fudge
#precalculus
tight compass
Can you post you work. for taking the derivative of both side of f(x^2) = f(x) + x^2.
That might be where your stuck at.
viscid thistle
sure give me a sec
river jasper
Or is f(x^2)=f(x)+x^2 satisfied by a fixed x?
viscid thistle
I know im wrong
cause there should be an x somewhere in the equation i think
ohhh
tight compass
Or is f(x^2)=f(x)+x^2 satisfied by a fixed x?
The thing is f is not defined for x = 1 since we have 0 = 1. But the domain for the derivative of f is not necessary the domain of f. Take the example of f(x) = |x|, f here is not differentiable at x = 1.
tight compass
derivative of f(x^2) = 2xf'(x^2).
tight compass
Then you just need to plug in x = 1.
river jasper
The thing is f is not defined for x = 1 since we have 0 = 1. But the domain for ...
I get it, but if f’(1) is defined wouldnt then f(1) have to be defined?
viscid thistle
Then you just need to plug in x = 1.
I don’t plug 1 into 2x right?
tight compass
I don’t plug 1 into 2x right?
You do, but that is not what you had for that line.
You will end up with 2xf'(x^2) = f'(x) + 2x.
For x = 1, we have 2f'(1) = f'(1) + 2.
Surely you can find f'(1).
Sorry giving you the answer since I have class soon.
tight compass
I get it, but if f’(1) is defined wouldnt then f(1) have to be defined?
Not necessary.
viscid thistle
You do, but that is not what you had for that line.
You will end up with 2xf'(x^...
Ahh all good. I already got the answer before. But x^2 doesn’t seem to work?
tight compass
I can't expand on that right now since I am about to drive off to class. I hope someone comes along.
Referring to Takumi.
river jasper
Ok thanks
viscid thistle
Ok thanks
i don;t think i can get it
what is the answer to this?
cause i got f'(1)=2
but that means f(x)=x^2
And that doesn't work
graceful fern
hello i need some help
my question is S(-6x³+9x²+4x-3)dx
how is -6x³ = - 3x⁴/2? and not - 6x⁴/4
willow bear
aside from your misuse of the equals sign,
-3x^4/2 and -6x^4/4 are one and the same
@graceful fern
vivid void
doing integrals but can’t do fractions
graceful fern
doing integrals but can’t do fractions
thats my problem
its just fractions
i can do cos and sin but not fractions
vivid void
well then you know what you need to get good at then
doing calculus when you can’t even do fractions is just
a terrible idea
graceful fern
yep
thats why im asking help
but u guys wont help me but instead give me life lessons which im not here for
graceful fern
well then you know what you need to get good at then
so can u help me with calculus fractions?
vivid void
no because i don’t feel like it right now
graceful fern
well ill ask others then
willow bear
no such thing as a "calculus fraction" tbh
graceful fern
no such thing as a "calculus fraction" tbh
sure buddy can u help me tho?
proud raven
use linearity and the power rule
proud raven
$\int\qty( x^{\sfrac 2 3} + 2x + 3 )\dd x$
obsidian monolithBOT
jan Niku (join us for @pomo)
graceful fern
use linearity and the power rule
Can u explain what that means
vivid void
parentheses aren’t required 
graceful fern
I know that the power is n+1
willow bear
linearity is $\int (f(x) + g(x)) \dd{x} = \int f(x) \dd{x} + \int g(x) \dd{x}$, or in other words that integration distributes over sums
obsidian monolithBOT
Ann
willow bear
(to be more precise this is just additivity; sth else that needs mentioning is the ability to factor out constants)
given that you are doing integral calculus you have some familiarity with derivatives, yes? @graceful fern
graceful fern
Ye
willow bear
okay
graceful fern
But idk what anti derivatives are
willow bear
so you know that differentiation also obeys linearity, yes?
graceful fern
Linear and quad
Idk what the difference between obeys and linearity
Idk obeysbut ik linearity
graceful fern
Ok
willow bear
you know how $(f+g)' = f' + g'$ and $(cf)' = c \cdot f'$ where $f$ and $g$ are functions and $c$ is a constant, yes?
obsidian monolithBOT
Ann
willow bear
yes.
graceful fern
The*
willow bear
these two properties are succinctly summarized as saying that differentiation is a linear map.
graceful fern
Ye ik what about it
willow bear
my point is that the same rules hold for integration
graceful fern
Okay
willow bear
and as far as symbolpushing goes, this means that if you have the integral of a sum, you can integrate each term separately and add up all the results and that'll be the integral of the whole sum
meaning that to find $\int (x^{2/3} + 2x + 3) \dd{x}$ you need to know how to integrate $x^{2/3}$ and how to integrate $2x$ and how to integrate $3$.
obsidian monolithBOT
Ann
graceful fern
2x power of -3?
willow bear
??
willow bear
do you know how to find $\int x^p \dd{x}$?
obsidian monolithBOT
Ann
graceful fern
x p+1/p+1?
willow bear
x^(p+1)/(p+1).
graceful fern
+c
willow bear
missing parentheses
graceful fern
O
graceful fern
x(2/3)+1/(2/3)+1 = 5/3
graceful fern
x(5/3)
graceful fern
what cha mean
willow bear
there are some symbols that you ought to be writing that you are not writing
graceful fern
Im on phone so yea
willow bear
....
willow bear
is that "u" as in me specifically, or a generic you
willow bear
no, i want you to explain what you mean.
but nevermind
i'll just assume (by necessity) that you mean me specifically
graceful fern
Ye
willow bear
$\int (x^{2/3} + 2x + 3) \dd{x} = \frac{3}{5} x^{5/3} + x^2 + 3x + C$
obsidian monolithBOT
Ann
willow bear
i would just go directly to the answer, seeing as i am fluent enough in fraction arithmetic to know that 2/3 + 1 = 5/3, that the reciprocal of 5/3 is 3/5, and that 2/2 is 1, and that multiplying something by 1 leaves it unchanged
willow bear
$\int (x^{2/3} + 2x + 3) \dd{x} = \int x^{2/3} \dd{x} + \int 2x \dd{x} + \int 3 \dd{x}$
obsidian monolithBOT
Ann
graceful fern
Ye btw dont worry ik what reciprocal means
willow bear
you KNOW what reciprocal means, and yet you act as if you DON'T???
