Also
#precalculus
winter comet
yYour an idiot ๐ค
winter comet
Isn't differentials Calc not precalc
precalc is everything under the sun
๐ตโ๐ซ
winter comet
Then why?
that time it treated e as a variable through and through
why it did it differently idk
elfin cargo
,w D[Power[e,x],e]
obsidian monolithBOT
elfin cargo
arctic dagger
Then why?
As cloud said, if u look closely, e looks the same
Euler e looks a little slant
I think
But it's not so obvious
It's not math anymore
It's forensics now
elfin cargo
Euler e looks a little slant
Yeah, I know about the font change but no idea why in my case it interprets e as a variable and not Euler constant
arctic dagger
Yeah, I know about the font change but no idea why in my case it interprets e as...
I did it look
,w de^x/de
obsidian monolithBOT
obsidian monolithBOT
elfin cargo
,w (d/de) (e^x)
obsidian monolithBOT
elfin cargo
elfin cargo
Did u do your query like that?
I try to use Wolfram Language but to no avail
,w D[Power[e,x],e]
obsidian monolithBOT
arctic dagger
Must be a bug
obsidian monolithBOT
obsidian monolithBOT
elfin cargo
,w D[a^x,a]
arctic dagger
,w d/di i^x
elfin cargo
,w D[i^x,i]
obsidian monolithBOT
obsidian monolithBOT
arctic dagger
,w d/dฯ ฯ^x
obsidian monolithBOT
arctic dagger
,w dฯ^x/dฯ
arctic dagger
Maybe special constant messes it up somehow
Looks like it's true
And here pi doesn't even look different
odd agate
i did NOT learn that in precalc
winter comet
Do u guys still remember numbers ?
nu- what now?
wicked sail
Oh sh...
winter comet
๐
winter comet
๐
stiff depot
river drift
it doesn't have to be a right triangle
tardy ridge
Calculus ruin lives .....
The fact this is considered intermediate math. I mean besides delta and optimization work, it's pretty normal if you know what you are doing.
winter comet
The fact this is considered intermediate math. I mean besides delta and optimiza...
yea ๐
wicked sail
Riemann hypothesis I solved it
river drift
vixra or it didn't happen
tame pine
Riemann hypothesis I solved it
But your proof would be too big so u leave it for the reader of your msg to prove it?
river drift
too big for the margins of a discord message ๐
wicked sail
I will solve riemann hypothesis and for that whether it takes my whole life
I will prove riemann wrong
I will work hard in mathematics ๐ฟ
ivory obsidian
I will work hard in mathematics ๐ฟ
Gambate
ivory obsidian
it doesn't have to be a right triangle
A trigonometry of a non right angle triangle?
I wanna know how we can solve this
willow skiff
A trigonometry of a non right angle triangle?
I wanna know how we can solve this
sine rule, cosine rule
ever heard of those before?
ivory obsidian
ever heard of those before?
Yes
rich spade
How do you solve math problems in the simplest way I always make it over complicated๐ญ?
willow skiff
Yes
there you go, that's what cloud was talking about
if tan is negative actually, that means that angle is obtuse (if it's in a triangle, so has to be less than 180 deg)
willow skiff
How do you solve math problems in the simplest way I always make it over complic...
practice, also worked solutions for similar problems can help
there's no shame in a long solution as long as you give problems a good attempt and reflect back on what you can do to make it more efficient
rich spade
It always happens with trigonometrical differentiations
willow skiff
It always happens with trigonometrical differentiations
oh like that's an odd one to overcomplicate
cause differentiation is just a set procedure
if you were overcomplicating say integration that would be much more understandable (and more challenging to improve upon)
you have an example or something?
harsh coral
Hi guys
I was wondering , why there is no voice channel here in this server ?
by the way , for people who love calculus , here u go :
harsh coral
integration by parts + u-sub
show me the solution please
harsh coral
btw, this is not precalculus
btw I don't know what do u mean by precalculus tbh , is is the primitive ?
signal fjord
Can u guys help me plot shaded sketch for qn2b and qn3
elfin cargo
btw I don't know what do u mean by precalculus tbh , is is the primitive ?
I have no idea what precalculus is either. Maybe it is something between algebra and calculus like trig function
odd agate
I have no idea what precalculus is either. Maybe it is something between algebra...
Yeah pretty much
The exact curriculum really depends on the school you take precalc at
elfin cargo
show me the solution please
I am too lazy to write the rest
shadow ether
I am too lazy to write the rest
This is calc literally stop using this channel for ut
elfin cargo
This is calc literally stop using this channel for ut
I just answered for the guy above.
winter comet
This is calc literally stop using this channel for ut
don't respond to the guy who responded, respond to the guy who brought it up๐
winter comet
I am too lazy to write the rest
i think you have to have a double integral
elfin cargo
i think you have to have a double integral
Wait what double integral?
winter comet
Wait what double integral? <:flonshed:629835071465062410>
not like i just meant you have to find the antiderivative of sin(x)/cos^4(x) dx before you integrate it
am i tripping
hold on
orchid nebula
i didnt know this channel existed
and i want to learn more pre calculus
i only know series and sequences ๐ฅฒ
winter comet
not like i just meant you have to find the antiderivative of sin(x)/cos^4(x) dx ...
u = x, dv = sin(x)/cos^4(x)
uv - int(vdu)
x int( sin(x)/cos^4(x) dx) - int( antiderivative of sin(x)/cos^4(x) dx)
elfin cargo
u = x, dv = sin(x)/cos^4(x)
uv - int(vdu)
x int( sin(x)/cos^4(x) dx) - int( anti...
Oh, yeah forgot about that. I am too lazy to u-sub sin(x)/cos(x)^4 
winter comet
๐
marble prairie
Heyy can someone help with the first one? I can't visualize how it increases until (0,1) but it starts concaving down at (0,-2)?
queen vale
primal skiff
someone explain what derivatives are. Isn't it the tangent point on a non-linear graph? When i put it in a graphing calculator, it comes up with a secant line intersecting 2 points.
winter comet
someone explain what derivatives are. Isn't it the tangent point on a non-linear...
did you graph the derivative function and the original function?
derivative functions give the slope of the line at each x point
winter comet
did you graph the derivative function and the original function?
so that wouldn't work
winter comet
yeah, it graphed f'(x) = 2x + 6
f'(x) gives you the SLOPES of the line at each point
so like at x = 0, f(x) = 9 and f'(x) = 6
which means the function value at x=0 is 9, and the slope of the tangent line at that point is 6
it doesn't actually give you the graphical tangent line
it gives you the slope of the tangent lines at each point
if you wanted to graph the tangent line at a particular point, you'd have to use linearization
scenic coral
someone explain what derivatives are. Isn't it the tangent point on a non-linear...
linear graphs have derivatives
non-linear graphs may or may not have derivatives
winter comet
non-linear graphs may or may not have derivatives
i dont think thats where the confusion is coming from but yeah thats true too
scenic coral
i dont think thats where the confusion is coming from but yeah thats true too
it's not, just adding to you
primal skiff
Ok thank you both
plush zephyr
I am happy
odd agate
I am happy
Congratulations!
willow skiff
I am happy
omedeto
proven night
Hello guys
odd agate
Ello
proven night
I am hs student and we skipped limits and just went straight to derivatives and soon will deal with integrals. I understand derivatives and can solve basic limits, but not mastered it and cannot solve harder ones
Should i master solving limits or just move on and dont waste time?
odd agate
Do you know directional limits?
proven night
Yes
odd agate
Youโll prolly be fine then
First unit of my calc class is mostly focused on teaching limits
Like if you have free time Defo work on limits
But you donโt need to worry about it too much
proven night
Do you know directional limits?
