, thats how i’d verify f...
Yeah
If you don’t know factor theorem then that’s how they probably want it
ivory fractal
remainder theorem or factor theorem
i’ve learnt them too
but im unsure
what to use
factor theorem is finding the zeros right?
raw hill
factor theorem is finding the zeros right?
Factor theorem says that if b is a root of a polynomial p, then p(b)=0
note that b being a root is equivalent to (x-b) being a factor of p(x)
ivory fractal
is that the same as f(c) (x-c)
raw hill
is that the same as f(c) (x-c)
f(x)=(x-c)g(x) for some polynomial g if c is a root of f if that’s what you’re asking
ivory fractal
oh yes that
spark anchor
.
west ice
Man somebody got any good questions
west ice
obsidian monolithBOT
Fionna The Unemployed
west ice
I wanna solve i don't wanna stop
Here you go
frail lion
Bro from where have ya given me this question
This is not some unsolvable question typo right ?
I mean I have a sussy feeling
west ice
This is not some unsolvable question typo right ?
It's solvavle
Do you want the answer?
west ice
Jus asking
You're Indian right? you should have everything it's needed to solve this problem
west ice
Bro from where have ya given me this question
If you don't like optimization type problems I can give you smth else
frail lion
You're Indian right? you should have everything it's needed to solve this proble...
What
I do have a pen and a paper
And a gaming chair
west ice
deft jetty
very nice problem
west ice
very nice problem
It's not for me, anything that require doing a bunch of calculations and algebra precisely is not nice
Yes I suck at algebra I know
deft jetty
i like it both cuz algebra but also cuz it reminds me of like a weaker moving sofa problem
west ice
i like it both cuz algebra but also cuz it reminds me of like a weaker moving so...
At first glance people think it is
west ice
This would waste a good amount of your time
frail lion
Wait hol up
I cracked it
Man im fucking genius
- Something???
Yeah or no
3.7
Precisely
frail lion
3.7
west ice
frail lion
Man hell yeah
frail lion
So your headache accounted to your grammatical error?
west ice
So your headache accounted to your grammatical error?
Yeh likely
I can't even think of anything
It's algebra
$\sqrt{5x^2+14x+9}-\sqrt{x^2-x-20}=5\sqrt{x+1}$
obsidian monolithBOT
Fionna The Unemployed
west ice
I also have this
west ice
Yk unpaid labour type
wdym
frail lion
Like they don't require brain
frail lion
**Fionna The Unemployed**
Like see this
Take the second term in lhs to rhs
Square both side
Then jus solve solve
west ice
Yes you can, but these problem have time limit of only 10-20 min
And that's gonna be a quartic
frail lion
20 min too much
frail lion
And that's gonna be a quartic
Yeah ik
west ice
20 min too much
Give it a shot
frail lion
Okie dokie vroski
west ice
What I want to say is, there's a way to solve this in only 3min
But you could try what you said
frail lion
Wait fuck i fcked up in front of da homies
frail lion
I'm sowy too long equation
This is nothing triaengle
west ice
Yeah you're right mam
This's one of algebra problem types in Math Olympiad
frail lion
This is nothing triaengle
Forget it and don't tell subway
uncut star
Forget it and don't tell subway
Alright
I mean it isn't like I would have tried something different
west ice
So that's okay to not solve it 
frail lion
I mean it isn't like I would have tried something different
What
west ice
This looks interesting
a problem in BMO1 prep
frail lion
Otherwise you'll form a perspective
frail lion
a problem in BMO1 prep
Ok wait Fionna hold on
uncut star
Otherwise you'll form a perspective
Hmmm so I will assume hard
west ice
If you do induction proof it's not that hard
west ice
Ok wait Fionna hold on
Yes
uncut star
All terms except n+1 and some powers of 2 cancel
Is this correct
frail lion
Is this correct
Tell answer
west ice
All terms except n+1 and some powers of 2 cancel
could be
uncut star
Tell answer
Uh I will have to count the powers of 2
west ice
Have you guys seen this, if so Im gonna delete it
uncut star
<:happy:908558103992225822> Have you guys seen this, if so Im gonna delete it
I haven't
west ice
Sure take a good look and then I'll delete it
west ice
imma save this one for Astreae to try
frail lion
Whos astreae
obsidian monolithBOT
frail lion
Ok broski
uncut star
Correct
I find such problems luck based for some reason
It depends on what i try
And it feels like i just stumbled upon it
Well that seems to be the case with pretty much all of maths
west ice
Have any of you learnt 3D coordinate ?
uncut star
I haven't but sam probably has
west ice
I have a 3D coordinate problem if any of you want to try
frail lion
Send once
west ice
Do you guy learn the sphere equation?
frail lion
Do you guy learn the sphere equation?