that's obnoxious at the very least.
but ok.
graceful fern
Ok so
willow bear
$\int x^{2/3} \dd{x} = \frac{x^{\frac{2}{3} + 1}}{\frac{2}{3} + 1} = \frac{x^{5/3}}{5/3} = \frac{3}{5} x^{5/3}$
obsidian monolithBOT
Ann
graceful fern
I add 1 then reciprocal it then use the recirpocal as my x
willow bear
.........................
graceful fern
**Ann**
Perfect explanation
That was exactly what i wanted
Tysm i appreciate u helping
willow bear
i can't help but think you don't mean any of that
and that you're only saying that sarcastically
graceful fern
I aint have time to be sarcastic
I dont joke
Anyways im gonna eat my breakfast
Have a nice day
uncut mulch
what seems to be your issue with these
tawny dirge
the radicals
idk how to solve them
i know we use distributive property
but aaaa
@uncut mulch
vivid void
do you recognize a(b+c) = ab+ac
the same thing is used here, just that a equals something a tiny bit more complex than a normal number
so in that first one, you have a = 1+i*sqrt7
the law a(b+c) still holds here
tawny dirge
i dont understand
uncut mulch
would you be able to expand
(a+b)(c+d)
(something with no radicals or complex numbers)
tawny dirge
yes?
uncut mulch
apply that to your question
if you are unable to simplify certain products just leave them as they are for now
and show us what you're able to do
clear venture
is arctan infinity equals pi/2
slate reef
is arctan infinity equals pi/2
yes
vivid void
is arctan infinity equals pi/2
no because infinity isn’t a number
,w lim as x approaches infinity of arctan(x)
obsidian monolithBOT
coarse swan
is this correct?
fair cave
is this correct?
yupp looks correct
rocky wind
,w sin(A+B) where sin(A) = -6/7 and tan(B) = 2/3
obsidian monolithBOT
rocky wind
,w sin(A+B) where sin(A) = -6/7, 3pi/2 <= A <= 2pi, tan(B) = 2/3, pi <= B <= 3pi/2
obsidian monolithBOT
rocky wind
,w sin(A+B) - (18sqrt(13)-26)/91 where sin(A) = -6/7, 3pi/2 <= A <= 2pi, tan(B) = 2/3, pi <= B <= 3pi/2
obsidian monolithBOT
viscid thistle
,w sum
obsidian monolithBOT
viscid thistle
,w k = 0 x.k
obsidian monolithBOT
viscid thistle
,w sum k = 0 x.k
obsidian monolithBOT
viscid thistle
,w f(x)= 4x
barren comet
I'll keep this in mind. Thanks.
turbid bane
can someone help with this
viscid thistle
who's tryna carry me in doing my 4 questions of precalc?
granite ice
who's tryna carry me in doing my 4 questions of precalc?
send over the questions i see if i can help
empty plume
is this correct?
That's all what you had to do in this question
empty plume
can someone help with this
Just differentiate profit function with respect to 'x' and then equate it to Zero to find Maxima. That will give you the maximum value which will be 20.
rose crown
how do you know what a general formula for your capital in future years with and interest rate of 0,04 and in year 0 your capital is 1207 euros
how do you know this is 1207 + 0,04^n
in general, what are ways to find a formula for sequences
can someone explain how this simplification is done?
obsidian monolithBOT
waris
rose crown
thank you
chrome grail
The inverse of the 2x2 identity matrix is itself right?
Or does it not have an inverse?
willow bear
the identity matrix is its own inverse yes
empty plume
The inverse of the 2x2 identity matrix is itself right?
Yes.
chrome grail
Ty
plucky slate
where are the global maximum points in this graph?
the obvious one is when x is 1, but what about when x is 5 or 7?
edgy blaze
2sin(3x) + sin(2x) + 1 = 0
is there actually a way to do this? I think they must have written it wrong because I'm not seeing how it works with 2x and 3x
viscid thistle
I got all of these wrong, how tf do u do it
tight compass
I got all of these wrong, how tf do u do it
Number 1,3,4 just requires looking at the graph of f to find the value f at a given x. Then you just scale it the value you got by 2 and -1/2.
What was your initial solution and reason for choosing that solution? So we can understand what you did wrong.
Number 2) just requires understanding function transformations. Here’s a source, trying going through it and try again to answer that question.
viscid thistle
Number 1,3,4 just requires looking at the graph of f to find the value f at a gi...
these were my answers for the questions
I got all of them wrong
tight compass
Ok, let’s tackle number 1.
Why did you decide f(3) = 4?
Look at the graph for f.
The tick marks values for the vertical axis is increasing by 1.
viscid thistle
is the answer 2
tight compass
Yes.
tight compass
Why do you have doubts that it’s not 2?
viscid thistle
my professor puts trick questions on exams sometimes
tight compass
No tricks to this.
viscid thistle
this is pre calc at a community college
tight compass
Ok let’s move on to number 2.
tight compass
Number 2) just requires understanding function transformations. Here’s a source,...
Did you read this link I send.
tight compass
Yep, the graph of f is shifted by 1 units to the left.
So what do you think g(0) is?
tight compass
i did 0 - 1 and that's how i got -1
If it was g(x) = f(x) - 1 then yeah.
tight compass
So what do you think g(0) is?
So what do you think?
tight compass
is it just 1 then?
No. I was mistaken. You don’t really have to think of function transformations in this one.
hushed sphinx
For 2 why speak of shifting left or right instead of just applying the definition?
hushed sphinx
g(0) = f(0+1) = .... ?
viscid thistle
is it just f(1)?
tight compass
Yeah.
tight compass
Look at the graph of f.
viscid thistle
2?
tight compass
Yes.
viscid thistle
so 2's the answer?
tight compass
Yes it is.
The rest of the problem just requires look at that graph and figuring out the value.
tight compass
Yep.
viscid thistle
I just find it confusing how he made f(x) into things like h(x) and g(x)
is -1 the answer for 4 btw?