But not always can solve it without pluggin in x value that is approximately equal to it
odd agate
Can you give me an example of a problem that you donโt know how to solve?
proven night
It will take a second, i need to find it
odd agate
No worries
proven night
Can you give me an example of a problem that you donโt know how to solve?
This one
I tried cube difference first
Than l'hopitals
Both methods gave me the expression where x is present
What should i plug in instead of x?
1.999...?
Can it be solved without pluggin in something close to 2 from left side?
willow skiff
it diverges, because the degree of the numerator is larger than the denominator
3 > 2
odd agate
You need to manipulate the function until itโs non-fractional
willow skiff
this is the same limit as $\lim_{u \to 0^-} \frac{(u + 2)^3 - 8}{(u + 2 - 2)^2}$, where $x = u + 2$
obsidian monolithBOT
south
elfin cargo
Can it be solved without pluggin in something close to 2 from left side?
$\frac{x^3 - 8}{x^2 - 4x + 4}$
obsidian monolithBOT
Closer
willow skiff
**south**
so you will have a u^3 / u^2 = u term in there
but then you will also have a (3 * 2^2 * u)/u^2 term in there, which diverges
if you work it out it's u + 6 + 12/u
(8 - 8 = 0 so it cancels out)
proven night
it diverges, because the degree of the numerator is larger than the denominator
What is diverging?
English is not my first language, so might not know some terms
willow skiff
What is diverging?
the opposite of converging
proven night
The creators of this problem simplified the fraction to (x^2 + 4x +4)/(x - 2) and said that x^2 + 4x + 4 approaches 12 and (x-2) approaches 0-, so 12/0- = -infinity
proven night
The creators of this problem simplified the fraction to (x^2 + 4x +4)/(x - 2) an...
Photomath had the last step the same
@willow skiff What do you think of this solution?
willow skiff
The creators of this problem simplified the fraction to (x^2 + 4x +4)/(x - 2) an...
oh that makes sense
yeah that approach was in the back of my mind, recognising that x^3 - 8 is a difference of two cubes and hence divisible by x - 2
proven night
But, can we just say that if x approaches 2 from the left side, then x - 2 = 0-? Is it allowed on exams?
It doesnt seem like analytical solution to me
willow skiff
But, can we just say that if x approaches 2 from the left side, then x - 2 = 0-?...
yep
constant/0 is an undefined form
0/0 is different, like (x - 2)/(x - 2) if x approaches 2
here's a huge list
willow skiff
https://en.wikipedia.org/wiki/Indeterminate_form#List_of_indeterminate_forms
these are the ones that you need to simplify, such as by cancelling
constant/0 is one of them that you just know can't evaluate to any finite number
proven night
0/0 is different, like (x - 2)/(x - 2) if x approaches 2
I wondered why 0/0 cannot be determined. Is my assumption correct, that the numerator is any number approaching 0 and so is the denominator, but this numbers are not equal, so the numerator can be even bigger then denominator and 0/0 might equal, for example +infinity?
willow skiff
I wondered why 0/0 cannot be determined. Is my assumption correct, that the nume...
yeah exactly, it's about how fast each term is approaching 0 (or not)
proven night
yeah exactly, it's about how fast each term is approaching 0 (or not)
But somehow if they both approach for example 12, then the limit is 1
Right?
willow skiff
for example $\frac{x}{x}, \frac{x^2}{x} \cdots$
obsidian monolithBOT
south
willow skiff
But somehow if they both approach for example 12, then the limit is 1
yes
winter comet
I wondered why 0/0 cannot be determined. Is my assumption correct, that the nume...
0/0 cannot be determined itself, so you have to go back to the actual limit and reason out what the answer is like you did
proven night
But somehow if they both approach for example 12, then the limit is 1
But why?
willow skiff
if both limits exist, then you can apply the four operations normally
proven night
12/12 = 1, but 0/0 = inderminant
willow skiff
12/12 = 1, but 0/0 = inderminant
you'll find out in real analysis
proven night
Is it some university level math?
willow skiff
Is it some university level math?
this is about sequences but same idea
proven night
Thanks
willow skiff
knowledge of the triangle inequality would definitely help
as well as modulus properties
the trick to make all these work for limits is if $f(x) \to L$ for instance, then set $a_1 = L + 1, a_2 = L + 1/2, \cdots, a_n = L + 1/n$
obsidian monolithBOT
south
willow skiff
then you've converted a function to a sequence that converges to a limit point
if L + 1 doesn't exist in the range, then take L + 1/100, or L + 1/10000 or whatever, then do L + 1/20000, L + 1/30000
you get the idea
hollow ibex
What all things are considered precalculus?
winter comet
What all things are considered precalculus?
everything is precalculus
hollow ibex
everything is precalculus
Like, everything?
hollow ibex
Lol okay
sharp minnow
What all things are considered precalculus?
necro ping, but i didnt learn anything about limits in my honors precalc class lol
the most we did was the difference quotient and we didnt even cover what it did
storm lodge
everything under the sun ๐
fr
in #precalculus you dont get precalc
you only get things that are beyond the scope of it
hollow ibex
necro ping, but i didnt learn anything about limits in my honors precalc class l...
What age is precalculus?
viscid thistle
What all things are considered precalculus?
Everything that is not precalc, except these things, the rest is precalc
viscid thistle
if L + 1 doesn't exist in the range, then take L + 1/100, or L + 1/10000 or what...
The joy of x got kinda boring
willow skiff
The joy of x got kinda boring
RIP
sharp minnow
What age is precalculus?
I was ahead a year, so it was junior year of HS for me
winged epoch
Iโm taking calculus however I skipped precalc so Iโm catching up (mainly with trig). Do I need to learn how everything works, like why cos=adjacent/hypotenuse and stuff like that? I do want to learn the ideas behind these things but could I just get by knowing the different ideas
summer ruin
Do I need to learn how everything works, like why cos=adjacent/hypotenuse and stuff like that?
yes
winter comet
> Do I need to learn how everything works, like why cos=adjacent/hypotenuse and ...
i don't know exactly why cos = adjacent/hypotenuse and i'm doing fine... ๐
kinda thought its more or less defined that way ._.
daring tapir
kinda thought its more or less defined that way ._.
๐ it is though? i mean id say the taylor series defintion is more correct
winter comet
๐ it is though? i mean id say the taylor series defintion is more correct
i mean you could 'define' it in multiple ways but one of them would be adjacent/hypotenuse imo
daring tapir
i mean you could 'define' it in multiple ways but one of them would be adjacent/...
like no cuz adjacent/hypotenuse is only for like the a right triangle and hence the angle are also bound to be in (0,pi/2)
the unit circle
or the taylor series
winter comet
but you can rotate anywhere on the unit circle
daring tapir
or the complex number definition is more correct
winter comet
and you can construct a "triangle" no matter the angle
daring tapir
and you can construct a "triangle" no matter the angle
but thats essentially forcing it, and anyways just say its the unit circle definition at that point
winter comet
but thats essentially forcing it, and anyways just say its the unit circle defin...
yeah
which is practically just adjacent/hypotenuse
๐
like you can explain it a little more but theres no big WHY
daring tapir
lmfao i aint winning this xD
winter comet
thats just the way its defined
winter comet
lmfao i aint winning this xD
๐
daring tapir
like you can explain it a little more but theres no big WHY
pretty much yea
winged epoch
> Do I need to learn how everything works, like why cos=adjacent/hypotenuse and ...
