precalculus

[gritty spade]

ello, could anyone tell me if my answer for this is correct or not?

[solar pagoda]

The graph is right but not sure about your choice on a.

You said 1 <= a <= infty, for a = 1 the limit of f does not exist since left hand and right limit are not the same.

Also that is not the only a values.

[gritty spade]

ive been scratching my head over this for the past few hours or so, is it possible you could help me out on this?

[solar pagoda]

Sure, what are you stuck in?

Did you understand why I said for a = 1, we have the limit of f does not exist?

Also just realizing this is not #calculus .

[gritty spade]

im not quite bright enough to see any thing in the graph that has the same limits for both left and right lmfao

[gritty spade]

i think i do

[gritty spade]

pardon?

[solar pagoda]

Limits are usually in #calculus

[gritty spade]

oh, my apologies

[solar pagoda]

I do one part, for a < -1, notice f approach f(a) from left and right hand side of a.

Take a = -2 for an example.

Do we have this behavior anywhere else on this graph?

[gritty spade]

wait, but how so

[solar pagoda]

You can see it right?

[gritty spade]

is it because its a less than -1 sign, we consider that as an "a" value?

[solar pagoda]

If we get close to a from left and right side f gets close to f(a).

[solar pagoda]

Not sure what this means?

Take a = -2 for an example.

[gritty spade]

but wouldn't the r.h.s be -1 instead?

[solar pagoda]

Is this for a = -1?

[gritty spade]

yup

[solar pagoda]

I was only considering a < -1.

Limit does not exist at a = -1 as you said lhs and rhs limit are not equal.

[gritty spade]

oh okay, so for values less than -1, the lhs and rhs are equal in this case?

oh shit, i see it
it's because it's a straight line

[solar pagoda]

Yep.

Do you see this behavior anywhere else on the graph?

[gritty spade]

okay, so the 'a' values would be a<-1 and -1<a<1 ?

[solar pagoda]

Yep and?

[gritty spade]

...shit i wasn't expecting the and there

there's more? damn

[solar pagoda]

.look carefully.

How about a > 1? Does we have the same behavior?

[gritty spade]

OH

I SEE

[solar pagoda]

I let you think on that. Ok, now work on a few more problems.

Like that.

[gritty spade]

thanks man, prior to the help, it seems i didn't even have an idea of limits

[simple pollen]

stewart chad moment

[gritty spade]

hell yea, got my unis starting soon so i thought id ask a senior for some textbooks so that i could have a headstart

[astral bobcat]

sorry, i have a question

y < 0, x^2 + y^2 = 4 and the question is the value of the slope of the tangent drawn from the root 3 abscissa point.
I came to a solution with the parabola under the x-axis of the circle with radius 2, but I did not understand the solution using the derivative of y with respect to x.

which goes like 2x + 2yy' = 0

and y' = -x/y = -root(3)/-1

i didn't understand the process if my question is clear

[verbal zodiac]

@astral bobcat can you share original question

Where does parabola come in?

[quartz inlet]

Hello, in a problem I am supposed to simplify $\sin x -\cos x$ into $\sqrt{2}\cos \left(x-\frac{3 \pi}{4} \right ) $, where as a hint it was said it might be helpful to use the addition formula later on.
\

How would one go about this? I tried googling about the derivation for this identity but with no avail. Appreciate any help.

[obsidian monolith]

Aslan

[edgy spruce]

Start with the fact that sinx=cos(x-pi/2)

let x=y+pi/4

You get cos(y-pi/4)-cos(y+pi/4)

Expand using the hint they told you to use

cosy/√2+siny/√2-cosy/√2+siny/√2

2(siny/√2)

√2xsiny and recall that siny=cos(y-pi/2(

So √2cos(y-pi/2)

Let y=x-pi/4

√2cos(x-3pi/4)

✅

[edgy spruce]

Did I answer your question the way you wanted it?

[quartz inlet]

@edgy spruce Yes, thank you!

[astral bobcat]

y < 0, x^2 + y^2 = 4 and the question is the value of the slope of the tangent drawn from the abscissa of root 3.

[verbal zodiac]

@astral bobcat

[young bolt]

can anyone help me with this one?

[edgy spruce]

7logx/(2log10+logx)=2
7/2=1+2log10/logx
5/4log10=1/logx
Logx=4log10/5
X=10^4/5

[young bolt]

Thank you

[burnt lodge]

Do you know double angle formula

[willow bear]

you do not need that here

[burnt lodge]

I can see that

[golden cobalt]

Hi! What are the steps to solving this question?

[burnt lodge]

Can you swap 2x and 4x

Whilst deleting negative exponents

[clever basin]

Where do you get those math equations from?

[mild swan]

Rewrite this expression with no complex fraction and no negative exponents

[uncut mulch]

multiply numerator and denom by x

[hot flame]

the wording of this question is confusing me can someone help me?

[cloud wadi]

how is this even possible

the base of the triangle isnt given, and neither is any of the sides of the rectangle

the only given here is the diagonal of the rectangle

[willow bear]

the radius of the circle is 1 so the height of the triangle is (2-H)/2 and the width of the rectangle is sqrt(4-H^2)

[cloud wadi]

the diameter of the circle is not equal to the base of the isosceles

it doesnt pass through the center

[willow bear]

but did i say the base of the triangle equaled the diameter?

i did not.

don't put words in my mouth.

[cloud wadi]

then how did you come to the conclusion height = (2-h)÷2

sorry im just trying to learn

[willow bear]

EF is a diameter of the circle

[cloud wadi]

yes

[willow bear]

x + H + x = 2

[cloud wadi]

ohhh

and when you find the width of the rectangle. you can find value of H using pythagoras

[willow bear]

it's the other way around

i'm finding W in terms of H using pythagoras

[cloud wadi]

there are 2 hs on the shape which are you referring to

[willow bear]

there's one that was there to begin with and one that was put there by me

and they are the same

[muted turret]

99% can do this question. It’s easy! Find the vertex of the quadratic equation 2x^2+4x-1 and find 4 points that the parabola from this equation goes through.

[willow bear]

indeed, but if you're not part of those 99% then we won't do this for you

[muted turret]

I will show you how to do it

So I can prove myself that I can do this question

[cloud wadi]

my maths isnt in english so i have no idea what that means

[muted turret]

@willow bear I can do the answer.

[golden cobalt]

Thanks it worked

[young bolt]

What's the formula for this?

[uncut mulch]

convert to polar and/or CiS form and apply exponent laws or DeMoivre

[hollow ibex]

i need help finding the sum of the finite series

[vapid plaza]

This is a geometric series

[hollow ibex]

ye i got the common ratio

[rapid inlet]

can someone please explain the intuition behind this?

thanks 🙂

[vapid plaza]

Each horizontal slice of the cone is a circle whose radius is proportional to the height on the cone (z-coordinate)

A bit like this

See that r1/z1=r2/z2

So z = (constant) * r

[burnt lodge]

Looks good

[viscid thistle]

can someone tell me if this is good?

[rapid inlet]

Oh ofc tysm

[burnt lodge]

Good

[clever basin]

E

[gentle vale]

How do we deal with the case where n = -1?

it's come up in a problem i'm doing and i'm desperate 😂

[willow bear]

int 1/x dx = log|x| + C @gentle vale

[gentle vale]

thanks a lot!

i'll find the proof myself somewhere

afterwards

[cloud wadi]

ok so i found h= 2/5 (thanks ann) by using area of both rectangle and triangle formula and used it to rearrange w and h but im the process w was eliminated and thus the value remained undetermined.
when i try to sub in h in the equation wh=(wb)÷2
(b being the height of the triangle) the equation is a dud and i get w=w. how do i find the value of w?