I wanted to major in math but this shit is not for me
im good at algebra but shit at these graphs + transformations
tight compass
is -1 the answer for 4 btw?
Yep.
See your understanding it.
This is all part of the learning process. Don’t feel discouraged.
Just keep practice sooner or later it becomes trivial and you start wondering why did I ever struggle with this.
mossy plume
Does anyone know how I could graph this?
you can't do this
if f(x) has 2 value for same value of x, its wrong
inner sparrow
i don't understand how you can contrive a generalization out of just odd. odd = even and rules of the like , e.g in example 6 the second function doesn't make for an odd function? and also in the first part of example 6 they conclude that ( 3 + x^4) only has even exponents and hence it must be even which is fine but it is then raised to 1/2 too do they not take that into account
willow bear
contrive a generalization out of just odd. odd = even and rules of the like
what generalization? it is really not hard to prove that the product of two odd functions is even without any reference to the functions' formulas.
also, something not stated here is that if a function g is even then so is the composition of f and g in that order - crucially, f can be any function at all
inner sparrow
well yeah i get it i misinterpreted the 3 in the (x - x^3) as 8
inner sparrow
> contrive a generalization out of just odd. odd = even and rules of the like
...
the exponents would follow the rules and hence we can conclude if they are even or odd right?
willow bear
hm?
what exponents?
can you show what definition of "odd function" and "even function" you are using?
i am pretty sure that neither definition makes any reference to any part of the formula of a function (if it even exists)
inner sparrow
well so it says any function with "only" even or "only" odd exp are even and odd funcs respectively
willow bear
it says that as the definition?
inner sparrow
willow bear
okay see
definition of even function
definition of odd function
no reference to exponents anywhere in those
willow bear
yeah and this is an example
not all functions are polynomials
not all functions are expressible in terms of polynomials, even if you allow things such as radicals
inner sparrow
i don't understand how you can contrive a generalization out of just odd. odd = ...
what im essentially asking for is a proof of (6) and (7) i guess
willow bear
did you mean a proof of (8) and (9)?
inner sparrow
yep my bad
willow bear
ok yeah sure like
there are six identities here
pick one and i'll show you how to prove it
willow bear
ok sure, odd * even ?= odd
let f be an odd function and let g be an even function and let h = f*g
we wish to show that h(-x) = -h(x) for all x
do you follow so far?
willow bear
h(-x) = f(-x) * g(-x) [definition of h]
= -f(x) * g(-x) [oddness of f]
= -f(x) * g(x) [evenness of g]
= -(f(x) * g(x))
= -h(x) [definition of h again]
this is the formal proof
if you want to build intuition, you can look at functions of the form x^n for n ∈ Z, whose parity-as-a-function matches the parity-as-a-number of n
inner sparrow
h(-x) = f(-x) * g(-x) _[definition of h]_
= -f(x) * g(-x) _[oddness of f]_
= -...
yeah makes sense thanks!
inner sparrow
if you want to build intuition, you can look at functions of the form x^n for n ...
but that would just help in knowing that x^even is indeed an even function ....right?
and x^odd is .......
willow bear
it may help build intuition for the rule by springboarding off your intuition for the properties of parity-as-a-number
hexed tartan
test
tidal phoenix
Anyone know how to do this
uncut mulch
analyse the derivative
muted hinge
Hi could anyone kindly explain this pls - the 1st pic is the question which I'm solving, where it asks for indicating whether the limit is +infinity, -infinity or undefined . This seems to suggest that when the limit is +infinity or -infinity, the limit is considered defined. However, when I check the textbook (2nd and 3rd pics), it says that a limit L is defined only when L is a real number. Online resources which I found seem to agree with the textbook as well.
My follow-up question will then be to confirm whether infinity limits are actually undefined or defined?
^hope i'm asking in the right channel, not sure if this is under precalculus or calculus
proud raven
Hi could anyone kindly explain this pls - the 1st pic is the question which I'm ...
someone may correct me but
i think saying that this distinction is mostly made to help visualize behavior when you are learning limits
you could think of the difference being like uhh
1/x around 0 isnt defined, because the limits approach different infinities as you get close to 0
but 1/x^2, while still divergent, has both limits diverging to positive infinity
but really it doesnt matter, infinity isnt a number, so its about as useful as if the limit weren't defined in the first place (at least in the context of limits)
muted hinge
but really it doesnt matter, infinity isnt a number, so its about as useful as i...
I see, thanks! So rule-of-thumb will be that defined limits = limit with a single real number?
proud raven
just your normal like
approach the same value from the left and the right
infinity isnt a number, so whenever you see infinity you should be thinking "diverges"
(even if your teacher makes you write that limit is equal to infinity)
but yea i think you got it
proud raven
I see, thanks! So rule-of-thumb will be that defined limits = limit with a singl...
really rule of thumb and intuition comes from epsilon-delta, you don't need to do a whole proof but understanding the idea of like "being arbitrarily close"
a limit that shoots off to infinity never approaches anything with that intuition and it begins to make more sense the distinction
muted hinge
rightt haha thanks alottt will dive deeper into it once i wrap my head around the basics 🙂
hushed sphinx
The sad truth is that "the limit is defined" (or "the limit exists") means different things at different times or to different people. Sometimes it includes the case where the limit is ±infinity, sometimes it doesn't. If you're reading an introductory textbook (or a very conscientiously written paper) there should be an explicit definition that says what it takes the phrasing to mean. In more informal contexts you'll need to guess which of the options makes sense in each case.
And if you're writing something yourself in such an informal situation and it isn't obvious that one of the readings won't make sense, it's useful to explicitly say something like "has a finite limit" or "the limit exists (but may be ±infinity)" to make it clear what you mean.
brave shale
Can anyone help me solving this limit? I dont understand...
arctic ore
Isn't it just infinity?
brave shale
how?
cerulean flower
quick question:
If arcsin(-1/2) = pi/6, why isn't 7pi/6 an answer?
because in the unit circle, sin is -1/2 at 7pi/6 as well
stable yacht
You could look at the domain of arcsin(x), which is [-1, 1].
trim hemlock
that's not really why, the simple answer is just because that's how arcsine is defined, it's just defined to have the range [-pi/2,pi/2] which is convenient enough to work with
modest vale
I was wandering if there was any recommendations on how to begin learning calculus from home
shut jewel
Can anyone help me solving this limit? I dont understand...
use lhopital once
glacial inlet
Can anyone help me solving this limit? I dont understand...