I gotta read proofs? 
summer ruin
yes
glossy carbon
Iโm taking calculus however I skipped precalc so Iโm catching up (mainly with tr...
yeah
you should do pre calc
steep jetty
but you can rotate anywhere on the unit circle
trig is not only about unit circles
have you heard of hyperbolic trig functions?
winter comet
have you heard of hyperbolic trig functions?
yeah, but thats not regular trig like cosine ._.
glossy carbon
ugh
steep jetty
so irregular is hyperbolic ๐
glossy carbon
ugh
steep jetty
bro
winter comet
so irregular is hyperbolic ๐
when someone says trigonometry
you're going to think of unit circle trigonometry
not hyperbolic trigonometry ๐
my internet is wack
winter comet
so when someone says trigonometry it could mean either
it can..
steep jetty
but usually it means unit circle trig
not in advanced classes
but yes in lower classes
winter comet
not in advanced classes
ok...
steep jetty
and trig branches off of unit circles anyways it starts to go more into calculus to use
in algebraic trig in most problems only the identites are used
so yeah
trig is very vast
thats why its very fun
winter comet
trig is very vast
i don't disagree ๐
steep jetty
i don't disagree ๐
haha yes ๐
river drift
hyperbolic trig is the same as unit trig but imaginary
winter comet
hyperbolic trig is the same as unit trig but imaginary
imaginary?
the entirety of math is imaginary what are you talking about ๐
steep jetty
math is just perspective
winter comet
mhm
river drift
cos(ix) = cosh(x)
sin(ix) = i sinh(x)
winter comet
cos(ix) = cosh(x)
sin(ix) = i sinh(x)
oh right
glossy carbon
math is just perspective
no
objective truth
ugh
what are they teaching yโall in school
winter comet
a problem can be viewed in so many different ways
True, I look at you differently now...
winter comet
๐
glossy carbon
Itโs literally like Itachiโs infinite tsukuyomi
like no body cares how many guys you took on in different ways
damn get some dignity
hasty lily
math is just perspective
No?
hasty lily
a problem can be viewed in so many different ways
Doesnโt mean itโs โjustโ perspective
You missed important aspects of math
hasty lily
trig is not only about unit circles
Trig is about the exponential function duhh
arctic dagger
It's always been a mystery to me why our highschool trigonometry included exp and logs. I thought trigonometry was also used as a general term for such topics. Now i understand that there's an actual connection between exp/logs and trig functions
winter comet
It's always been a mystery to me why our highschool trigonometry included exp an...
i mean i kinda assumed they were taught as non-algebraic functions so kinda grouped into one category of learning...
arctic dagger
Oh yea that makes sense
steep jetty
fr canโt even look at this dude the same
bro
i wasnt talking to you so dont judge please if you are going to say things that can hurt
its a math server ๐
winter comet
i wasnt talking to you so dont judge please if you are going to say things that ...
this was a joke ๐ ๐
winter comet
dumb question my mind is blanking, (-infinity,-2) U (-2,2) U (2,infinity) as a domain means all real numbers excluding -2 and 2, right?
because the union means the numbers can appear in any of these sets...i think
scenic coral
dumb question my mind is blanking, (-infinity,-2) U (-2,2) U (2,infinity) as a d...
yup
river drift
you can also write it as R \ {-2,2}
obsidian monolithBOT
ืจื-ืืช
viral hill
loud cliff
It's always been a mystery to me why our highschool trigonometry included exp an...
Well log() does prepare one for the future in math. Like in cases where you figure out a difficult exponent.
arctic dagger
True
willow skiff
yes
uneven nexus
nvm im dumb
uneven nexus
how can i graph this by hand?
willow skiff
how can i graph this by hand?
sub theta = -pi/2, -pi/3, -pi/6, 0, pi/6, pi/3, pi/2 and join the dots together
btw I made this graph using the half angle sub
surreal crescent
how can i graph this by hand?
create a table with three diff lines theta, x, y, the find all the values of special right angles between -pi/2 amd pi/2, (prob just use pi/3) and graph the x and y
sweet grove
the handwriting is unreal HOWWWWWWW
:(
steep jetty
bro if we could use this on tests it would've been so nice
steep jetty
the handwriting is unreal HOWWWWWWW
\:(
i didnt even know it was someones handrwiting i thought it was typed
sweet grove
oh also why is it 0.360 deg
steep jetty
oh also why is it 0.360 deg
its 0, 360 deg because 0 degrees and 360 degrees mean the same thing on a unit circle but not necassarily on graphs
sweet grove
its 0, 360 deg because 0 degrees and 360 degrees mean the same thing on a unit c...
oh ok i thought it was a decimal 0.360 lol
steep jetty
oh ok i thought it was a decimal 0.360 lol
yeah lol its probably a comma
uneven nexus
how can i find the point M on the curve r^2=sin2theta with the maximum x-coordinate and determine its angle where is in the range 0โคฮธ <2ฯ?
willow skiff
how can i find the point M on the curve r^2=sin2theta with the maximum x-coordin...
x = r cos theta = sqrt(sin 2 theta) cos theta
differentiate and set to 0
also note that a shift $\theta \mapsto theta - \pi$ doesn't change the equation, so $r = -\sqrt{\sin 2 \theta}$ and $r = \sqrt{\sin 2 \theta}$ are the exact same curve
obsidian monolithBOT
south
uneven nexus
x = r cos theta = sqrt(sin 2 theta) cos theta
differentiate and set to 0
Could you Tex it?
obsidian monolithBOT
south
uneven nexus
Ooh
In polar coordinate, ฮธ is symmetric with respect to the origin in the first and third quadrants and ฮธ is not defined in the second and fourth quadrants?
willow skiff
In polar coordinate, ฮธ is symmetric with respect to the origin in the first and ...
yes, that's correct for this function if you graph it out
uneven nexus
I can't know this until graphing it?
willow skiff
I can't know this until graphing it?
o wait you can figure it out
yeah for sqrt(sin 2theta) to exist, sin 2 theta >= 0
so that excludes $\theta \in (\pi/2, \pi) \cup (3 \pi/2, 2\pi)$
obsidian monolithBOT
south
willow skiff
and then sin(theta) = -sin(theta + pi) so that explains the symmetry
daring tapir
and then sin(theta) = -sin(theta + pi) so that explains the symmetry
umm am i tripping or did you miss a negative sign
uneven nexus
how can i calculate the arc length of r=asin^3(theta/3)? from 0 to 3pi
daring tapir
how can i calculate the arc length of r=asin^3(theta/3)? from 0 to 3pi
from where to where?