Sphere equilibrium is crazy
west ice
It's math
obsidian monolithBOT
Fionna The Unemployed
west ice
frail lion
It's Math
Wait yeah
Then idk I'm doing 12th calculus now a days
I have 11 th too to manage
And 12th maths too
So it will take me time to reach
strong python
You're from 11th?
frail lion
You're from 11th?
Yeah
strong python
India
west ice
Yeah
frail lion
Yeah
strong python
Cool same bro
west ice
I only show those questions above to Indian
frail lion
I only show those questions above to Indian
Racism
west ice
Cuz no one in there mind willing to do it and have enough knowledge to do
Sure sure whatever
frail lion
Nah actually man only some people here in India are actually intelligent
Or have atleast basic civic sense
But yeah out of topic
frail lion
So it will take me time to reach
To reach 3d co ordinate
west ice
,ti
obsidian monolithBOT
The current time for fionna_fx is 11:50 PM (+08) on Mon, 03/11/2025.
uncut star
I only show those questions above to Indian
The racism is insane
frail lion
The current time for **fionna_fx** is **11:50 PM (+08)** on **Mon, 03/11/2025**.
Gah damn ok
sweet hearth
**Fionna The Unemployed**
This is a family of spheres I think
sweet hearth
I have never studied actual 3d geometry, but this closely resembles normal geometric problem atleast in its core logic,so I am gonna extrapolate from that
The point (E) and vector direction should give us the equation of the tangent in terms of s,we know that the sphere is at all moments passing through point M,so we need to find the equation of the family of spheres from these two things,the eq of the constantly moving tangent and the fixed point we already know(M)
than we would probably get the coordinates of the center(I) in terms of s,and we need to find a way to eliminate s using the fact that R is a known quantity perhaps? idk really
for the cone thing,we are already given the radius is constant,so essentially we need to form an equation between the height and radius of the cone with the radius of sphere,which comes out to be
R square= r square+h square.
after this we would probably need to eliminate h or r from the equation 1/3πr square h by putting the value from the equation we found, and than use some calculus or something to find the maximum volume
also btw I might be wrong about the family of spheres thing,i thought because we have a family of circles technically there should be a family of spheres,which is just a best guess
😭holy yap bro no one is reading that
uncut star
I got flashbanged
waxen peak
too white
clever fox
brisk dragon
whats the biggest tip you guys can give me for ap pre cal?
raw hill
<@&268886789983436800>
frail lion
😭holy yap bro no one is reading that
No bro I aim gonna read
frail lion
I got flashbanged
Man my reaction was same
wooden horizon
whats the biggest tip you guys can give me for ap pre cal?
Touch up on your algebra and trigonometry
brisk dragon
what books or lectures can you recommend for me
wooden horizon
Also watch professor Leonard on youtube.
cloud valve
Idk how to differentiate them and it’s my last attempt
I am actually struggling with matching graphs so bad
vernal grail
Also watch professor Leonard on youtube.
yo thats my goat 😋
sweet hearth
No bro I aim gonna read
so uhh did you read it
sharp wing
need help on solving x^3 - 3x less than our equal to sqrt(3)
sweet hearth
What exactly did you do? or like do you have any basic idea about what you have to do or do you have no idea at all?
fathom hearth
I am actually struggling with matching graphs so bad
im not even supposed to be here but curiousity got to the best of me, yeah this shit cooks my brain as soon as i look at it
lone temple
can ayone help me understand the dx in integral🥺
frail lion
so uhh did you read it<:flonshed:629835071465062410>
Yeah I read it