[hybrid pewter]

do we know that such an n even exists?

we can certainly find an n such that f is 0 exactly once in [0, sqrt(3)/2], but a minimum n such that there is no 0 might not exist

as in its possible n in (a, b) gives no zeroes on [0, sqrt(3)/2], so there would be no minimum

[delicate relic]

it does

[wise spoke]

I am trying to figure out the turning points of this function, but I keep on getting two turning points but the answer says one.

$y = \frac{x^2+2x}{x^2+x+4}$

[obsidian monolith]

∫Inheritanc-e ♦

[willow bear]

show work?

[wise spoke]

Showing

[willow bear]

ah, hang on.

wait, does the answer key explicitly state there's only one turning point

or what

[wise spoke]

Yes

[willow bear]

in that case the answer key is wrong

there are two

[wise spoke]

The question asks how many turning points are there

[willow bear]

your x looks a lot like n though

[wise spoke]

And when I check it shows 1

[willow bear]

there are two

[wise spoke]

Hmm

Ok thanks

[willow bear]

"the answer key states there is only one"

is not the same as

"i graphed it and only see one"

[wise spoke]

I don’t get what u mean

[willow bear]

i am pointing out what might be a communication error on your part.

you are not properly reporting what exactly it is that doesn't add up.

there's a difference between "my answer does not match the answer key" and "my answer does not match desmos"

[wise spoke]

My answer does not match the answer key

[willow bear]

show the answer key.

ideally also show the original problem statement, just to be sure we're looking in the right place.

[wise spoke]

okay

This is the question

And this is the r answer key

[willow bear]

hm

thats strange.

there are definitely two turning points though

[wise spoke]

yep

[viscid thistle]

hi can anyone help with this?

[burnt lodge]

The equation here is an ellipse

The other is a circle

Can you graph these functions

[hybrid pewter]

you can write the second equation as (x-1)^2 + (1/4)(y+4)^2 = 25

then comparing that with the first equation should make the solution clear

[opal tree]

Haha conics, I hate them

[proud basin]

Can anyone help me with the text in red I'm having trouble knowing what it is

[alpine wraith]

do you know what sine, cosine, and tangent values for each radian are?

That, Id assume means the coordinate values.

Which means including rad3/2 , 1/2

Stuff like that for each point

[proud basin]

Oh really?

Yeah I know the values for sine cos and tan etc

[alpine wraith]

just put like

s = whatever coordinate, like rad2/2

c = whatever, like rad2/2

t = y point over x point solved to simplest form

That way you can fit it all

[proud basin]

I've made this

[alpine wraith]

I’d not bother with coterminal radians

That’s not necessary

[proud basin]

Oh ok

[timid cedar]

How much guess work is acceptable when finding factors?

I did a guess that (x^3 - 1) is divisible by x-1, because it looked neat with x^3 - 1^3

[summer ruin]

at least here it's perfectly acceptable to find roots by guess work, in fact some cubics have roots +-1, +-2 and so on which you can find by guess work if you're stuck with it and then divide by said root

you can observe that x=1 is indeed a root of x^3-1

hence x^3-1 is divisible by (x-1)

(this is because each polynomial can be factored into a product of polynomials e. g. (x-a)(x-b)(x-c)(ax^2+bx+c) and so on, here the quadratics are assumed that they're no longer factorable with real numbers)

[wise spoke]

The curve C, is given as y = $\frac{x^2 + ax + b}{2x-1}$. Given that one of the asymptotes is y = $\frac{x}{2}$ + $\frac{5}{4}$ and one of the points of intersection is (0,4)

[obsidian monolith]

∫Inheritanc-e ♦

[wise spoke]

We know that the oblique asymptote is expressed as y = Q(x) + $\frac{R(x)}{D(x)}$. And we take the Q(x) part as the oblique asymptote. So what I'm wondering is, in the question above is y = $\frac{x}{2} + \frac{5}{4}$ the Q(x) or y = Q(x) + $\frac{R(x)}{D(x)}$

[obsidian monolith]

∫Inheritanc-e ♦

[willow bear]

it's the Q(x)

[wise spoke]

Right. Thanks

[wise spoke]

Okay. I couldn't figure out how to do it.

Could someone help me

i need to find the value of a and b

the value of b is -4

but idk what the value of a is

could someone help me do this?

[willow bear]

$\frac{x^2 + ax + b}{2x-1} - \frac{x}{2} - \frac{5}{4} = \frac{x^2 + ax + b - x(x - \frac12) - \frac54(2x-1)}{2x-1} \ = \frac{x^2 + ax + b - x^2 + \frac12x - \frac52x + \frac54}{2x-1} \ = \frac{(a-2)x + (b - \frac54)}{2x-1}$

[obsidian monolith]

Ann

[willow bear]

you want a-2 = 0 so that this fraction approaches 0 as x -> ±∞

[wise spoke]

hmmm

[opaque timber]

Can someone help me with this?

[chilly cobalt]

hey guys ik this is like a very very dumb question cus im just starting to learn precalc but like how did they got those numbers ( in red circle) im so confuse omg 😭

[viscid thistle]

uhh
that is 5^2+1
and 3^2
they got these numbers through solving the equation

[chilly cobalt]

what is "^" that

omg sorry for such a dumb question ; _ ;

[viscid thistle]

that is the exponent notation

[viscid thistle]

nah I'm happy to help anyone lol

[chilly cobalt]

what does that thing do omg sorryyyyy omg

[obsidian monolith]

Ann

[chilly cobalt]

ooooh

so like multiply by itself or something

[viscid thistle]

yes

[chilly cobalt]

like 5^2 = 5x5?

OOOOOOOOOOOOOOOOOOOOOOOH

[viscid thistle]

mhm

[chilly cobalt]

omg im a math genius teheee

thankyou!!! ❤️

[viscid thistle]

np

[chilly cobalt]

hey um can i add you?

[crisp stirrup]

wait what u are doing precalc and not knowing exponents

[burnt lodge]

He doesn’t know that notation

[crisp stirrup]

ok

[rocky spruce]

About your question @finite bobcat

Try the substitution X = 3^x

[viscid thistle]

im still confused on how limits work

say f(x) = {
x, x>0
1, x = 0
x, x<0
}

then how are you computing limit (x->1) f(x) from left and right?

[willow bear]

well f(x) happens to be equal to x in a neighborhood of 1

so $\lim_{x \to 1} f(x) = \lim_{x \to 1} x$

[obsidian monolith]

Ann

[viscid thistle]

how?

proof?

[willow bear]

if you want to be concrete, here's an example of such a neighborhood:

(0.5, 1.5)

[summer ruin]

to evaluate the limit you don't have to have function even defined in your limit point, like if you had f(x) = sin(x) everywhere, but undefined at x= 0, you still can figure out that the limit at x = 0 is 0

[willow bear]

if you ask me why i chose this neighborhood i'll choose another one

[viscid thistle]

ok but how do you know firstly that the limit exists

[willow bear]

i do not

[viscid thistle]

ok

so you choose a neighbour

[willow bear]

the equality is an equality of elements of $\bR \cup {+\infty, -\infty, \mathrm{NaN} }$

[obsidian monolith]

Ann

[willow bear]

i do not choose a "neighbor"

i assert the existence of a neighborhood on which f(x) equals x

and i presented such a neighborhood to you

[viscid thistle]

okay

then?