The L'hopital rule says that for lim x-> a [f(x)/g(x)], and f(a)/g(a) becomes 0/0 or infty by infty, then,
lim x->a [f(x)/g(x)]= lim x->a [f'(x)/g'(x)]
If after applying the rule you get the same answer, apply it again
till you get something like 2x, x, x^2, e^x, etc
glacial lantern
how to convert x = 4a to polar ofrm
glacial lantern
what
whats a constant and magnitude
ut says in exercises 33-48 convert the rectangular equation to polar form. assume a>0
glacial lantern
I quit math
muted hinge
The sad truth is that "the limit is defined" (or "the limit exists") means diffe...
Just saw this, but thanks so much for clarifying! I sometimes do feel the different wording used across materials, especially online, to be quite a challenge when doing mathematics 😅
coral token
Hello! I'm studying Precalculus (Khan Academy)
Why does it use | |a| | instead of | a | ?
willow bear
double bars are often used for vector lengths in higher math
coral token
Oh, okay
willow bear
helps not confuse them with absolute value
keen walrus
can someone please teach me how to convert from rectangular to parametric without any given t values?
cosmic glade
for y = f(x) you can always just set x = t and y = f(t)
can also use various forms of the Pythagorean identity to go from rectangular to parametric easily
slate reef
the angular coefficient of a line is the tangent of the angle the line makes with the x-axis
viscid thistle
the angular coefficient of a line is the tangent of the angle the line makes wit...
is the slope tan 150 degrees
so the equation is y = -0.577350269x + 2
??
just need to confirm
slate reef
is the slope tan 150 degrees
yeah it should be right
kindred sluice
Anyone know if theres a good book on just the basic algebra graphs for a beginner to study? Like cubic graphs, and basic quadratics? I mean I have a precalc textbook, but I'm looking for a slightly deeper explanation. I want to understand it a deeper level. So basically a book that focuses heavily on precalc graphs is what I'm looking for.
hardy patrol
Anyone know if theres a good book on just the basic algebra graphs for a beginne...
I recommend videos on the internet over a textbook
maybe you can find content about this on 3b1b?
kindred sluice
I recommend videos on the internet over a textbook
There are good videos on the internet its actually currently what I use as well. I just want some of them to go deeper. Maybe its possible though because I'm currently at such a low level of math there just isnt that much depth to find. I might be looking for depth where there is none. I'm not sure though lol
hardy patrol
Yeah there's not much depth to quadratics and cubics at this level
You're looking for insight on these topics right
if you want a deeper understanding of matmathmatics as a whole the YouTube channel 3 blue 1 brown does just that
kindred sluice
Yeah there's not much depth to quadratics and cubics at this level
Yea I had a feeling I was kind of at ground zero. But I thought maybe there might be a chance of something existing. I dont find it confusing I just want to know more I guess lol?
hardy patrol
Love that youtube channel
minor forge
Can anyone help me with this problem
kindred sluice
if you want a deeper understanding of matmathmatics as a whole the YouTube chann...
Yea Ive seen a couple of his vids I will have to revisit him
hardy patrol
Can anyone help me with this problem
I believe that the length of the cables attributes to the tension in some way
I don't know how to use trig in physics just yet though
minor forge
r for each triangle is tension which should equal 0 I believe
minor forge
I don't know how to use trig in physics just yet though
Do you know anything about vectors
hardy patrol
nahhh lmao
minor forge
You in trig
hardy patrol
yea I'm in trig rn
only 2 more days left of it though
and I'll be done with trig in pre calc
minor forge
Same
quaint fossil
Can anyone help me with this problem
Take the tensions in the wires as T1 and T2 then resolve them in in i and j directions . You will get two equations :-
T1 cos55 + T2 cos40 = mg
T1cos35 = T2cos50
Now simply solve for T1 and T2.
oak slate
Hello can someone help me on these?
willow bear
@oak slate do you still need help with any of these, and if so then which one would you like to start with?
oak slate
<@613667013126258693> do you still need help with any of these, and if so then w...
Hi, yes i took these on a test and got them with partial credit and some with no credit. we can start with 5
willow bear
oh so you can share the working you did on the test then, yes?
and then i could look through it and tell you where you went wrong
oak slate
Ok is it ok if i dm you my answers?
willow bear
why DM? you could share them here just as well.
willow bear
aight lemme see
so this here is your work for #5?
it looks unfinished to me
you've arrived at (e^x = 2 or e^x = 1) correctly, now you need to get the values of x from this
oak slate
Ohhh ok thank you 🙏
willow bear
for #6, while your arithmetic checks out, after getting the solutions you should ask yourself whether or not each one of them makes sense in the original, logarithmic equation
in this case, x=-1 does not. logarithms are undefined at negative inputs after all
#7 is correct
#8 is somewhat unclear but looks unfinished
knotty island
gusy can I ask for help with this?
cedar pawn
Ye
viscid thistle
gusy can I ask for help with this?
Bro it's not precalculus
And these are such ez q.s that u can search them on google
knotty island
Bro it's not precalculus
I'm not very knowledgeable in this subject but I do think it's pre cal, it's literally what my teachers classified it as.
knotty island
And these are such ez q.s that u can search them on google
I tried doing it but I'm not finding any sources that can help answer this questions. Do you have a source for it? If you do can you please tell me?
vapid plaza
Bro it's not precalculus
What would precalculus be to you then 💀
Check out the description of this channel, precalc is very wide
knotty island
Check out the description of this channel, precalc is very wide
Hi, do you know where I could find solvers for logarithmic functions?
vapid plaza
I don’t think you should be looking for sth like that
There are a lot of techniques in solving these types of problems that you should get familiar with
mossy hemlock
I'm doing difference quotients rn and i find it a lot easier to just take the derivative of the function, but my answers are getting marked incorrect because I'm not putting any hs. Any tips on how to find where the hs will be without doing the difference quotient?
willow bear
none
if you're asked to find the difference quotient then there really isn't a way around it
other than just doing it
presumably you're also just learning about derivatives and so by taking derivatives as you're saying you are actually applying techniques you don't have access to just yet
winter solstice
yo I usually don't struggle with these problems but this time it's saying I'm wrong
This means the inverse of f is multiplying to the inverse of g right?
willow bear
no, this is a composition, not a product.
winter solstice
huh, my past teachers told me it was multiplying. Thank you I can solve for it now :3
knotty island
guys can I ask for help with these?