the formula is
arclength = integral of (sqrt(1+ (dy/dx)^2)) dx
just apply this
um do you know theta = arctan(y/x) and r = (sqrt(x^2+y^2))
oh nvm you can just use the formula for polars
uneven nexus
arclength = integral of (sqrt(1+ (dy/dx)^2)) dx
you can never firgure it out with this formula, first you need to convert Polar to Cartesian Coordinates, then it'll be much of hassle, or else you can try, i failed this way
daring tapir
you can never firgure it out with this formula, first you need to convert Polar ...
yea just use the formula for polars
daring tapir
this one
shut quarry
is saying "stricly positive " the same as "bigger than 0" (not eq to 0)?
uneven nexus
how to find the total length of the curve y=$\int^x_{-\frac{\pi}{2}}\sqrt{cost}dt$
obsidian monolithBOT
miyo
storm lodge
this surely is precalc
daring tapir
this surely is precalc
i mean they asked the question i just helped-
storm lodge
its just funny
daring tapir
how to find the total length of the curve y=$\int^x_{-\frac{\pi}{2}}\sqrt{cost}d...
thats an unsolvable integral
storm lodge
how #precalculus is literally just a calc channel
daring tapir
how <#363224154469826562> is literally just a calc channel
xD i mean we have #calculus
but some people dont have uni channels
storm lodge
its just calculus but disguised as pre uni
daring tapir
soo they dont see it
uneven nexus
sorry i just remembered i learned that in hs so i asked in this channel
proven night
hello guys
i have to solve this logarithmic equation
5^(log x) = 50 - x^(log 5)
how do i solve it without sketching a graph
daring tapir
5^(log x) = 50 - x^(log 5)
Convert everything except the 50 into e^ln form
proven night
e^(ln 5 * log x) = 50 - e^(ln x * log 5)
daring tapir
e^(ln 5 * log x) = 50 - e^(ln x * log 5)
Write the log in ln form too
Or ln in log form
Your pick
daring tapir
You mean, i need to change the base of logarithm?
Yea
daring tapir
e^(ln 5 * (ln x / ln 10)) = 50 - e^(ln x * (ln 5 / ln x))
Notice how the variable terms are equal
proven night
e^(ln 5 * (ln x / ln 10)) = 50 - e^(ln x * (ln 5 / ln x))
here is just ln 5
daring tapir
e^(ln 5 * (ln x / ln 10)) = 50 - e^(ln x * (ln 5 / ln x))
And that should be ln 10
In the denominator
For the second one
proven night
so 50 - 5 in RHS, right?
daring tapir
so 50 - 5 in RHS, right?
No no
It should be
e* lnx * ln5/ln10
Since the base is 10
So yea
proven night
but ln x cancel each other
hasty lily
In the denominator
?
proven night
I mean, ln x * (ln 5 / ln x)
daring tapir
I mean, ln x * (ln 5 / ln x)
Thats not ln5/lnx though its ln5/ln10
daring tapir
the RHS is 50-5
They wrote it wrongly ๐ญ
hasty lily
They wrote it wrongly ๐ญ
Yeah
daring tapir
5^(log x) = 50 - x^(log 5)
.
Nd i just realised i shoulda have them use log instead of ln
But its alright
proven night
So what is rhs, did i make a mistake?
daring tapir
Thats not ln5/lnx though its ln5/ln10
Its this.
daring tapir
So what is rhs, did i make a mistake?
Yea
proven night
Yeah you are right
daring tapir
Hmm
proven night
e^(ln 5 * (ln x / ln 10)) = 50 - e^(ln x * (ln 5 / ln 10))
What should be done next?
daring tapir
e^(ln 5 * (ln x / ln 10)) = 50 - e^(ln x * (ln 5 / ln 10))
Notice the e^something terms are equal
So bring them to one side
Then ln the shit out of it
proven night
yeah, so if i bring them to one side, it will be e^((ln 5 / ln 10) * ln x) = 25?
daring tapir
Yea
proven night
okay then, just use ln on both sides
daring tapir
Yea
proven night
Thank you
Photomath didnt manage to solve it
But how did you understand how to solve it so quickly?
I mean, converting bases and logs using lns
daring tapir
I mean, converting bases and logs using lns
Thats like the general rule of the thumb, make sure the base is same for all the variable exponents and logs
And x^log(smthn) terms are ugly
So yea
proven night
Understandable
And, do you consider solving logarithmic and exponential inequalities an important part of precalculus?
I hate these types of inequalities, i more into equations
daring tapir
And, do you consider solving logarithmic and exponential inequalities an importa...
um im not from the US so i dont really know what is considered important there
proven night
Neither am i
daring tapir
isnt precalc like a majorly US term-
proven night
But, the thing is, i dont know what is the crucial point in math when i should switch to calculus
daring tapir
anyways i didnt see any use for that until like as much of calc 2 ive covered ๐
tho just know the basics
daring tapir
But, the thing is, i dont know what is the crucial point in math when i should s...
you can switch if you know basic definitions of everything and can deal with trig and exponentials rather easily
inequalities arent really used as far as i know but they are prolly needed for higher courses so idk about that
proven night
Okay, thanks
I am just trying to learn math beyond the scope of my math course in school
And there is no something kind of math roadmap, so
I am currently trying to get better at solving log equations and move to calculus, but i am already quite familiar with it apart from integrals
daring tapir
I am currently trying to get better at solving log equations and move to calculu...
๐ man been there i just kinda did whatever i felt like- so yea i have knowledge gaps but ehz for the important stuff it is almost always covered in something else you try to do so yea
proven night
So you just did whatever you like and didnt care much about possible gaps that didnt affect your overall math skills?
daring tapir
yea i wouldnt reccommend it tho ๐-
winged epoch
costheta = cos(-theta) because cos = x, and if theta is negative, x is still on the same position in the unit circle, which is why costheta = cos(-theta)?
and then similarly, sin(-theta) = -sintheta, because sin = y, -theta would mean a -y?
i'm not sure if i'm understanding correctly
daring tapir
costheta = cos(-theta) because cos = x, and if theta is negative, x is still on ...
cos = x?
winged epoch
yeah, the points on the unit circle are (x,y) = (costheta, sintheta)
daring tapir
yeah, the points on the unit circle are (x,y) = (costheta, sintheta)
๐ญ say that-
viscid thistle
yeah, the points on the unit circle are (x,y) = (costheta, sintheta)
We learned that in algebra 2
daring tapir
and then similarly, sin(-theta) = -sintheta, because sin = y, -theta would mean ...
and yes
viscid thistle
Yes bc in the unit circle, sin(-theta) would be sin(theta) flipped over x axis
You can tell from this visual
winged epoch
We learned that in algebra 2
i dipped from the end of the year last year when we were doing trig and now i'm playing catch up cause my calc teacher gave us limits with trig functions
winged epoch
Yes bc in the unit circle, sin(-theta) would be sin(theta) flipped over x axis
so why isn't it -sin(-theta)?
i understand why -sin but if the angle is negative why isn't it put there?
split reef
man im so confused bruh
river drift
so why isn't it -sin(-theta)?
well now you have a double negative so it cancels out
chilly salmon
what should i do first after doing caculus - differential equations or multivaribale calculus
hasty lily
what should i do first after doing caculus - differential equations or multivari...