[willow bear]

$\lim_{x \to 1} x = 1$, as should be obvious and/or easily provable by epsilonics.

[obsidian monolith]

Ann

[viscid thistle]

Ah I should look up the precise defenition of limits

thanks

Sheesh proving limits are hard

had to find delta and all that

how are limits a prereq and not taught in the calculus

[willow bear]

as far as the computation of limits goes, there exist a few rules that lend themselves to easy application without worrying about epsilons.

[summer ruin]

well in this specific problem $\delta = \epsilon$

[obsidian monolith]

Transparent_Elemental

[summer ruin]

$\forall \epsilon > 0 \ \exists \delta > 0 : 0 < |x-1| < \delta \rightarrow |x-1| < \epsilon$

[obsidian monolith]

Transparent_Elemental

[viscid thistle]

how come you can do
lim f(x)g(x) = lim f(x) lim g(x)

will i be proving it in further courses rather than calculus 1?

[acoustic vault]

Yes you will prove it in analysis

Though it’s quite simple to prove, but proofs are generally not covered until analysis

[summer ruin]

you can do that only if the right hand side limits exist

[acoustic vault]

That’s true the hypothesis is provided f(x)—>a and g(x)—>b

[acoustic vault]

for a basic proof

The idea is that $\lim_{x\to a} f(x) = a$ if and only if for every sequence $x_n \to a$ and $x_n \neq a$, we have $\lim_{n\to \infty} f(x_n) = f(a)$

[obsidian monolith]

Andrew071

[acoustic vault]

Thus it suffices to prove $x_ny_n \to xy$ provided $x_n \to x$ and $y_n \to y$

[obsidian monolith]

Andrew071

[acoustic vault]

To do so, $\lvert x_ny_n -xy \rvert \leq \lvert y_n \rvert \lvert x_n - x \rvert + \lvert x \rvert \lvert y_n -y\rvert$. Now let $n\to \infty$. (Note we have implicitly used the fact that convergent sequences are bounded, the triangle inequality, limit of sum of convergent sequences equals the sum of the limits, and the squeeze lemma)

[obsidian monolith]

Andrew071

[deft meteor]

if there is a precalc

is there a postcalc?

[hushed sphinx]

That's usually called "analysis" of various sorts.

[vagrant yew]

hello, I have a question about periods for sum/differences of trig functions

say you have the function y = sin2x - csc3x and you want the period. I found the period of sin2x which is pi, and the period of csc3x which is 2pi/3, and I found the lcm which is 2pi, and so I said the period is 2pi.

this was ultimately correct, but it seems you have to do more to determine whether or not 2pi is the period? apparently all I did was show the graph repeats at 2pi but is not necessarily the period since there could be something smaller. I was wondering how to find that period, or how to prove that 2pi is the smallest period.

any help would be appreciated

[summer ruin]

period of a function $f(x)$ is any number $T$ such that for any $x \in dom f$ the equality hold $f(x-T) = f(x) = f(x+T)$, so if the function repeats at $2\pi$ and $\pi$ then both of those are periods

[obsidian monolith]

Transparent_Elemental

[vagrant yew]

but what if you're trying to find the smallest period

[vagrant yew]

sorry I worded this wrong

[hybrid pewter]

the lcm will indeed be a period of the sum but its not necessarily the smallest (positive) period. For example consider the sum of sin(x) and -sin(x)

idk if theres a general formulaic way to find the smallest period or not

[hushed sphinx]

If it's a simple linear combination of sines and cosines, and you've already collected like terms and thrown out ones whose coefficients vanish, then due to the uniqueness of Fourier series, it cannot have any shorter period than the lcm.

(On the other hand "unqueness of Fourier series" is probably not a good argument to float in precalculus :-D )

[vagrant yew]

I see, if possible could you explain how you would show that 2pi is the smallest period of my example

[hushed sphinx]

In this example, you can see that the function blows up to infinity due to the cosecant exactly 3 times per pi, and it does so with different signs every other time.

So the smallest period must be a multiple of 2pi/3.

On the other hand, plugging in a few numbers allows you to see that the period isn't 2pi/3 or 4pi/3.

[vagrant yew]

that's pretty intuitive, I like it

thank you

hmm I'm wondering how you would find the period of something like sin2x - cos3x, where there aren't any asymptotes to take advantage of

[hushed sphinx]

That's where I'd resort to the Fourier series argument. :-(

[vagrant yew]

:(

that's probably why my textbook gave the csc example

welp desmos says the period is 2pi

[hushed sphinx]

There are probably more brute-force calculational approaches for ruling out short periods in concrete situations, and then you can eliminate the larger divisors of the lcm by plugging in values. But stating that as a general procedure feels rather complicated.

What I mean: If we forget "PREcalculus" for a moment, you can calculate the derivative of such a sum easily, and bound its magnitude globally. Now if you find two points with different function values, that gives you a lower bound for the period. Then there are only finitely many possible divisors of the lcm to eliminate by direct calculation.

[vagrant yew]

rip idk calculus yet

it seems so cool though, finding the area under curves

[viscid thistle]

@vagrant yew Pre Calculus prepares you for calculus

[vagrant yew]

yes ik

[viscid thistle]

Calculus is really hard it’s probably one of the hardest courses in our school may be another course in your school

[vagrant yew]

our high school has linear algebra

[viscid thistle]

Well what’s the grade 12 math called

[vagrant yew]

it depends

[viscid thistle]

Cause different schools have different education systems

[vagrant yew]

some seniors take statistics, some calc 1, some calc 2, some linear algebra

[viscid thistle]

Yeah

It depends dude

You got to think about this

“what is my goal going into college”

What job do I want, etc?

[vagrant yew]

lol idrc I just like math

[viscid thistle]

Fair enough haha

[vagrant yew]

I'm not particularly good I just like math :/

[viscid thistle]

You taking calculus

[vagrant yew]

I'm prepping for a placement test

[viscid thistle]

My strongest subject is math personally 😂

[vagrant yew]

if I do well I can get on the 12th grade linear algebra track

[viscid thistle]

Our school system teaches different though

I’m probably going to take Pre Calc Honeslty

I can’t take Calc it will be too hard for me 😂

[vagrant yew]

rn subjects I still need to study are conic sections, probably need to review trig stuff and basic proofwriting

[verbal rock]

CALC LOOKS HARD

[opal tree]

It's really not too hard

It's just patterns

Like pre Calc is harder than Calc AB and BC

[vagrant yew]

so I'm trying to find the solutions to sinx - cosx = 0
I tried substituting cos in terms of sin using the pythagorean identity, and I got 4 solutions (work shown below). but then I realized if you just set sinx = cosx the answer becomes quite obvious and there are only 2 solutions. can someone explain why substituting doesn't work?

[uncut mulch]

,rotate

[vagrant yew]

oh btw I'm solving for x is in 0 to 2pi

[uncut mulch]

cos(x) isn't the same as sqrt(1-sin^2(x))
and squaring can lead to the generation of extraneous solutions

[vagrant yew]

oh I see

cosx is only sqrt(1-sin^2(x)) during certain angles

[fallow isle]

|cosx|=sqrt(1-sin^2(x))

Bc the sqrt only give positive outputs but cosine oscillates between negative and positive values

[thorn valley]

Hello

Can anyone help me find the trigonometric form of 7-7i?