I need to answer 10 of these
<@&286206848099549185>
winter solstice
I'm not a helper but it should be 200% since you are simply adding another *2 to change h(8) to h(9)
knotty island
I'm not a helper but it should be 200% since you are simply adding another *2 to...
how about this? I only need to answer 10 questions correctly, I would deeply appreciate it if you can help me with this
winter solstice
wait no 100% since it's increasing by
nvm might not be the best to ask me but its not decreasing
knotty island
wait no 100% since it's increasing by
it's correct, it was 100%
knotty island
wait no 100% since it's increasing by
I'm really desperate, but I won't force you of course
winter solstice
it's correct, it was 100%
apologies for my initial mistake
knotty island
apologies for my initial mistake
it's alright
crisp bronze
<@&286206848099549185> how woujld i solve this?
I'm not a helper but I think it's best if you drew it
the ladder would make a certain type of triangle when placed on the wall according to the problem
crystal osprey
rate of change problems are always a lot better to visualize if you draw out a diagram of the question and label all of the knowns, and the unknowns
Will help with how you want to setup your function equations and finding their derivatives
It might help to think of the ladder and the wall and the ground as a right-angled triangle relation
willow bear
a substitution naturally suggests itself
viscid thistle
and i dont really know what to do
viscid thistle
yes
willow bear
ok then solve the equation x^2 + (-x+6)^2 = 20 as you would normally solve a quadratic equation.
willow bear
i mean this is a 'messy' quadratic equation but if you expand (-x+6)^2 it should be evident that there are no powers of x higher than x^2
cursive patio
,help
obsidian monolithBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
plain sable
Hey I’m not able to understand why this is wrong:
The volume of the hemisphere can be found by integrating (pi)r^2 (dr) as the base area will be pi r^2 and we can add that up until r becomes 0… so it should be ((pi)r^3 )/ 3
Can someone help?
tough cliff
How to approach this q?
What should I do about that comma
Ping me if anyone knows
willow bear
f takes as input a pair of numbers and its output is also a pair of numbers
you could do something like writing down $(x+y, x-y) = (u, v)$ to solve for $x$ and $y$ in terms of $u$ and $v$ and get an expression for $f^{-1}(u,v)$ this way
obsidian monolithBOT
Ann
orchid vale
ay its Ann
velvet zenith
how can i solve this problem?
69
willow bear
@viscid thistle do you still need help with this / have you made any progress so far
willow bear
mkay
there are at least two slightly different but overall equivalent ways to solve this problem
you have two unknown quantities: the amount of 10% solution, and the amount of 60% solution
give names to one or both of them, then translate the problem statement into a system of equations.
willow bear
where have you written what the letters x and y stand for?
willow bear
you should not write "10% = X"
you should write "amount of 10% solution = x"
but ok
willow bear
in that light, these equations are now correct.
viscid thistle
but im still not too sure on what to put for the second equation
viscid thistle
you should write "amount of 10% solution = x"
thank you for the correction
willow bear
didn't you put 0.4*25 already
viscid thistle
that was right?
willow bear
the first equation concerns the amount of solution while the second concerns the salt content
tough cliff
you could do something like writing down $(x+y, x-y) = (u, v)$ to solve for $x$ ...
Oh I see
Lemme try
tough cliff
you could do something like writing down $(x+y, x-y) = (u, v)$ to solve for $x$ ...
And what should I do next
willow bear
you have the first (x) and second (y) component of f^-1(u,v) already
you can write down f^-1(u,v) = ( (u+v)/2, (u-v)/2 )
viscid thistle
Yo
Idk how they got these answers
I'm trying a bunch of stuff on my calc i don't seem to be getting anywhere.
proper flint
tough cliff
you can write down f^-1(u,v) = ( (u+v)/2, (u-v)/2 )
f^-1 (x, y) = ((x+y)/2, (x-y)/2)
Thanks for explaining. I now understand the steps but I don't really get the intuition behind it. Like, why there is this "swapping" involved?
an example
f(x) = 3x+2
y= 3x+2
x=(y-2)/3
swap
y=(x-2)/3
f^-1(x)= (x-2)/3
I've been doing this swapping but don't really get it
viscid thistle
how bout diff it and equate it to zero for (i)?
I'm unsure about v and vi.
If you diff it
and make it equal to 0
yes you get 10/a and (27a+10)/4a
but why do we make them equal each other?
<@&286206848099549185>
tough cliff
well, diff it again and put these values in it
these are first and second derivative tests
Well, I'm interested too
Let's see what the helpers say
tight creek
I'm looking at page 5 of the Student guide for Marsden and Weinstein Calculus Vol1. Does anyone know why when he factors x^6-1 he stops at (x^3 +1)(x^2 + x +1)(x - 1) and doesn't continue to (x^2 - x +1)(x + 1)(x^2 + x + 1)(x - 1)? Why doesn't he further factor x^3 + 1 ?
willow bear
in what context is the factorization of x^6 - 1 necessary?
tight creek
The question just says "Factor: x^6 -1 "
willow bear
strange
also i think you should be consistent in whether you denote the variable with X or x
orchid vale
The question just says "Factor: x^6 -1 "
u can do differences of squares
you can do x^3+1 and x^3-1
then u can factor these 2
ill leave it to you @tight creek
viscid thistle
but why do we make them equal each other?