Multivar
serene elbow
hii
willow skiff
what should i do first after doing caculus - differential equations or multivari...
both are fine, I actually enjoyed differential equations, cause of how applicable it is
multivar is also useful but moreso in a physics or engineering context
with multivar you'll be starting from unfamiliar territory and working your way deeper
with DEs it's not quite the case, cause somewhere you should have seen equations which are separable or linear first-order (y' + p(x) y = q(x))
river drift
what should i do first after doing caculus - differential equations or multivari...
multivar if you're choosing which do do first, diffeq if you're choosing which to do at all
wintry drum
cos theta = log theta base sin theta
Btw in the US, does Calc Honors have sequences, polar coordinates, conic sections, and vectors?
Idk what to try studying beforehand (yeah I know I can check khan)
rough sierra
Any 1 know how to do this
olive carbon
Any 1 know how to do this
literally just state between which x values f(x) is decreasing
negative slope
rough sierra
literally just state between which x values f(x) is decreasing
its confusing to me like writing it in this format
viscid thistle
iโm taking pre calculus in fall 2025
You've an fucking onlyfans brother?
fickle iron
You've an fucking onlyfans brother?
yes i make bread
viscid thistle
loaf
flint finch
willow skiff
Any 1 know how to do this
'when is the graph of x going down'
that's literally the question
viscid thistle
i got the wrong answer to this
the answer is option b but i don't understand why 4 is excluded
raw hill
the answer is option b but i don't understand why 4 is excluded
Open circle -> not included
viscid thistle
Open circle -> not included
okay i got it. My whole confusion arose because i forgot that the brackets were only meant for the end points and didn't explain the inclusion or exclusion of the rest of the elements in that interval.
winter comet
is it just me or does it look like 3.9 is not included instead of 4 ._.
viscid thistle
He a gay star I swear
Lol
mellow sorrel
I need help on this one because I don't understand it
daring tapir
I need help on this one because I don't understand it
what did you even say-
mellow sorrel
I need help on my homework because I can't really understaned it
daring tapir
I need help on my homework because I can't really understaned it
what you sent makes no sense whatsoever- so yea that might be the reason you dont get it
mellow sorrel
I know icos and sin but I'm unfamiliar with the capital sigma
mellow sorrel
what do you mean?
daring tapir
the image you sent means nothing
mellow sorrel
then how do I make it something?
willow skiff
yes i make bread
lol it's not a real profile, or otherwise mods would get onto you
willow skiff
I think an OF joke is in bad taste
cause there are people who could be 13 in here
you know all the Kris Tyson drama and now there's Jack Doherty's 'girlfriends' who are advertising OF to literal preteens and kids in their TikToks
not a good time to make this joke
viscid thistle
then how do I make it something?
Is that the complete question?
winter comet
do u think iโm 20 or smth
a 6 year old can make an inappropriate joke and its still inappropriate ._.
fickle iron
a 6 year old can make an inappropriate joke and its still inappropriate ._.
Buddy 13 year old are not babies
paper tartan
Buddy 13 year old are not babies
it does not matter
if it is against server rules, it is against server rules
winter comet
Buddy 13 year old are not babies
depends on the 13 year old... ๐
shadow summit
I need help on this one because I don't understand it
Is that floor(icos(20)+sin(20))?
rustic hatch
great now do the course challenge
aw hell na
id probably get like 1 or 2 wrong
and then itd level down ๐ฆ
also it takes 6900000 howers to complete
sinful halo
fr
makes you master the whole lineup when you only want to master one specific thing
sinful halo
lock in
spiral radish
is this doable in like 4 hours a day for 3 days if i know all the algebra :
- Solving and Graphing Equations and inequalities
A. Linear
B. Quadratic*
C. Exponential
D. Logarithmic - Operations with Expressions and Factoring
A. Polynomials
B. Rational Expressions
C. Long/Synthetic Division and Rational Root Theorem - Operations with Radicals and Laws of Exponents
A. Rationalizing Denominators
B. Operations with Complex Numbers - Functions, their Properties, and their Graphs
A. 12 Basic Functions
B. Operations with Functions
C. Compositions and Inverses
D. Transformations
E. Rational Functions
F. Even versus Odd Functions
G. Asymptotes - Solving Systems of Equations
- Trigonometry
A. 6 Trigonometric Functions and their Graphs
B. Unit Circle, including Coterminal Angles
C. Degrees versus Radians
D. Pythagorean Identities and Simplifying Trigonometric Expressions
E. Law of Sines and Law of Cosines
shadow summit
is this doable in like 4 hours a day for 3 days if i know all the algebra :
1. ...
No
Depends how in depth you go
willow skiff
is this doable in like 4 hours a day for 3 days if i know all the algebra :
1. ...
what do you mean by 'know all the algebra?'
fickle iron
if it is against server rules, it is against server rules
the fuck i didnโt break any server rules ๐คฆโโ๏ธ
paper tartan
the fuck i didnโt break any server rules ๐คฆโโ๏ธ
I did not say whether or not you did
fickle iron
I did not say whether or not you did
okay so why ru bringin it up
paper tartan
I simply said that the argument that 13 year olds are not babies is not a particularly strong one
and should not be used to justify what is allowed on the server
fickle iron
and should not be used to justify what is allowed on the server
okay so what does something being allowed in the server have to do with me saying 13yr olds arenโt babies
๐ญ๐คฆโโ๏ธ
paper tartan
I agree with south when he says this though
I think an OF joke is in bad taste cause there are people who could be 13 in here
fickle iron
i didnโt make any onlyfans jokes in the server
whatโs being in my profile โ me saying smth
paper tartan
okay so what does something being allowed in the server have to do with me sayin...
because this message is, to me, implying that it's okay to make these kinds of jokes because of your age
#precalculus message
paper tartan
whatโs being in my profile โ me saying smth
I agree, and I am not saying that you did
I do still sort of think that it's not a particularly funny joke to include in your profile, but I will not tell you what to do
daring tapir
is this doable in like 4 hours a day for 3 days if i know all the algebra :
1. ...
Most of it probably, but trig nah
rustic hatch
is this doable in like 4 hours a day for 3 days if i know all the algebra :
1. ...
pretty much
I did it in like 2 weeks for 30 minutes a day
muted aurora
guys is it possible to learn all of the listed topics in the picture before 2024 ends?
willow skiff
guys is it possible to learn all of the listed topics in the picture before 2024...
yeah
sinful halo
guys is it possible to learn all of the listed topics in the picture before 2024...
You got this bro
muted aurora
that seems a lot as i have adhd i can get carried away by other things easily :((
muted aurora
I'm still on domains and ranges which had been taught in senior secondary (high school)
digital fable
guys is it possible to learn all of the listed topics in the picture before 2024...
yes you can.... ๐
paper tartan
guys is it possible to learn all of the listed topics in the picture before 2024...
most certainly
you can do it even quicker than that, in fact
tough kestrel
guys is it possible to learn all of the listed topics in the picture before 2024...
Thatโs like where it starts to get kinda interesting so probably yes
heady brook
is this doable in like 4 hours a day for 3 days if i know all the algebra :
1. ...
W study plan. Although I'm not sure, you would have to be doing only a few questions each subject if you were going for 4 hours. I think this is doable, just make sure you spend more time on topics you arent as familiar with and less time on the topics you are more familiar with.
heady brook
guys is it possible to learn all of the listed topics in the picture before 2024...
yeah man, just hunker down and learn it. W you for taking the initiative to learn this
cerulean harness
does anyone know what the "this example is for" is referring to here
shouldnt the x is greater than or equal to be y ๐ญ
old linden
that seems a lot as i have adhd i can get carried away by other things easily :(...