[willow bear]

@thorn valley still need help with that?

[thorn valley]

I got it but in a little bit I'll probably get to an advanced question I can't answer 😦

[sand dune]

you didn't show what you have tried

[viscid thistle]

^ is just a computer syntax for exponent

[viscid thistle]

Well, I am getting 4x + 2h as the solution and when I simplified it, I am getting 2(2x + h). Can somebody else please check this? Thanks.

My Work:

[frank vine]

I think good

[viscid thistle]

Thanks bro.

[fiery river]

what is precalculus and calculus, in simple words?

[viscid thistle]

pre calculus is before calculus and calculus is basically integrals and differentiation with also differential equations.

[fiery river]

In which grade/class do we learn it?

[viscid thistle]

depends on the country

what country are u in

[fiery river]

Lithuania

[fiery river]

but mostly?

[viscid thistle]

ok, bro. I do not know about Lithuania but usually in most countries, it is 11th and 12th grade.

[fiery river]

yeah thanks

I'm going to grade 11th, what I should know? For what I should prepare?

[hushed sphinx]

"Precalculus" as a particular grouping of mathematical topics seems to be mostly an American thing.

Assuming your country's curriculum design is not insane, the reasonable default answer to "what should I know" would be "whatever you were taught in previous grades".

[loud tundra]

@fiery river I have heard that this book https://www.stitz-zeager.com/ is great for precalc. Maybe check it out to give yourself an idea of what precalculus is. I want to go through it

[fiery river]

Thank you mate, appreciate it

[fiery river]

@loud tundra There's also video on YouTube I have found https://youtu.be/eI4an8aSsgw

[gentle vale]

If I know about derivatives and integrals and the methods used to solve them, is learning partial derivatives a small step or a big step to learn?

[summer ruin]

basically you already know how to take the partial derivative if you know how to take the regular derivative, but it's very important conceptually

[gentle vale]

thanks

[upper agate]

Does anyone know how to use a unit circle to solve cos -17pi/3

[opal tree]

Find what angle -17π/3 is coterminal to. Should be between 0 and 2π

[cloud star]

Frankly, I think precalculus is barely necessary. It did not help with calculus at all. Algebra 2 accomplishes everything precalculus may have accomplished. I would recommend just diving into calculus.

Note: Precalculus is only an American thing.

[delicate relic]

Hi

I want to learn advanced calculus, so where can i start (i know basics)

[summer ruin]

what do you know?

[delicate relic]

substitution and ibp

i know differentiation

[summer ruin]

have you done definite and improper integrals, infinite series?

[delicate relic]

Nope

@summer ruin

[summer ruin]

then do that

[fiery river]

https://youtu.be/HfACrKJ_Y2w

You think, this should help?

[cloud star]

If you want a quick and easy intro i would go with professor Leonard’s calc series

[fiery river]

It's in YouTube?

[cloud star]

https://youtube.com/playlist?list=PLF797E961509B4EB5

You can watch at 1.5 to 2.0 speed

If you get annoyed slow talk

He also has calc 2, calc 3, and differential equations.

And you can probably watch all the videos from calc 1 - differential equations in 1 month then run through a textbook on weaker concepts

[fiery river]

Thank youu

I will watch it for sure

[vagrant yew]

hello, I'm studying conic sections and I want to know if there is a way of constructing a hyperbola in real life, just like with an ellipse and parabola

[viscid thistle]

Yes

Hyperbola with a lamp...

[vagrant yew]

I meant like on paper, though there definitely is a cool physics explanation for that

physics I wouldn't get

[viscid thistle]

you will if you try

[vagrant yew]

I'm just tryna visualize a hyperbola

I can trace out a parabola and an ellipse using the definition in my mind, but not really hyperbola

[summer ruin]

hyperbola also has definition similar to ellipse

[viscid thistle]

Yeah cuz an ellipse is a special case of a circle so i am assuming that a hyperbola is a special case of a parabola?

[summer ruin]

parabola has eccentricity = 1 and hyperbola has eccentricity > 1

[viscid thistle]

yeah

circle = 0; ellipse is between 0 and 1, parabola = 1 and hyperbola is greater than 1

for eccentricity

btw, if we were able to make a wormhole, won't it be similar to a hyperbola?

[vagrant yew]

I meant like the foci definitions

[summer ruin]

well yes there is one

[vagrant yew]

yeah but how do you draw a hyperbola in real life taking advantage of that definition

like you can take a string, tie it to two pins and draw and ellipse that way

and you can take a ruler and a pin with a string to draw a parabola

[summer ruin]

something like this? https://youtu.be/mldZ_7QwLvs?t=113

requires a special ruler though

[vagrant yew]

yes yes

thanks

[grizzled bough]

any good books about trachtenberg and pre calc?

[trim skiff]

I do not know books. But check out organic chem tutor on yt

In my opinion he is pretty good

[wet socket]

Find the roots of the equation:
x+1=x.2^x

[lucid trench]

i love precalculus 😌

[lucid trench]

are you asking for this?

[viscid thistle]

yes and ig the no. of root is 2

[grim jay]

wait maybe wrong channel

[grim zephyr]

is there a meaning behind the 0

im trying to figure out how u would interpret it

ik that u cant really use the pythagorean theorem for complex numbers

and u would use the modulus

[viscid thistle]

its a joke

[obsidian monolith]

Plazzi

[viscid thistle]

Im dumb nvm

Its late

didnt read the last sentence i apologise

[lucid trench]

?

[viscid thistle]

bro, u must be stupid. Can't u see he is showing pictures of his notebook of precalculus and his pen. He wants us to find the area of the pen by using precalculus. And then his second photo shows the top of his pen. That is a damn circle! The eq for a circle is (x-h)^2 + (y-k)^2 = r^2

lol

[lucid trench]

oh

[coarse fog]

Its better thought of as distance instead of length. A complex number might have a distance of -1 from 0 while not being -1 on the cartesian plane.

[lucid trench]

oh i just didnt know the context lol

[coarse fog]

0 is just the sum of the distances

[viscid thistle]

bruh, the way he posted them photos. i thought that was the hardest math question ever...

and what was even funnier was G4J's "?"

[ashen flare]

Today I have found myself in the need of denesting $$\sqrt[4]{-7+4\sqrt3}=\sqrt{\sqrt{-7+4\sqrt3}}$$

[obsidian monolith]

TheHappyDragon

[ashen flare]

I know the following identity $$\sqrt{a\pm\sqrt{b}}=\sqrt{\frac{a+\sqrt{a^2-b}}{2}}\pm\sqrt{\frac{a-\sqrt{a^2-b}}{2}},\quad a,b\ge0$$
so the radical could be denested into $$\sqrt{2i-i\sqrt{3}}$$

[obsidian monolith]

TheHappyDragon

[ashen flare]

However, I am unsure how to justify using the real identity above to denest the bottom one

I can't simply pull out the i as far as I know since such real properties do not apply to complex numbers

[viscid thistle]

why

[ashen flare]

$2=1+1=\sqrt{1}+\sqrt{1}=\sqrt{(-1)(-1)}+\sqrt{(-1)(-1)}=\sqrt{-1}\cdot\sqrt{-1}+\sqrt{-1}\cdot\sqrt{-1}=i \cdot i+i \cdot i =i^2+i^2=-1+-1=-2$

[obsidian monolith]

TheHappyDragon

[viscid thistle]

damn

[ashen flare]

If I blindly plug 2i and -3 into this formula though I do get the correct value. how do i justify plugging in a negative for b and an imaginary number for a here?

