precalculus

[grim zephyr]

Help

How do you derive half angle identities

Like ik I could search it up

But I might forgot so what’s the logic behind it

Like how double angle can be adding the same angle twice so u can just use angle addition

[grim zephyr]

<@&286206848099549185>

[grizzled sable]

Do you remember the double angle derivation

like sin2x = 2cosxsinx

[tulip lily]

I'm gonna start learning precalculus tommorow

[granite holly]

hello can someone help me finding the formula

[lone peak]

Since A and B both have to lie on the curve, we know that
$0.5 = \frac{a}{b}$ and
$8 = a \times b $.
Hence b = 2a, and 2a² = 8, meaning that a = 2 and b = 4 or a = -2 and b = -4. Both are acceptable answers to this question.

[obsidian monolith]

OutOfNosh

[granite holly]

so like y=1/2(8)^x

[lone peak]

Yes.

Wait. No

As in 8 = a * b^1.

And 1/2 = a * b^(-1) = a/b.

[granite holly]

whatt

confused

im sorry

y=2(4)^X?

[lone peak]

The equation y=a(b)^x means that to find the y value, you raise b (which we don't yet know) to the power of x, and then multiply that by a.

So we know that if we raise b to the power of 1 (as in (1,8)), and then multiply that by a, we get 8.

And since b to the power of one is just b, that means a times b is 8.

[granite holly]

ohhh okay, thank you so much, i have one more question

[lone peak]

Shoot.

[lone peak]

It is known that the angles on the inside of a triangle add to 180°.

That symbol in the top-right means that that angle is 90°.

So 90 + 48 + β = 180.

Which is just a subtraction problem.

[granite holly]

okay thank you so much

can u verify the answer for the last one^^^

[lone peak]

I don't understand what you mean by that.

[granite holly]

like what should have my final answer been

[lone peak]

For β?

[granite holly]

noo, for the other question

[lone peak]

Oh right.

[lone peak]

So from this, there are two possible correct answers, with you being asked you give only one. You can either give ||y = 2(4)^x|| or ||y = -2(-4)^x||, both formulae contain the points given.

I have to go to bed now, so if you need help finding a and c you're either going to have to ask for someone else's help or wait 7 hours. Best of luck to you.

[granite holly]

its okay i got it, thanks sm!

[abstract cloak]

Does anyone know a good precalculus book?

[tight compass]

Is there more stuff after 0.5^k? If not 0.5^k is not dependent on t so the inner sum is summing up a constant value. After that you end up with a sum of a finite geometric sequence. Try writing out the sum S = r^1 + r^2 + … + r^K and the sum rS then solve for S.

@icy cypress

[icy cypress]

Nope nothing after k

[half coral]

Who invented calculus?

Was he bhaskara II or Issac newton?

or German philosopher Gottfried Leibniz

?

[willow bear]

would probably be best to say that calculus as we know it today is not based upon the work of one single person

[hushed sphinx]

Leibinz and Newton had a public and bitter priority dispute, but a more balanced view is that calculus as we now know it is a combination of ideas developed by several people starting in the mid-late 1600s (sometimes discovered by several of them independently) and refined throughout the next 150 years or so.

[willow bear]

even some of archimedes' work (i think? it was someone from ancient greece) on calculating the area of a parabolic segment could be considered a form of integral calculus

[fiery quartz]

wow i didn't know about bhaskara ii that's so cool

so bhaskara i invented the symbol for zero, bhaskara ii figured out the essentials of calculus

based

[indigo rain]

Any help

[viscid thistle]

what's log(-infi)?

[strange echo]

Undefined?

[willow bear]

yeah, undefined

log(x) is undefined for x ≤ 0

[obsidian monolith]

Pebble

Pebble

Pebble

Pebble

[minor oxide]

how is the -5 involved in this?

[willow bear]

the constant term controls the distance from the parabola to the intersection of the asymptotes, to put it loosely

[minor oxide]

how to use tho

[willow bear]

well you could just graph your curve's x and y intercepts idk

if you want to graph it by hand

[minor oxide]

dang ok

[viscid thistle]

As the constant changes the curve gets closer or gets farther to the vertical and to the horizontal asymptotes. See DESMOS slider graph below to understand it better

https://www.desmos.com/calculator/gmwmt3saa7

Hi I am new here! @viscid thistle

[flint bloom]

reference angles should always be between 0 and pi correct?