Same
willow skiff
shouldnt the x is greater than or equal to be y ๐ญ
that's confusing
$x > 0$ and $x \le 0$ just means $x$ is all real numbers
obsidian monolithBOT
south
stiff sluice
lone dragon
How do I memorize the unit circle? Any tricks tips?
rigid cove
Wdym by memorise the unit circle
stiff sluice
Help
proven night
Are hyperbolic trig functions worth learning?
Are these just other ways of defining trig functions or are they a completely different thing?
lost junco
dire aspen
Are hyperbolic trig functions worth learning?
um depends if they are in ur syllabus
proven night
They aren't
dire aspen
i mean if ur rlly keen on learning them why not ig but if its like not needed right now then u shouldnt have to worry about it ur better off focusing ur learning on stuff thats actually relevant rn yk
wintry orbit
olive trellis
dark thorn
Iโve noticed a lot of word problems in general are geometrical if they go beyond simple algebra.
lapis sphinx
viscid thistle
Its not aljebra@lapis sphinx
rare stump
this seems calculus by looking at it
winter comet
this seems calculus by looking at it
its ordinary differential equations
odes
the odes part of odes and pdes
stiff sluice
If ( f ) is a function that satisfies ( x^2 \cdot f'(x) = 8 \cdot f(x) ) and ( f(2) = 1 ), then its Taylor polynomial of order 2 at ( x = 2 ) is ( P(x) = )
\begin{enumerate}[label=\alph*)]
\item ( 1 + 2(x - 2) + (x - 2)^2 )
\item ( 1 + 2(x - 2) + 2(x - 2)^2 )
\item ( 1 + 4(x - 2) + 2(x - 2)^2 )
\item ( 1 + 4(x - 2) + 4(x - 2)^2 )
\end{enumerate}
obsidian monolithBOT
เถเถเถ
stiff sluice
help please
hollow condor
If ( f ) is a function that satisfies ( x^2 \cdot f'(x) = 8 \cdot f(x) ) and ( f(2) = 1 ), then its Taylor polynomial of order 2 at ( x = 2 ) is ( P(x) = )
\begin{enumerate}[label=\alph*)]
\item ( 1 + 2(x - 2) + (x - 2)^2 )
\item ( 1 + 2(x - 2) + 2(x - 2)^2 )
\item ( 1 + 4(x - 2) + 2(x - 2)^2 )
\item ( 1 + 4(x - 2) + 4(x - 2)^2 )
\end{enumerate}
obsidian monolithBOT
Aaditya
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
stiff sluice
If ( f ) is a function that satisfies ( x^2 \cdot f'(x) = 8 \cdot f(x) ) and ( f(2) = 1 ), then its Taylor polynomial of order 2 at ( x = 2 ) is ( P(x) = )
\begin{enumerate}[label=\alph*)]
\item ( 1 + 2(x - 2) + (x - 2)^2 )
\item ( 1 + 2(x - 2) + 2(x - 2)^2 )
\item ( 1 + 4(x - 2) + 2(x - 2)^2 )
\item ( 1 + 4(x - 2) + 4(x - 2)^2 )
\end{enumerate}
obsidian monolithBOT
เถเถเถ
stiff sluice
help please
manic ledge
Is this okay notation? Domain: $\mathbb{R} \backslash { 0 }$. Can anyone else confirm that this means ||all real numbers except 0||?
obsidian monolithBOT
Primordial
worldly crater
What kind of formula could I apply for this question?
stiff sluice
- Let $f: \left[ 13, \frac{125}{2} \right] \to \mathbb{R}$ be defined by $f(x) = \frac{\sqrt{2x - 25}}{x}$. Determine the absolute extrema of $f$ and indicate at which points of the interval $\left[ 13, \frac{125}{2} \right]$ they are reached.
obsidian monolithBOT
เถเถเถ
stiff sluice
help please
rustic hatch
Is it a free course?
khan academy
stiff sluice
okay
rustic hatch
youll have to create an account
stiff sluice
can u send a link
rustic hatch
stiff sluice
so Is easier
rustic hatch
click courses
stiff sluice
okay
rustic hatch
and then go to your desired one
stiff sluice
rustic hatch
bruh
go to khan academt .org
there will be a button called courses at the top
you might need to sign up or smth
there will be a button called courses
just click that
get in
will be a list of courses
when you click the courses button
just choose the one tou want
coarse ginkgo
is the answer to this around 18.248?
rustic hatch
is the answer to this around 18.248?
why wouldn't they allow you to use law of cosines
just use it to check
anyways
you can use arctan I think
not arctan
uh
I forgot
its the same as polar coordinates
or rotating vectors
willow skiff
is the answer to this around 18.248?
,calc sqrt((9 sin(pi/3))^2 + (9 cos(pi/3) + 12)^2)
obsidian monolithBOT
Result:
18.248287590895
yes
rustic hatch
oh wait
just find the unit vector
cos(120), sin(120)
then match the magnitude
then distance
willow skiff
yes
coarse ginkgo
why wouldn't they allow you to use law of cosines
Itโs some physics math test to check our math skills for this year
willow skiff
Itโs some physics math test to check our math skills for this year
true in physics they want your ability to resolve vectors horizontally and vertically
tacit grotto
hello fellow pre-calc
users
whatever
uhh, perchance does anyone know where I can get practice problems for circles, parabolas, and ellipses?
word problems
daring tapir
uhh, perchance does anyone know where I can get practice problems for circles, p...
Level?
daring tapir
Uh isnt high school 4 years
tacit grotto
oh dam i didn't know google has these practice problems
daring tapir
No not like google itself but therell be some site
opaque arch
People, i need help, i am doing this exercise from Khan Academy, Probability using combinations
the task is, find the probability of flipping exactly 3 heads from 8 coin flips
talking about combinations i think i understand them in case with unique items, lets say we have 8 people (ABCDEFGH) and we have to choose only 3, so how many unique groups of 3 people can we choose having 8 people
8! = 40320, which is number of all possible arrangements of 8 people . since we dont need a group of 8, we need a group of 3, we divide 8! by 5!, so we cut 5x4x3x2x1
now we have 336, which is a number of all possible arrangements of 8 people in a group of 3, e.g. ABC, BCA, CAB, DHG etc. Since order is not important and 3 distinct items can create 3! = 6 possible arrangements, we divide 336 by 3! and get 56 distinct groups of 3 different people. ABC, ABD...etc CBA e.g. is not included, cause we collapsed all arrangements of 3 with same items. This is more or less clear
With coins .... is not the same, but in terms of formula it is same its 8!/3!x5! then divided by 256
if we have a coin and flip it 8 times we have 2x2x2x2x2x2x2x2 = 256 possible outcomes, TTTH HHTT, or HHHT THTH etc, 256 unique outcomes
in formula 8!/3!x5!, 8! is all arrangements of positions of flips, if we name positions as 1,2,3,4,5,6,7,8, and this part is confusing to me,
8!/5! is 8x7x6 which is 336, which is all possible arrangements of any 3 flips, from possible 8,,,?
then we divide by 3! and get 56, which is amount of 3 heads...how?
viscid thistle
,calc (4/5)^-1
obsidian monolithBOT
Result:
1.25
Explanation?
elfin cargo
Explanation?