I feel like this is trivial somehow but i cant figure it out lmao and idk which channel to correctly ask this in

[viscid thistle]

so laws of exponents dont work here right

[ashen flare]

there are restrictions to this rule yes

[viscid thistle]

ahh ok

soo what are the laws of exponents for complex nos

[ashen flare]

? I dont know which spefici law I would apply lol

[viscid thistle]

i had these type of confusions for a long time

never were resolved

[ashen flare]

My conjecture for why this works is simply just that if we have $\Re(a, b, c)\ge0$ then $$\sqrt{a\pm b\sqrt{c}},=, \sqrt{\frac {a+\sqrt{a^{2}-b^{2}c}}{2}} \pm\sqrt{\frac {a-\sqrt{a^{2}-b^{2}c}}{2}}$$ would hold

idk how to prove this lol

[obsidian monolith]

TheHappyDragon

[viscid thistle]

it is like completing the whole square

[ashen flare]

?

[viscid thistle]

wait

hmm like if we want to find root of 7+4root3 then we would make the thing under the root perfect square and solve it

maybe here also we would do something like that

[ashen flare]

ive relady sovled the initial root lol

i just want to justify why i could use the formula with complex numbers

[viscid thistle]

COMPLEX NOS ARE COMPLEX LOL

[ashen flare]

i gues

[viscid thistle]

why u said real part ig this formula should not applicable for complex nos

or it should be

[viscid thistle]

ig if we answer this then we ll get why u can use this fromula for complec nos

[viscid thistle]

if u get th e answer then ping me ok?

[ashen flare]

ok

[ashen flare]

well im conjecturing that it does lol

[viscid thistle]

Couldnt you write $\sqrt{2i-i \sqrt{3}} \ =\sqrt{2-\sqrt{3}} \cdot e^{i \cdot \frac{pi}{2} \cdot \frac{1}{2} \ =\sqrt{2-\sqrt{3}}\cdot \cos{(\frac{\pi}{4})}+i\cdot \sin{(\frac{\pi}{4})}$

[obsidian monolith]

Plazzi
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[viscid thistle]

This is why $i \neq \sqrt{-1}$

[obsidian monolith]

Plazzi

[viscid thistle]

Well it is, but it isn't the Definition of i

[ashen flare]

this is literally the definition of i

[ashen flare]

🤷 i guess this relationship can be visualized by writing sqrt(ki) = sqrt(k) * sqrt(i) which is true for all k>=0 for a real number k

you dont cross the branch cut that way

[wanton shell]

Hii
Could someone help take a look at this

Does the limit exist?

My reasoning
No, left side limit isn't equal to right side limit

Left side limit doesn't exist

True?

[wanton shell]

If we take 0.99 as x for left side limit

It becomes undefined

Domain is (1,infinity)

[acoustic vault]

That does mean it doesn't exist

[viscid thistle]

what would happen if u just plugged in 1 rn

and computed it

[acoustic vault]

You look at whether the limit exists based on the domain of the function. Whether or not the function isn't defined in an open interval containing c does not mean the limit as x-->c does not exist

[wanton shell]

Ahhh I see

Thanks for the help
Much appreciated

[acoustic vault]

To clarify, you do need to be able to plug in values arbitrarily close to c

For example, suppose f is defined at the point 3, but if there is a r>0 such that f is not defined at all (besides at 3) on (3-r,3+r), then the limit is not defined

However, you need not f be defined on the entire open interval, only to be able to plug in points which can be very close to 3

[viscid thistle]

wtf

[acoustic vault]

For example, f is defined for all rational numbers >=3, but nowhere else

Then we can still take the limit of f as x goes to 3

[viscid thistle]

well i found this on brilliant.in site

https://brilliant.org/wiki/complex-exponentiation/#:~:text=z %3D x %2B i y %3D r,multiplying together their absolute values.

[ashen flare]

well yes this is what i have stated before xd

[ashen flare]

Both the left(a+bi, bi->0, a=0) and right handed limits both agree with each other to be 0. The function is continuous. You can also directly plug this in and see its answer. If you want to consider the domain of the function it also includes the point at 1 lol. I'd argue that it exists

[viscid thistle]

so ur root iota would have al ot of answers

but u can pull iota out it can be done bro there are restrictions to that u just would have variety of diff answers

[viscid thistle]

You do

[cedar totem]

how to solve sqrt(x+2) = 1.1x^5 ?

--> ((x+2)/(x^10)) = 1.21 --> (2/1.21)^(1/9) = x ?

[summer ruin]

I don't think you can solve it

[viscid thistle]

hey so can u write underroot of ab = root ofa x root of b where a and b are complex nos

[ashen flare]

if their real parts are positive yea i guess

[ashen flare]

This turns into an unsolvable dectic equation with half of the solutions extraneous lol

You can probably numerically approximate solutions to your desired precision

[viscid thistle]

i dont think so

ig real parts dont matter

nor imaginary

u can write any complex number into re^iotatheta format

and then can then find their roots

ig

[winter ravine]

Taking this class in the 11th grade, hope it's not difficult as hell

[minor zodiac]

guys quick question. Why the vertical asymptote of a rational function is x -value where the denominator of the function is zero?

[summer ruin]

the vertical asymptote isn't that, an asymptote is a line to which the functions approaches

or another way to say it is that the distance between function and that line approaches 0

[minor zodiac]

is it different from the discontinuity of rational function?

[summer ruin]

it doesn't have anything to do with discontinuity even

1/x has an asymptote y = 0 regardless of whether you consider the discontinuity at x = 0 or not as long as your domain of 1/x is (a,+inf)

where a>=0

or a simpler example of that would be arctangent which is perfectly continuous function

[minor zodiac]

so in this case, there are two vertical asymptotes when x = -7 and 3?

[summer ruin]

no, again asymptotes have nothing to do with discontinuity

you need to check the limit as x approaches the point of interest to make conclusions about an asymptote

[minor zodiac]

ok thanks

[opal tree]

An asymptote only exists if the 'simplified' form of the equation's denominator = 0

You can cancel out (x+7), you'll be left with (x-3) on the denominator

So -7 is a removable discontinuity, 3 is a vertical asymptote

[minor zodiac]

Oh I didn't know that! Thanks

[ashen flare]

you'd cross a branch cut if you have negatives lol

[viscid thistle]

okk

[viscid thistle]

well, imagine the people that take AP Calc BC or even HL Mathematics.

Now, this is only for USA. Don't get me started with what 11th graders take in India, China, Russia, Singapore, and some other countries. Boi, like lol...

[lucid trench]

lol im taking this in 12th grade

[grim badger]

lol i took this this summer

which i finished like 2 weeks ago

[wanton shell]

Hai
Could someone help me with this question

I would try to find the left side limit and right side limit but its impossible given the domain

Does the limit exist?

[summer ruin]

left and right side limits are both 1

[uncut mulch]

I would try to find the left side limit and right side limit but its impossible given the domain
wdym

you don't really care about whether its defined at x=4, when considering the limit as x→4

[wanton shell]

Tqvm

[viscid thistle]

its not that hard bro u just have to attend regular classes and notes and do problem solving

[muted oasis]

it should be 1
as said above, because it is a limit, you kinda ignore what happens right at that point
the graph sinks to -1 at exactly 4, but for any other value of x it is 1

is this channel also for differentiation and integration?