<@&286206848099549185>
I need assistance in v and vi please
willow bear
u can do differences of squares
have a feeling that someone didn't read OP's question
willow bear
shame on you for not doing so ngl 
orchid vale
It’s impossible to talk to you
willow bear
how's it impossible? you're literally talking to me at this very moment.
viscid thistle
shame on you for not doing so ngl <:KEK:586240877358350341>
bruh you kinda toxic to Terrance
you gotta calm down
tight creek
u can do differences of squares
Hi, and thanks for the reply. Yes that is how I solved it 😀 I was wondering if anyone had any thoughts on why the author of the student guide in his solution didn't further factor the x^3 +1 he stops at (x^3 +1)(x^2 + x +1)(x - 1) and doesn't continue to (x^2 - x +1)(x + 1)(x^2 + x + 1)(x - 1).
uncut mulch
oversight
strange echo
How do I find the end behavior asymptote
the end behavior is how the graph reacts when it goes to ∞ or -∞
mental steeple
Yea
strange echo
here is a tip for horizontal asymptotes
•if the degree (exponent) of the x in the numerator is less than the one in the denominator, the horizontal asymptote is 0
•if the degree of the x in the numerator is the same as the one in the denominator, the horizontal asymptote is the quotient of the coefficients of the x's (if you have something like (4x-3/3x-7), the horizontal asymptote would be 4/3)
•if the degree of the x in the numerator is greater than the x in the denominator, there is no horizontal asymptote
mental steeple
But the answer they got is y=1+x/4 @strange echo
strange echo
what?
strange echo
oh
well you can find it by dividing the polynomials
or finding the horizontal/slant asymptotes
but since we know that there are no horizonal asymptotes
mental steeple
I’ll do the dividing
strange echo
all you have to do is divide
mental steeple
If there is a horizontal asymptote can I still divide
mental steeple
Ok show me
strange echo
umm
mental steeple
I don’t have a problem with an asymptote lol
strange echo
heres the work
mental steeple
Quick question would I set it up like this and go from there? @strange echo
Oh lol
mental steeple
lol
strange echo
but yea you would set it up like that
mental steeple
Thanks
Hey man kind of confused what I did wrong here it’s not equaling 0 @strange echo
For the second one
strange echo
its a remainder so you used the remainder theorem thing
also you made a mistake for the first step
you did -4x^2 instead of -4x
@mental steeple
viscid thistle
Yo can someone help me with this worksheet
mental steeple
They got -x/4-1/4 as there answer @strange echo
viscid thistle
i dont understand it at all
mental steeple
Where did the other -1/4 come from
viscid thistle
strange echo
I think cosine should be x/r
so cos^-1 should be r/x
oh wait nvm
is there a specific quadrant that it has to go to
viscid thistle
Please help, I dont understand these two questions
Transform the following into the form Ax+By+C=0
strange echo
I think it only means that you have to put everything in one side so that the other side will equal 0
mental steeple
is there a specific quadrant that it has to go to
Doesn’t say
crude rover
gloomy crater
(4(x+2)/-2)-2
steep stream
$\frac{4}{\frac{-2}{x+2}}-2=\frac{4(x+2)}{-2}-2=-2(x+2)-2=-2x-6$
obsidian monolithBOT
Wa3Wa
steep stream
@mental steeple
mental steeple
Thank you
I’m confused with 81
@steep stream can u help me
I created a triangle
vapid plaza
Do you know what is cot
viscid thistle
Cot=b/p
mental steeple
??
vapid plaza
?
viscid thistle
Base/perpendicular
vapid plaza
For our purposes, the cotangent is simply the x-coordinate over the y-coordinate
So the answer would be…
vapid plaza
Ye
mental steeple
Maybe 7/24 is tan
Because it says suppose that theta is an angle in standard position
So when it asks for cot you flip it
Idk
vapid plaza
mental steeple
Correct me if I’m wrong
vapid plaza
From where did you get the answer?
mental steeple
From where did you get the answer?
The answer sheet my teacher made for us
Look @vapid plaza
muted hinge
$\frac{d}{dx} \ln{x^2}
=\frac{2x}{x^2}
=\frac{2}{x}$
obsidian monolithBOT
Shin
muted hinge
May I check if my explanation is correct : I'm allowed to cancel x from top and bottom going from the 2nd to 3rd step, because differential is taking the limit of the change in y/change in x, and not at the particular point itself?
steel tulip
You're just using exponent laws there
That step doesn't really have anything to do with derivatives
muted hinge
yea because i'm still confused when I can cancel and when I can't cancel from both numerator and denominator
I remember something like cancelling will result in loss of the roots of the equation in some cases
uncut mulch
0 isn't in the domain of the original function
so there's no issue with cancelling x like that
(as x can't be 0)
muted hinge
oh yeah that is true
steel tulip
If you have something like $f(x) = \frac{2\cdot(x+1)}{x+1}$ then f isn't defined at x = -1. you could simplify it to f(x) = 2 but you'd also have to say that f isn't defined at x = -1. So sometimes by cancelling you are losing some information
muted hinge
thanks 😓
obsidian monolithBOT
Tiessie
steel tulip
In this case it indeed doesn't matter
uncut mulch
x is also present in the denom of the final result 2/x
(also implying x can't be 0 so no info is lost here)
muted hinge
If you have something like $f(x) = \frac{2\cdot(x+1)}{x+1}$ then f isn't defined...
^ah ok that makes sense, so it's more applicable when I'm simplifying plain equations?
steel tulip
Not really sure what you mean by plain equations
muted hinge
sorry meaning everytime I'm doing any cancellation for algebraic fractions, I need to check if I'm losing any information from the final result for the variable x?
steel tulip
Yeah basically
muted hinge
ok thanks for the clarification 🙂
willow bear
the numerator is a difference of squares
mental steeple
Oh
I think I did it wrong
Wait
@willow bear am I doing it right
Oh wait
Nvm got it
What do I do next
I’m stuck
willow bear
does 86 have the same instructions?
i.e. "simplify the expression so there are no quotients"?
mental steeple
Yep
willow bear
well then doesn't the original expression already fit that bill
willow bear
well you could write $\frac{1}{\sin(x)} - \sin(x)$ as $\frac{1-\sin^2(x)}{\sin(x)}$ and then as $\frac{\cos^2(x)}{\sin(x)}$
obsidian monolithBOT
Ann
willow bear
but what troubles me is that you're expected to just ignore that their directions make no sense as-is
mental steeple
Wait that makes no sense
Then how did they get cotx cosx
:/
These are the options
willow bear
Wait that makes no sense
what does? my remark or the steps i wrote?
mental steeple
The answer they got
steep stream
well you could write $\frac{1}{\sin(x)} - \sin(x)$ as $\frac{1-\sin^2(x)}{\sin(x...
cos(x)/sin(x) = cot(x), so it can be simplified as cot(x)cos(x) @mental steeple
mental steeple
where does the other cosx come from
At the end
Is it because it’s squared?