$(\frac{4}{5})^{-1} = \frac{5}{4}$
obsidian monolithBOT
Closer
viscid thistle
$(\frac{4}{5})^{-1} = \frac{5}{4}$
Perfect
So it changes the position
,calc 64^(1/3)
obsidian monolithBOT
Result:
4
,calc (25/16)^(-(3/2))
obsidian monolithBOT
Result:
0.512
,calc sqrt(27)
obsidian monolithBOT
Result:
5.1961524227066
,calc 3*sqrt(27)
obsidian monolithBOT
Result:
15.58845726812
just asking on behalf of someone else, are you able to post an image in this channel?
proven night
Hello
How do i know whether i am ready to move to Calculus? I have already have a good grasp of what limits are, i can find functions extrema, solve basic optimization problems, but i dont know whether i have covered all essential precalculus topics. So are there any kind of precalculus roadmaps or something so that i can know what i missed and should master
willow skiff
How do i know whether i am ready to move to Calculus? I have already have a good...
read through this and see how many of these misconceptions/errors you are making
also there are a list of common calculus errors which should be useful
proven night
thanks a lot, but are there a list of topics that are usually covered in precalculus course?
proven night
https://www.siue.edu/~zagusti/Math150F08/Common_Math_Errors.pdf
i mean, these are common mistakes
willow skiff
thanks a lot, but are there a list of topics that are usually covered in precalc...
no, it varies too much to say
like maybe you can go back and study matrices, the four operations and solving 2x2 equations using matrices
or you could study conic sections, focus and directrix of an ellipse, parabola, and hyperbola and their equations
but I hardly think that would be necessary for calculus
those are just bonus topics that don't really fit anywhere and that's why they're taught at this level
for example there is a list of topics here
but who can say that list or any other list is authoritative
proven night
thank you
proven night
By the way, if i can solve exponential equations / inequalities, logarithmic equations/inequalities, trig euations, can i move to calculus? Are these the harderst topics in precalculus?
willow skiff
By the way, if i can solve exponential equations / inequalities, logarithmic equ...
there is harder but I'd say you have all the fundamentals, you're ready for calculus bud
just make sure you didn't rush over those topics and that you studied them well
taking in a lot of different examples and learning from those problem-solving techniques, so that yourself can do them well
quality > quantity
opaque arch
just asking on behalf of someone else, are you able to post an image in this cha...
no idea
opaque arch
People, i need help, i am doing this exercise from Khan Academy, Probability us...
no need to explain, i think i got it...)
gentle blade
hello im looking for help on pre calc ]
i am very confused
would these be my inflection pointsw
pulsar vessel
Trying to work out a similar problem but mine is in meters. Can I ask why my professor put -1/2 in front of (32)t^2?
Like would I need to do -1/2(9.8)t^2 for my problem in meters?
night herald
Trying to work out a similar problem but mine is in meters. Can I ask why my pro...
As for the why is there a -1/2 in front of (32)t^2, you will surely know the equation of motion is s = ut + 1/2(a)(t^2), thus the 1/2 and there is a minus because the velocity is in upward direction and and the acceleration due to gravity and displacement are in downwards direction. Also because the problem in the picture gives us the quantities in feet, we use g = 32 ft/s^2, but in meters it converts to g = 9.8 m/s^2 or for simplification g = 10 m/s^2
arctic dagger
would these be my inflection pointsw
Middle is correct. Do you know what inflection points are?
willow skiff
while eating chicken i became enlightened
wild
willow skiff
while eating chicken i became enlightened
2nd derivative = 0
means d/dx (f'(x)) = 0, 2nd derivative is the derivative of the first derivative
so that's when the derivative = gradient of the graph isn't changing
or when a tangent line fits the graph really well, cause the gradient of a straight line doesn't change
brazen valley
2nd derivative = 0
means d/dx (f'(x)) = 0, 2nd derivative is the derivative of t...
2nd derivative zero <== point of inflection
but not necessarily the other way round
rancid panther
arctic dagger
We need a pinned reference for conics equations
willow skiff
2nd derivative zero <== point of inflection
Really? How isn't it an if and only if
Oh wait
brazen valley
If the 2nd derivative is zero it can be a minimum, maximum or a point of inflection
Try x^4 for example
at x=0
willow skiff
Right yeah you could have x^2 at x = 0
brazen valley
yeah
willow skiff
Yeah the test is inconclusive got it
brazen valley
u need to do higher derivative tests
or just check points on either side
If the third derivative was non zero then it would be a point of inflection
If the third derivative was zero as well as the second
Then itโs a min or max
brazen valley
If the third derivative was zero as well as the second
An intuitive explanation for this is like
A point of inflection is where the second derivative changes sign
If the third derivative is zero at this point then the second derivative is not changing
itโs a stationary point in the second derivative
So it cannot change sign at this point
eternal belfry
can someone explain how to slove this
willow skiff
can someone explain how to slove this
$2 = \sqrt{m - 4} \implies 4 = m - 4$
obsidian monolithBOT
south
willow skiff
square both sides
eternal belfry
thankyou
willow skiff
npnp
willow skiff
thankyou
you know what would happen if we had $-2 = \sqrt{m - 4}$ instead?
we would still get $4 = m - 4$ actually
obsidian monolithBOT
south
willow skiff
so after squaring both sides and solving
ALWAYS sub your value back into the original equation
to check it
cause -2 is not sqrt(8 - 4)
but 2 is sqrt(8 - 4)
unique candidate that fails
mellow sorrel
**Closer**
can you please explain your answer?
elfin cargo
can you please explain your answer?
Do you know about: $a^{-1} = \frac{1}{a}$
obsidian monolithBOT
Closer
dawn jasper
how do i go about learning calclulus?
summer ruin
watch lectures, read a book, do exercises, repeat
willow skiff
find a copy of Stewart's Calculus if you have no idea
I mean Khan Academy is decent for calc I
viscid thistle
What are minimum points? it's just popped up in a question and I haven't learned about it yet
willow skiff
What are minimum points? it's just popped up in a question and I haven't learned...
points where the function is at a minimum
pretty self-explanatory
for example, you can find the minimum point of the quadratic y = ax^2 + bx + c without calculus, if a > 0 ofc
sub in x = -b/(2a)
but for other types of functions you need calculus
viscid thistle
Oh damm, I thought it would be something crazy lol
willow skiff
lol
viscid thistle
So it's just (kinda) error bounds?
willow skiff
So it's just (kinda) error bounds?
how is that related to error bounds?
viscid thistle
Idk my brain just drew a line
viscid thistle
how is that related to error bounds?
(Good point)
So like how would I do this (i)
willow skiff
So like how would I do this (i)
is that A level maths
willow skiff
So like how would I do this (i)
,rotate
obsidian monolithBOT
willow skiff
you should learn the sum rule, constant multiple rule, and power rule for calculus first
then come back to this question
viscid thistle
is that A level maths
Level 2, so GCSE further maths
willow skiff
Level 2, so GCSE further maths
ah that makes more sense
hasty lily
This is also calculus
night herald
for minimum point or minima dy/dx = 0, and second derivative is positive at the point where the first derivative is 0.
dy/dx gives you the slope of the tangent at a certain point(the point provided), hence the tangent and the normal form a 90 degree angle the products of their slopes will be equal to -1[(m1)(m2) = -1], from here you find the slope of the normal line, to form the actual normal line, just put the given point in the original equation for an (x,y) satisfying the given equation. You now have the slope and a point satisfying the normal line, use the slope point form, which is --> (y-y1) = m(x-x1), to find the equation of the normal line.