[viscid thistle]

Taking honors precalc in 10th grade

[lucid trench]

nice

[vapid plaza]

That would go in #calculus

[viscid thistle]

Calculus

[muted oasis]

hmm

[minor zodiac]

guys quick question. Is x³ a polynomial?

[lucid trench]

no

it's a monomial

[minor zodiac]

then this guy is wrong?

[lucid trench]

i'm pretty sure he was just generalizing

but yeah

[minor zodiac]

Ok so polynomials include a monomial?

[lucid trench]

yeah

[minor zodiac]

Ty!

[lucid trench]

no problem

[tender dune]

Is Algebra and Trigonometry enough for learning calculus? Or do I need to learn topics such as matrices, conic sections and sequences

[cedar beacon]

matrices, conic sections and sequences, no need for these

u should have some basic understanding of sequences though

there are not many prerequisites for calc, it's pretty straightforward

[tender dune]

Tyvm

[summer ruin]

sequences is calculus

you can't even define a limit without a sequence

[acoustic vault]

Sure you can

And in fact the ordering of the sequence is irrelevant to the convergence of the sequence and so one may disregard “sequences” entirely and deal with neighborhoods instead

[steel olive]

I think sequences are a bit too general to give to calculus

I would say series are calculus

But sequences are common for many non-analytic reasons

[viscid thistle]

try solving somebody

in 60 sec or less

[willow bear]

yes

[viscid thistle]

c)

[unkempt flame]

Is answer options c

[viscid thistle]

Yes, the answer is c.

good job both of yall but did yall do it in 60 sec or less?

and did not guess?

[crisp stirrup]

how? can you have a brief explanation?

[weak umbra]

sec(x) + tan^3(x) cosec(x)
sec(x) + tan^2(x)sec(x)
sec(x) (1+tan^2(x))

Since sec^2(x) = 1 + tan^2(x),
(1+tan^2(x))^3/2
(2-e^2)^3/2

@crisp stirrup

[stark laurel]

Does anyone mind helping me

[viscid thistle]

What have you tried?

[visual hinge]

tan(2x)^x as x approaches 0 is my last question

[crisp stirrup]

ok thx

[fleet tendon]

Just wanted to solve this

In a different way just for fun

Solutions are -1 and -2

I only got -1

Oh wait

Yea i did it wrong

lmao

Well, it doesnt matter anyway

Would be +-(+- so its the same thing

There’s no way i can get the second solution by doing this?

Is it impossible?

[uncut mulch]

you didn't manipulate your equation properly after
x^2 = -2 - 3x
what exactly were you doing that lead to the next line

[fleet tendon]

$\sqrt{x^2}=\sqrt{-2-3x}$

[obsidian monolith]

Zarpa Negra

[fleet tendon]

jmmm

Yea i see it

im so dumb

[weak umbra]

this probably aint the best way to solve it

[fleet tendon]

It isnt

It was just for doing something different

And a little bit more tricky

[weak umbra]

u could use that ig for numerical iterations ig

[fleet tendon]

Does this has any solutions in complex?

[tender dune]

Do I have to learn this section for calculus or is trig functions, identities and equations enough?

[steel tulip]

For calc not really imo

[viscid thistle]

imo has NOOOO calc

but the algebra geometry number theory etc ques are extremely difficult and require severe damn analytic thinking and a logical mindset

[wild comet]

same, im a bit nervous about it considering i didn't do so good in algebra 2

[weak umbra]

sqrt(x) by definition is the positive root so that aint possible

[weak umbra]

they meant imo as in “in my opinion” lol

[viscid thistle]

principal square root is postive

[viscid thistle]

bruh

[fleet tendon]

Theres still a discontinuity in sqrt complex function tho

[weak umbra]

hmm, im not sure about complex square roots

[viscid thistle]

if u say imo in a MATH server, anybody is gonna think it means International Mathematical Olympiad.

[weak umbra]

the contexts gives it away

[viscid thistle]

yeah, i did not read the entire convo and i just say that so i was like no.

[fleet tendon]

Like, $36e^{i2\pi}$ works if $(a^b)^c=a^{bc}$

[obsidian monolith]

Zarpa Negra

[fleet tendon]

Which idk if that happens in complex

[weak umbra]

surely it should

[fleet tendon]

It could be false, or it could just create discontinuity

[lucid trench]

imo i find precalculus to be quite necessary because there are a bunch of important topics my school doesn't talk about in algebra ii, such as matrices, specific trig identities, binomial theorem, convergence or divergence, etc etc

[acoustic vault]

yes, we somewhat did those things, and then I forgot about them the moment I started calc

truthfully, you will probably just forget those things even if you learn them, and it probably won't make much difference to have seen it once before in precalculus

[keen anchor]

How did tan^3θcscθ
Become tan^2θsecθ?

How did tan^2θsecθ
Become (1+tan^2θ) ? Where did the sec(θ) on the left go?

[weak umbra]

tan(x)csc(x) = sin(x)/cos(x) * 1/sin(x) = 1/cos(x) = sec(x)

(1 + tan^2(x)) sec(x) = (1+tan^2(x))^1/2 * (1 + tan^2(x)) = (1 + tan^2(x))^3/2

for the tan^2(x) sec(x) + sec(x) i factor out a sec(x)

[astral root]

How can i find the explicit formula when given the reursive formula a_(n+1) = 2a_n + 1 and given a_1 is 4?

[hybrid pewter]

heres a hint
a_(n+1) + 1 = 2(a_n + 1)

(think of a recurrence relation for an exponential)

[astral root]

Hmm

Not sure still

[hybrid pewter]

ok so we have a_1 = 4 and a_(n+1) = 2a_n + 1 for all n >= 1
Now rewriting the recurrence relation as a_(n+1) + 1 = 2(a_n + 1) for all n >= 1, we can define a new sequence b_n := a_n + 1 for n >= 1.
Writing our recurrence in terms of b_n gives b_(n+1) = 2b_n, and from here we recognize that this is the recursive formula for an exponential, giving us b_(n+1) = (b_1)2^n or b_n = (b_1)2^(n-1)
Rewriting in terms of a_n we have a_n + 1 = (a_1 + 1)2^(n-1) or that a_n = (5)2^(n-1) - 1 for n >= 1

[wanton jasper]

hi! i needed help on solving a polynomial inequality

4x(x-5)(x+8)^2(2-x)>0

what i have so far

[surreal berry]

so they want you to find at which points that polynomial functions is positive since yk they gave p(x) > 0

you already have the zeros of the polynomial

actually you missed one, x = 8

not just -8

since you have (x + 8)^2

both 8 and -8 satisfy it

so what's the problem?

[wanton jasper]

ohhh i see

thank you!! i was looking at my answer key and one of the solutions was 2<x<5

and it didn't look right because from what i did, it wasn't a solution

[surreal berry]

[wanton jasper]

thank you sm !!

[wanton jasper]

i’m not sure how to solve this

[willow bear]

make a sign table

[wanton jasper]

not sure how -2x^2 and (x-9)^3 fits into the table

[summer ruin]

first you should do is get rid of the unnecessary minus sign

then realize that x^2, (5-x), (x-9)^3 etc are just polynomials that have their zeros and you should think how their sign changes as x passes over their zeros

starting from some large x to get the first sign

and you would also have to exclude points where the fraction is undefined from final answer

[minor zodiac]

guys quick question! what does ''rounded to nearest hundreds'' mean?