So there are 2 cosx
steep stream
yes
mental steeple
Am I doing this right @steep stream
willow bear
there are 2 factors of cos(x) yes
mental steeple
Or sin^2x-1 doesn’t = cos^2x
Oh nvm it would be -cos
Ok so I got -cos^2x/sinx
What do I do with that
Oh wait
steep stream
i was thinking of $\frac{\sin{x}^2-1}{\sin{x}}=\sin{x}-\frac{1}{\sin{x}}=\sin{x}-\csc{x}$
obsidian monolithBOT
Wa3Wa
steep stream
Or sin^2x-1 doesn’t = cos^2x
wasn't cos(2x) = 1 - 2sin^2(x)?
mental steeple
If it was 1-sin^2x then it equals cos^2x
But if it’s the other way around
Then it’s negative
steep stream
🆗
mental steeple
mental steeple
🆗
Hmm what did I do wrong
The answer is 2csc^2x
Which is wierd
Oh
nvm
Did I do 89 right?
steep stream
yes
mental steeple
nvm I got it
steep stream
ok
tight ether
<@&286206848099549185>
rocky wind
this question better goes to #linear-algebra
tight ether
thanks
bright stirrup
deltamath😭
zinc plaza
minor zodiac
I have a question guys! cosine is a ratio of length of side right? then why it can have minus answers? Length can't be minus right?
vapid plaza
The ratio-of-lengths definition is only one of the definitions; the unit circle definition, for instance, is much more general and can take in any angle as input, no matter acute or not
This is the definition
As you can see, if theta is between 90 degrees and 180 degrees, the orange point is on the left of the y-axis and it’s x-coordinate (=cos(theta)) is negative
In fact, sin(theta) can be negative as well if we, for instance, let theta = 220 degrees
viscid thistle
Who wants to learn math from precal -> cal 3 || for 5-10 dollars || not promotion just an inquiry
muted fern
obsidian monolithBOT
せんく
rocky wind
you can check your work with a calculator
if the values match then you've done a right work
viscid thistle
👍
signal wigeon
A pebble is embedded in the tread of a rotating bicycle tire of diameter 60cm. If the wheel rotates at 4 revolutions per
second, determine the relationship (equation) between the height, h, of the pebble above ground, in centimetres, as a
function of time, t, in seconds using a sine function. Assume that at t=0, the pebble is located halfway between the
ground and the top of the tire.
someone helppleaseee
viscid thistle
hi all, can i have a little help understanding a question?
It’s asking how much did the sin diagram shift upwards
For this 1 I think it would be 0.5
granite holly
thank you, i thought it was 1
icy cosmos
hi can I get help with this question, I have already found the parametric equation and I know that I need to plug in the x,y,z point but I'm am a little stuck on where to plug it in because all of the Parametric equation has 2 unknown variables
pallid stone
is x = y^2 a function
the calculus textbook I'm going through says:
"A function is a mapping from a set of inputs to a set of outputs with exactly one output for each input."
but, say the input is 4, then the output would be 2 and -2
unless we're saying the graph I posted isn't a function
then I'm cool with that
pallid stone
I got a period of 5 but textbook says it’s less than 4
So the best thing to do here would be to manually write a graph for 7
so on the horizontal axis, write t, and on the vertical axis write f(t)
then plot the function on a coordinate plane, and find the period
viscid thistle
So the best thing to do here would be to manually write a graph for 7
thats what i did
isn't it a cos graph
so the period is 5
pallid stone
so the period is 5
how did you get 5
pallid stone
I got a period of 5 but textbook says it’s less than 4
also, the textbook is asking whether the function has a period less than 4 or not
so if it's <4, then your answer would be "yes", if it's >4 your answer would be "no"
viscid thistle
this is why i said the period is 5
also the textbook answers said yes for this question
that the period is less than 4
pallid stone
also the textbook answers said yes for this question
that means it's not 5
pallid stone
this is why i said the period is 5
the 5 here is the input value, the t, not the period
the period is the difference between the peaks on the graph from what I read
viscid thistle
still a little confused but ty for trying to explain
ill watch a youtube vid on it
potent wigeon
From the graph, it seems that the period is 3. This is because f(t+3) = f(t) and there is no c less than 3 such that f(t+c) = f(t).
slate reef
still a little confused but ty for trying to explain
yes its what yuki said
the graph repeats itself every 3 units in the x axis
from 0 to 3 the graph draws a triangle then it does it again from 3 to 6 and so on
rose basin
How do I write the domain and range for this graph? There are no circles or dots for interval notation on this graph.
rare zephyr
you still up for some assistance?
rare zephyr
How do I write the domain and range for this graph? There are no circles or dots...