Hope this helps
uneven nexus
Might be a silly question, how can we determine the monotonicity of cos(sinx) ?
willow skiff
Might be a silly question, how can we determine the monotonicity of cos(sinx) ?
on which interval?
night herald
just tell on any one there is period of pi
night herald
no pi
night herald
Yeah, isn't it clear
the period is pi
it repeats after pi
[0, pi/2] or [pi/2, pi] these are the intervals are in which function is increasing or decrasing(strictly)
willow skiff
[0, pi/2] or [pi/2, pi] these are the intervals are in which function is increas...
yeah exactly
periodicity is something completely different
night herald
I know that, i just meant that is the period of function is of pi, then we can split it based of points for which first derivative is 0
willow skiff
Might be a silly question, how can we determine the monotonicity of cos(sinx) ?
you can prove that in general, if g(x) is decreasing and f(x) is increasing, g(f(x)) must also be decreasing
night herald
Oh, I have definitely read that somewhere
willow skiff
$x_1 < x_2 \implies f(x_1) < f(x_2)$
$g(f(x_1)) > g(f(x_2))$, sub $ f(x_1) < f(x_2)$ in
obsidian monolithBOT
south
night herald
https://math.stackexchange.com/questions/813301/f-is-strictly-increasing-and-g-i...
must have slipped my mind
willow skiff
cause the definition of a decreasing function is if a < b, then g(a) > g(b)
cool nw
steel forge
can someone explain the formula for sigma notation? also idk if itโs considered pre calc or algebraโฆ?
river drift
sigma notation is just a way of denoting a sum. for a simple example:
,, \sum_{\underbrace{n = 1}_{\text{start}}}^{\overbrace{3}^{\text{end}}} n^2 + 2n + 3 = (1^2 + 2\cdot1 + 3) +(2^2 + 2\cdot2 + 3) + (3^2 + 2\cdot3 + 3)
obsidian monolithBOT
cloud
river drift
so we are starting with the variable n being 1, then adding up the formula for every value of n until we hit the ending value of 3
gusty storm
can you tell me what application(or whatever) is this
daring tapir
can you tell me what application(or whatever) is this
Desmos
uneven nexus
Is the derivative of a non-odd, non-even function also a non-odd, non-even function, or is it an odd/even function?
or it can vary, any cases is possible?
twilit eagle
viscid thistle
Can someone explain how you get x>1 from 2x-2รทx^2>0
summer ruin
$2x - \frac{2}{x^2} > 0 \iff x > \frac{1}{x^2} \iff x^3 > 1$
obsidian monolithBOT
Transparent Elemental
viscid thistle
Ok, ty
verbal rock
y is there none in pre-university
dense sage
this is pre university calculus
verbal rock
here?
dense sage
yeppp
verbal rock
ohh kk
for qs like this whats the difference between
minimum and maximum
ohh is it like
dense sage
whats the standard equation of circle of this general equation
verbal rock
if it x^3 then theres 3 stationary points
summer ruin
whats the standard equation of circle of this general equation
complete the square
dense sage
minimum and maximum
minimum meanโs cannot be lesser than the given, maximum means cannot exceed or more than the give
verbal rock
minimum meanโs cannot be lesser than the given, maximum means cannot exceed or m...
watr
whats my teacher doing here
viscid thistle
whats my teacher doing here
looks like theyโre creating a sign graph for fโ(x) to ascertain the nature of stationary points
verbal rock
looks like theyโre creating a sign graph for fโ(x) to ascertain the nature of st...
is there a different way to do it
or is that the only way
viscid thistle
i would say itโs one of the easier ones
verbal rock
i dont like it ๐ข
viscid thistle
feel free to find your own preferred way
verbal rock
feel free to find your own preferred way
whats the next eaisest way
verbal rock
thats easier
willow skiff
note that if f''(x) = 0 the test is inconclusive
(consider f(x) = x^2, x^3, -x^2)
cool
hoary iris
$n! = \prod_{i=1}^{n}i$ for $n > 0$
Is this correct?
obsidian monolithBOT
KingDanger
hoary iris
<@&286206848099549185>
tall folio
**KingDanger**
better say n>1
keen hull
Yeah because 0! Is also 1
keen hull
And a sum from 1 to 1 is just not nice looking
hoary iris
$n! = \prod_{i=1}^{n}i$ for $n > 1$
obsidian monolithBOT
KingDanger
tall folio
**KingDanger**
it is not a concrete definition I say
tall folio
Yeah because 0! Is also 1
due to this fact
hoary iris
**KingDanger**
Can this be definition for factorials?
tall folio
Can this be definition for factorials?
It works for all positive integers though
hoary iris
it is not a concrete definition I say
Then what is the concrete definition?
tall folio
Then what is the concrete definition?
actually idkโ ๏ธ
valid gulch
$n! = 1 * 2 * 3 * ... * (n-2) * (n-1) * n$ or $\prod_{i=1}^{n}$ for $n > 1$
obsidian monolithBOT
TLauncherGD
tall folio
Then what is the concrete definition?
some people say Pi function, but IDK if it is the right place to state it
hasty lily
**KingDanger**
for n >= 0
hasty lily
$n! = 1 * 2 * 3 * ... * (n-2) * (n-1) * n$ or $\prod_{i=1}^{n}$ for $n > 1$
The first one is unnecessarily expanded
@tall folio ?
valid gulch
The first one is unnecessarily expanded
yeah
hasty lily
It's correct
tall folio
The first one is unnecessarily expanded
can't have 0
hoary iris
But 0! =1
tall folio
<@809691997672964096> ?
what?
tall folio
for n >= 0
yeah this statement is false
tall folio
Let me ask you a simple question
ok
obsidian monolithBOT
Catgod
tall folio
**Catgod**
it is dumb notation nothing else
hoary iris
Substitute 0 in (n+1)! = (n+1)(n!)
hasty lily
it is dumb notation nothing else
It's still valid
thus the product notation for factorial works with 0
tall folio
https://en.wikipedia.org/wiki/Empty_product
here, they stated that P_0 =1, separately
you can't include it in the product
hasty lily
here, they stated that P_0 =1, separately
hasty lily
you can't include it in the product
A product that has no term has the value of 1
a product over an empty set, rigorously
tall folio
A product that has no term has the value of 1
okay I'm not smart enough but lemme ask someone else
hasty lily
okay I'm not smart enough but lemme ask someone else
Then don't incorrectly correct someone
tall folio
Then don't incorrectly correct someone
wait a min
hasty lily
$\sum_{i=1}^{0}i$ is 0 by the way
obsidian monolithBOT
Catgod
hasty lily
hoary iris
@hasty lily you're super fast! ๐๐
hasty lily
Yeah
hoary iris
Substitute 0 in (n+1)! = (n+1)(n!)
Is this correct explanation?
hasty lily
But my mathematics book gave this as a proof for 0 factorial is 1
It's hand wavy but it sorts of work
depends on how your book defines factorial