[summer ruin]

1.11 rounds to 1.10 and 1.15 rounds to 1.2

[minor zodiac]

OH I see. TY!

[willow bear]

hundredth, mind you.

[winged juniper]

Any web pages for practicing calculus properly?

[lucid trench]

khan acamedy

and also wdym properly

[winged juniper]

Other

Like I want to practice with exercises on the daily basis

[glacial lantern]

https://gyazo.com/0a6fd0b448acb89a6da86ad555855dec

[worldly lantern]

So I watched a video that explains that multiplying outside a function either shrinks or stretches the function. But they never really explained if it should stretch or shrink

What value should you multiply to shrink a function?

Nevermind I got it

But you multiply with fractions or divide with numbers

[viscid thistle]

idrk where to ask this -- but I feel like most of the mistakes I make math-wise are bc of not having enough time or making a dumb mistake, so how do I fix that? Like get quicker and have more understandable concise work

Bc I feel like it will only become more of a problem if I don't fix it by the time I get to Calculus

[opal tree]

Understand patterns really

Mathematics is just logic in patterns

But some people have a harder time finding patterns than others

So there's no real "method" of getting faster other than to hopefully realize the patterns that make up the foundation of mathematics

[mint narwhal]

Hey, I don't know if this is the right place to be asking this, but can someone help me understand how to find the derivative of a function using the power rule? I've tried to search it up online but nothing explains it well enough for me to understand.

Actually, scratch that, I got it.

[viscid thistle]

Easy

d/dx [x^n] = nx^n-1

[mint narwhal]

Alright, thank you!

[viscid thistle]

The organic chemistry tutor explains it the best

[lost grove]

khan academy is better

[viscid thistle]

Yes, I agree but for a faster explantion, just go to the organic chemistry tutor. Both are good and I actually prefer Khan sir. But, I only watched org chem for derivative so I told him to watch org chem.

[summer ruin]

those two are different

yes

[elder junco]

what is a directrix

I understand it's some sort of line but why do I care

[rustic swallow]

i need help

help me and ill venmo 1$

[stray fable]

please help him

because i need help w the same thing

[rustic swallow]

<@&286206848099549185>

help please my dad is having an abortion

[wary summit]

What do u need help with

[rustic swallow]

help

[viscid thistle]

Its [0,3]

Not (0,3)

(0,3) excludes 0 and 3

[lost grove]

should be closed interval i think

[hollow summit]

Range should be [0, 4]

[hollow summit]

Range should be [0, 3]

[oak gulch]

does anybody have notes from their precal lessons? preferably under 11th grade

[carmine bobcat]

can someone help with this?

[viscid thistle]

Answer is 8.

[wintry jacinth]

F(2) = 4x - 9 how do I find function value

[hollow summit]

F(2) = (2)^2 +(2)(2) -3 = 4+4-3 = 5

[willow bear]

do not give out answers.

[brisk pasture]

Oh sorry

[limber patrol]

can anyone help me
Q: if f(x) = x² + 5x + 3 find f`(2) using definition
this is the solution in my book but i can't understand the last 3 steps(the zoomed in picture)

[summer ruin]

you just factor out $\Delta x$

[obsidian monolith]

Transparent_Elemental

[summer ruin]

then divide by it and evaluate the limit

[limber patrol]

thanks for the help i understood it

[summer ruin]

figure out where the function is undefined and exclude those points from the real line

[queen plaza]

Anyone know how to write a polynomial function with real coefficients whose zeros and their multiplicities include those listed
Degree 3; zeros:√5, -√5, 3

<@&286206848099549185>

[lost grove]

i have never heard of a reverse cubic formula

but maybe there is one

[queen plaza]

bro im so confused

[lost grove]

?

[queen plaza]

like i can get a polynomial function but the degree it gives me is to the 4th

how do i get it to 3

[lost grove]

what

[gray hound]

Factor out a x and then solve the quadratic?

[lost grove]

are you trying to find a polynomial of degree 3 that has those roots or smth?

[queen plaza]

yeah

[gray hound]

Also every term in bottom has x and so does top so you can make every x go down one degree

[lost grove]

then try to find some kind of reverse cubic formula or smth

i don't have one

[gray hound]

factor out an x from denominator then solve the quadratic

Also is this a test btw?

@silent quartz

[opal tree]

Set the denominator = 0

[opal tree]

Who tf pinged

[viscid thistle]

uh me

[viscid thistle]

I mean to reply to the person who sent the question not you. lol

[opal tree]

Bruh

[tacit light]

one way to do it is $P(x) = (x-\sqrt{5})(x+\sqrt{5})(x-3)$. another way is $P(x)=(x^2-5)(x-3)$

[obsidian monolith]

emily (she/her)

[tacit light]

the key here is that if a polynomial looks like $p(x)=(x-a)(x-b)...(x-z)$ then the zeroes are $a, b, ..., z$

[obsidian monolith]

emily (she/her)

[queen plaza]

Yeah i already got it dw

thank you tho

[brisk gale]

Ello

How would I approach a partial fraction whereby the Denom is a quadratic and numerator is linear

But quadratic is in form (x-4)^2

Wouldn’t the a and b be the same

Once x is found as x = 4

Then implement 4 into linear eq

[brisk gale]

Thanks so much bro

Imma try figure it out from here

I’ve had help - 8 open for an hour lol

[summer ruin]

you should be able to find a more general explanation for what to do when you have repeated roots i. e. complete squares or cubes, etc

[hushed sphinx]

You haven't shown what the question is, which makes it difficult to help meaningfully.

But the handwritten calculation you show would probably make more sense if (5-1)² should have been (5-(-1))².

[oak gulch]

Wait

Let me send the problem

[tepid trout]

i got (x-6)^2+(y+1)^2=40

[oak gulch]

Like this?

[brisk gale]

What about this type

X^2+x-4

All over

X+2

How do I partially fractiate that?

[summer ruin]

polynomial division

if you have a calculus book it should fully explain how to solve each type of a fraction

otherwise just look it up on the web

[brisk gale]

I’ll try that thanks

[paper sand]

Help 😭

[hushed sphinx]

That doesn't make much sense. As stated there, you could just set u(x)=x and then essentially do nothing.

There must be additional requirements that u(x) needs to satisfy, which are not shown in your snippet.

[paper sand]

Yeah, I am confused as hell

[viscid thistle]

is there a main statement to the problem?

[paper sand]

Nope

[lost grove]

where did you get this problem

what context

if it's something to do with u sub, then u would be 3x+11

[gritty nest]

feel free to disagree with me but the way i see it this problem can be solved in more ways than one. basically they want you to make y a function of u and u a function of x?

so then any of the following substitutiins should satisfy this:

$u= 3x$

[obsidian monolith]

Joe591

[gritty nest]

or

$u= 3x+11$

[obsidian monolith]

Joe591

[gritty nest]

both get rid of x completely.

the only question is why would you choose one over the other.

[hushed sphinx]

What do you mean by "where the crossing of the x-axis would be"?
Would be if what?

[tight ore]

Can sm one tell me how to solve that 21 th one

[willow bear]

try drawing a few of these intervals on the number line

[tight ore]

Bruh the ans is that

But still i don't t get that

Bruh u there?