[willow bear]

0 to pi/2

[flint bloom]

oh bc its the distance to the x axis

so at most it is pi/2 which would happen at pi/2 + 2pi*k

[viscid thistle]

the reference angle is the acute angle formed by the "terminal side and the x-axis"

this is the reason why it is between 0 and pi/2

[lunar forum]

hey can someone help with a derivative for a radical

[viscid thistle]

you have ti eliminate h from the denominator

after that you replace h with 0

here is an example for you to follow https://youtu.be/Bi5Eop1fw18

[jovial elk]

Not sure if this falls in late algebra 2 or pre calc but can some please give me the steps to this

And this one too plz

[toxic remnant]

Can anyone point me to something that will help me learn how to use the trigonometric functions with pi? Or am I meant to just use a calculator, given this assignment hasn't told me I'm not allowed to? I have exams coming up soon that make me worried because I know I'm not allowed to have a calculator there, and I'm wondering if this is just the fact that I don't understand much about trig and it's something somewhat trivially worked out or if it's actually a "Well, use a calculator." problem here for this assignment.

I just understand that these functions are a huge gap in my knowledge, and when I try and find information on them I get lost in sohcahtoa which I already understand

[mystic tendon]

anyone able to help me

[vapid plaza]

what are you having problem with

[toxic remnant]

Moreso I'm wondering if I'm meant to be able to work out, for example, sin(13*π) without a calculator

sorry, the value that's meant to be in both of those equations is negative pi, not positive

[vapid plaza]

you know that 2pi is a full circle right? so 13pi is 13 half-rotations

[toxic remnant]

ah... okay, I've been taught how to convert radians to degrees and back, and that should've given me the knowledge that 2pi radians=360deg... I didn't make that connection and I haven't been explicitly taught that yet. Thank you for the point in the right direction :)

[stark mango]

how do u do this

[slate reef]

call the first angle x
the second is x+10
the third is 3*x

[stark mango]

Anyone have trigonometry resources

[stark mango]

ty i got the answer

[granite holly]

please help

[willow bear]

have you made any progress so far?

are you familiar with things like the law of sines and the law of cosines?

[viscid thistle]

How do I go about solving this by any chance

[strange echo]

Between?

[stark mango]

Is anyone particularly good at trigonometry

[hushed sphinx]

https://dontasktoask.com/

But preferably in #geometry-and-trigonometry

[granite holly]

39 degrees between them @strange echo

[lapis eagle]

Read what Ann said

The message below yours

[river jasper]

Hint: Plug in (x-1)/x as x

[limpid wasp]

Just substitute x = 2 for f(2) and x = -1 for f(-1)

[viscid thistle]

I know that part

Ok nvm I figured it out, was a lot easier than I thought lmao

[obsidian monolith]

Ebeere

[river jasper]

Because it is a relation between the values that f takes at x and at (x-1)/x

[proper field]

Hello what does p(x) means

Does it have the same meaning as f(x)

[hushed sphinx]

In the sense that both of them mean "whatever it has been defined to mean in the context", yes.

[proper field]

Help pls how do I determine whether p and q are positive or negative

[hushed sphinx]

Is your earlier question related to that? The "px" in that image just means p multiplied by x; both letters stand for numbers.

[proper field]

Um no

It's another question

Last one is this

p(x)

Not related to the graph

[hushed sphinx]

Okay, there p is the name of a function that could just as well have been called f.

[proper field]

ok

[hushed sphinx]

You can see from the definition y=(px+5)²+q that the value of y must be at least q.

Since it is clear from the graph that y does depend on x, p cannot be 0 because that would make y the same for all x.

This means that there must actually be a value of x that leads to y=q, namely the one that solves px+5=0.

So q is actually the minimum value of y.

And the x-coordinate where that minimum is achieved has px+5=0.

[vivid quail]

8. A baseball is hit at a point 5 feet above the ground toward the left field fence. The fence is 10 feet high and 375 feet from home plate. The path of the baseball can be modeled by the parametric equation x = t * 115cos(x), y = 5 + t * 115sin(x) - 16t^2. Will the ball go over the fence if it is hit at an angle of x = 35 degrees? (Parametric mode, degrees)

Yes or no?
If yes, how far above the fence will the ball be when it goes over?
If no, how far below the fence will the ball be when it hits the fance?