I think assuming to use () would be fine
rose basin
I'm good now, but thanks for the help anyways.
rare zephyr
use s=rθ
granite holly
heelloooo
i hope someone can help me with this real quick
can someone help me solve the equation for this
hushed sphinx
You image tells you to use an equation of such-and-such form, but use it to achieve what?
granite holly
like the formula,
ik its y=3sin(pi-??)
im confused
i mean x
but i thought it was 2pi
but i guess not
storm lodge
Plug in values
granite holly
Plug in values
thanks, but that is what im confused about lol
rustic pond
rustic pond
based on this graph we can see the amplitude is 3 and the period is 4pi so what we can do is write this as 3sin(2pi/4pi * theta) which simplifys to 3sin(1/2 * theta)
rustic pond
based on this graph we can see the amplitude is 3 and the period is 4pi so what ...
if your confused on why multiply theta by 1/2 think of it like this. say im at 2pi multiplying by 1/2 gives me pi and if im at 4pi multiplying by 1/2 gives me 2pi which is a full period of the sin function
rustic pond
@floral holly yes it is. I got hung up on that one for a moment. But yes they are the same
floral holly
ty
rustic pond
np
granite holly
based on this graph we can see the amplitude is 3 and the period is 4pi so what ...
thank you so much! i figured it out last night and got exactly that! thank you sm
viscid thistle
hello, ive been given this problem but no examples, and cant find any online. assigment is titled "demoivre's theorom". any help is appreciated, thank you
viscid thistle
cis(x) * cis(y) = cis(x+y)
what do i do with the coefficients?
willow bear
they are being multiplied by the cis
this all is a product of four things
2, 3, cis(30°) and cis(225°)
act accordingly
viscid thistle
this all is a product of four things
thank you
obsidian monolithBOT
HstgH2
rustic pond
thank you so much! i figured it out last night and got exactly that! thank you s...
yw
gray lance
What is the domain of the derivative of sin(x)^x I got U (2kπ, (2k + 1)π) k ∈ N but I don't know if it is correct.
willow bear
Z, not N, surely?
willow bear
the union needs to be taken over Z and not N in order to be correct
terse kernel
net change formula is b-a or f(b)-f(a)?
compact tulip
hello vsg
granite holly
hello
can someone help me with this real quick
i think its y=2sin(3x)
actually nvm ik it is, i get it now lol
strange echo
Amplitude =$\ |a|$
obsidian monolithBOT
D00M_Re1ated
obsidian monolithBOT
D00M_Re1ated
strange echo
Knowing that we have the trig function Asin(Bx - C) + D here, we can use the above information to make the equation
Since amplitude is the absolute value of A, we can use 2sin(Bx - C) + D to get rid of A
For the period, we see that the formula is 2pi/b, and since we are given that the period is 2pi/3, we know that B = 3, and now we have 2sin(3x - C) + D
For Phase Shift, we are give that it is 0, and B is 3. Since we are given that Phase Shift = 0, C must equal 0 as well.
Since we know we do not need the D for this equation, we are left with 2sin(3x), thus we have our final answer
So yes you would be correct
i just realized you figured it out yourself...
cinder karma
$F = {F_{x} \in F_{c} : (|S| > |C|) \cap
(minPixels < |S| < maxPixels) \cap
(|S_{connected}| > |S| - \epsilon)
}$
floral holly
can someone show me how it converted to this
viscid thistle
Should be -4/3
subtle sentinel
How would cosine degree be affect if the interval is 270,360
hushed sphinx
cos(270°)=0 and cos(360°)=cos(0)=1, and it the value of the cosine increases monotonically between these points.
subtle sentinel
How would it work out for cos theta = 0.9
hushed sphinx
Your calculator will tell you that arccos(0.9) is about 26°. You can use standard cosine identities to find the unique theta between 270° and 360° that has the same cosine.
Specifically cos(-x)=cos(x) and cos(x+360°)=cos(x).
subtle sentinel
Would that be 336 then?
hushed sphinx
No, but close.
(You probably have the right calculation, but double-check your arithmetic).
hushed sphinx
Yes.
subtle sentinel
Thanks
granite holly
Since we know we do not need the D for this equation, we are left with 2sin(3x),...
omg thanks sm, i did figure it out but thank you for explaining even more I really appreciate it!
obsidian monolithBOT
D00M_Re1ated
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
strange echo
@granite holly
granite holly
i originally got that but it was wrong, so im so confused @strange echo
thank u tho for explananation
explanation lol
do i flip it to addition in order to get pi/6?
strange echo
wdym by that?
granite holly
pi/2 +pi/4?
granite holly
hmmm, okay i see
last mist
how are you doing calculus but don’t know how adding fractions work
slate cove
math class carries on even if you don't understand it
hushed sphinx
<@946646675106181191>
Um, no, sin(pi/4) is not 1/2 -- but sin(pi/6) is.
hushed sphinx
do i flip it to addition in order to get pi/6?
To get pi/6 you just fix Doom's wrong value for the x that gives sin(x)=1/2. He's right that your equation is the same as 2sin(x)=1, but the x that solves that is x=pi/6.
(You can see that pi/4 doesn't work by looking at the graph of a sine. We have sin(0)=0 and sin(pi/2)=1 -- but the graph is clearly concave between those two points, so the sine of the point halfway between 0 and pi/2 must be larger than halfway between 0 and 1).
strange echo
Um, no, sin(pi/4) is not 1/2 -- but sin(pi/6) is.
Oh my bad
Forgot unit circle for a second
viscid thistle
hello! i need some help with this problem.
i have some idea on how to do it. im just not sure how to graph the information or if my graph is right
stable yacht
Where did i go wrong here
First line to the the second line. If you factor z^3 out from z^3, it does not become 0.
rustic pond
hello! i need some help with this problem.
whereever the derivitive is negative then you are decreasing and where ever the derivitive is postive then you are increasing
viscid thistle
whereever the derivitive is negative then you are decreasing and where ever the ...
Of course, cause a derivative is rate of change
thick rain
find the values of m to make the following complex nb a real one
any idea how to solve this??
a hint?
rustic pond
Of course, cause a derivative is rate of change
i was responding to @viscid thistle
viscid thistle
i was responding to <@456226577798135808>
just saying…
rustic pond
alright
glossy breach
who know this one
viscid thistle
who know this one
Given the sin(theta) function, we can assume from trigonometric ratios that since sin(theta) is equal to the opposite/hypotenuse, the opposite is 3 and the hypotenuse is 5
We can then find the adjacent using pythagoras theorem, which would be 4. Giving us the common 3-4-5 triangle
From there, we can assume that sin(theta) is 3/5, cos(theta) is 4/5, and tan(theta) is 3/4
After that, you can input your values into the half angle formulas shown below and see what you get
Although, since it mentions how the angle is in the second quadrant, following the ASTC rule, only the sin function would be positive, while cos and tan would be negative
viscid thistle
whereever the derivitive is negative then you are decreasing and where ever the ...
alright thanks!
rustic pond
yw