[chrome garnet]

so first of all the intersection of all such intervals for all n positive integers is the limit as n-> inf of this interval bc you are taking in cosideration all positive integers from n = 1 to inf

now try evaluating the limit as n-> inf of the right endpoint alone and the left endpoint alone

then the answer should be clear

are you there @tight ore

[limber patrol]

can someone explain how to solve this (proof of second picture)

[summer ruin]

you're given y, use it

[uncut mulch]

if you are unfamiliar with the notation,
$y^{(4)}$ indicates the 4th derivative

[obsidian monolith]

ℝamonov

[viscid thistle]

This is a differential equation btw if you want to look some things up

[limber patrol]

thanks for all of your help my problem was mostly the notation

[unique mauve]

for the second question, shouldn't the answer be 0.5 since at t=0.2 f(0.2)=.5

[willow bear]

what's f?

there's no function named f in the problem

[unique mauve]

no, i thought f(t) = s

[willow bear]

ok sure

s(0.2) = 0.5

but you are not asked for s(0.2)

you are asked to estimate the velocity at t=0.2

not the position!

[unique mauve]

ah ok

[pulsar wind]

can someone help me with 39?

[summer ruin]

the solution is exactly the same as in previous questions

[eager plank]

can someone help me simplify this? i tried 3 times and got 3 different answers
(csc(x)-sin(x))sec^2(x)

[tiny badger]

hey

whats some good pre-cal books?

i wanna leanrn it as fast as i can

[brisk pasture]

I think it would be 1/cos^2x or just distribute the sec^2

[eager plank]

someone explained it to me and i got cscx, thank you though (my fault for not deleting here)

[fleet tendon]

This is wrong, what are the conditions?

[alpine wraith]

Honestly don’t really need a book

Most classes treat it as algebra 3

And you’ll just reinforce a lot of topics you already should know

And then you’ll cover trig

Hopefully

So learn the unit circle

[tiny badger]

I dont want to learn it in class. I want to learn it as fast. as i can so i can get into calculus.

[fluid ivy]

Same here

[surreal berry]

use khan academy then

[fluid ivy]

Ye

[fresh marsh]

Help I've been abandoned

In help#5

[elfin hull]

Why is the value above x^2 a constant instead of linear (Bx+C)? I thought the numerator has to be one degree lower than the denominator...

[summer ruin]

it doesn't matter whether it's $\frac{A}{x} + \frac{B}{x^2}$ or $\frac{Ax+B}{x^2}$

[obsidian monolith]

Transparent_Elemental

[elfin hull]

I see, thanks for clearing that up

[clever pewter]

Use openstax precalculus it's great

[hot sigil]

Could someone explain how to do these problems, I don’t understand what evaluate means in this context

[fiery eagle]

its just asking you what the output of g(x) is when the functions input is -3.

so you'd look at the graph, find where x = -3, then find what the corresponding y value is.

[hot sigil]

So 13 a is -2

[fiery eagle]

not quite, it wouldn't be negative because the line is in the positive quadrant of the y axis still.

the 2 is correct though

[hot sigil]

Or yeah 2 my b

So b is g(0) bc it gives you the y value

[fiery eagle]

exactly. since when g(x) = 3, the x-value is at 0.

so g(0)=3 mhm

[hot sigil]

Cool, ty

[fiery eagle]

np

[hot sigil]

What about for 17. And so on, graphing the points makes a horizontal line, idk what to do with that

[fiery eagle]

for 17-20 you would just plug in the x value into the functions. So for example, for question 17, I'll evaluate f(-4). 3(-4)-7 = -19

then you'd just repeat that process for every function they are asking you to evaluate for questions 17-20

[hot sigil]

Do I do the same equation 5 times with all 5 values?

[fiery eagle]

yeah, for each question you would evaluate each of those 5 inputs they are giving you: f(-4), f(-2), f(0), f(2), and f(4)

so you'd evaluate all 5 of those for each of the 4 questions

[keen vault]

can i ask ab some simple limits in here?

[hot sigil]

Alright, Tysm

[fiery eagle]

sure bugmi, still have a bit before i gotta study so go for it

[keen vault]

asked earlier in #calculus but

what does determining a limit graphically mean? do i just like draw a graph and then say smth like "this graph suggests that the limit blah blah"?

my textbook threw the graph in one of the examples to the side and just wrote the little sentence

[fiery eagle]

do you have a homework or a graph question i can see to give an example of what it means

if not i'll just draw it out in paint

[keen vault]

i can take a picture rq

its smth like this

[fiery eagle]

okay onesecond, let me graph this in desmos and then draw it out

[keen vault]

ight

the answer is 1/2 i think, but im unsure how to determine it grapgically

since u just factor or whatever then plug in the 1

[fiery eagle]

egh, gotta use l-hopitals rule for this

[uncut mulch]

the answer is 1/2 i think
since u just factor or whatever then plug in the 1
yes

[fiery eagle]

well guess not since it's graphically, yeah the answer is 1/2, ill draw it out so u can see what it means graphically

[uncut mulch]

did they provide you with the graph?

[keen vault]

nope

[uncut mulch]

i suppose they may want you to use a graphing program?

[keen vault]

so i wouldnt have to draw a graph?

i do have my calculator and i did put the function through it

[uncut mulch]

i think you'd still be expected to provide a rough sketch

[fiery eagle]

i imagine they are wanting you to use a software like desmos, draw it approaching from both sides, and show where the limit would be.

[keen vault]

rough sketch is fine

can i just draw like an open circle instead of what u did or nah

[fiery eagle]

an open circle? like where (1,1/2) is a graph to express it as a hole?

or do you mean like drawing a hole around the location on the graph instead of the lines approaching from both sides

[keen vault]

the latter ig

[uncut mulch]

you'd draw the hole at the coordinate (1,1/2)

[keen vault]

oh ok

so i just make a rough sketch with the coordinate, then mark it with a hole?

[uncut mulch]

yeh

[fiery eagle]

uhm, maybe? I imagine the professor wouldn't be satisfied with that though. the lines approaching from both sides expresses what a two-sides limit is graphically. Then the hole at the coordinate expresses it's a hole at that location.

ye

[uncut mulch]

and then draw arrows from each side i suppose

[keen vault]

gotcha

[keen vault]

ok im mad since i just noticed the instructions on the google classroom only said algebraicly

💀

wasnt that much extra work anyway so idrm

[livid dew]

I'm hoping this is the right place to ask this. I desperately need to do well in precal, but have made ZERO progress in the class. Is there a known online course that's proven to work? mathhelp was a godsend for my entrance exams (been out of school 7 years), but they don't do precal

[civic cedar]

Hi! Does anyone have any idea how to solve this? Could you possibly walk me through the steps?

[viscid thistle]

Maybe Take mirror image of this graph wrt the line y=x and then u will get the graph of finverse

[sand bane]

hey guys, is it okay to ask a favor?

[eternal thistle]

No it isn’t

[gentle talon]

Ive been trying to find answers but I just cant seem to find it..

Pre calculus Circle Real life Functions

Can anyone help me :/.

[summer ruin]

you're just asked to find an equation describing a circle with specified parameters

[gentle talon]

Yeah that too I can already find the radius

which is 25

Is that on the rules that I should not ask that? @summer ruin

Like asking for the answers :v.

[summer ruin]

there's like 50 people each day asking, so I guess not

[gentle talon]

:/ but do you know any equation from this problem though?

[summer ruin]

do you know the equation describing a circle?

[gentle talon]

Well yes but like from this example look.