[obsidian monolith]

dackid

[hushed sphinx]

Just set r² to (x0-h)²+(y0-k)²?

[summer basalt]

Help

[lunar forum]

dont know where to start

tried multiplying by 4x/4x

[obsidian hinge]

have you been taught l'hopitals

[lunar forum]

are u asking me

[obsidian hinge]

yes

[lunar forum]

no

[obsidian hinge]

are you in precalc?

[lunar forum]

yes

[obsidian hinge]

hm

what is 1/sin(x)

[lunar forum]

what do u mean

[obsidian hinge]

nvm

hm

i think this limit diverges

[lunar forum]

so it doesnt exist?

[obsidian hinge]

yes

i think

im like 99% sure

[lunar forum]

what work would u show to prove it

[obsidian hinge]

i think you should graph it

i would graph this one

[lunar forum]

ok

[crisp palm]

you cant even use l'h

[obsidian hinge]

and it obviously doesn't go to the same value on 0

[lunar forum]

yea that makes sense

thanks

[obsidian hinge]

yeah that's why i went nvm lol

[crisp palm]

yeah

[obsidian hinge]

forgot it required 0 or infinity on both sides

[lunar forum]

were on the last unit in my precalc class so were just learning our first part of calc

[crisp palm]

https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

watch this series

NOW

[lunar forum]

no

[obsidian hinge]

you really should

essence of calculus is amazing

[lunar forum]

ill do that next year

remind me

[crisp palm]

but why

[lunar forum]

why am i not watching it or why am i waiting until next year

[crisp palm]

waiting

[lunar forum]

cuz thats when im taking calc

[obsidian hinge]

fair enough honestly

[weak wharf]

Does anyone know of a function with a jump discontinuity that is not piecewise-defined?

eg. not absolute value, or floor, or ceiling, etc

[opal tree]

sgn(x)

There's also

6mod(x)

Or any modulo function

But those are well beyond pre-Calc lol

In desmos you can try mod(x^2, x)

[weak wharf]

i could have sworn I ran into some combination of exponential functions that happened to be piecewise around the y-axis, but I just couldn't remember

[opal tree]

(-1)^x?

There's this

[weak wharf]

I think it looked something like this

but it's alright, maybe i dreamt it or something

[blissful stone]

What are series used for?

I see them so often in high school maths

[willow bear]

a lot of things

for example one of many equivalent ways to define the exponential function is as its power series: $e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$

[obsidian monolith]

Ann

[blissful stone]

So series go through the amount of equivalent ways to define functions

[willow bear]

.......

no

you're missing the forest for the trees

[blissful stone]

Definitely, I need to find the perfect place for the trees so they didn’t grow on rocks

[fallow basin]

Can anyone solve Q2?

[opal tree]

A lot of things. They can be used to find a total sum of things, represent trigonometric functions, formulas, etc

[lapis sentinel]

can anyone please explain the fourth result

[odd cloud]

@fallow basin existence and unique of minimum can be shown using completeness axiom, because f(x) is bounded below by 0. But finding the minimum can be tricky.

[viscid thistle]

hyperbolic functions

[smoky kelp]

yes or no and why

[stable yacht]

If you know the definition of a one-to-one/many-to-one function, you should be able to see this graphically.

[bitter current]

(1+m)/2

[bitter current]

I doubt high school math teaches the completeness theorem lol

[frank vine]

Anyone can explain why using synthetic division of polynomial with rational root theorem yields roots of polynomial and how to do this process?

[frank vine]

Like find possible roots by p/q theorem and then test by synthetic division

But test positive first then from whatevers left test negative of same number on it

<@&286206848099549185>

[viscid thistle]

<@&286206848099549185>

Please i need help

[faint scroll]

what does bearing exactly mean?

[viscid thistle]

angle in degrees measured clockwise from north

Trig

[faint scroll]

maybe 270 degrees

[viscid thistle]

Less 249.5

[faint scroll]

Why would the distances coverd by the taxi will affect the angle?

The taxi has just gone south first and then west, so if we measure the angle anticlockwise from north, we get 90 degrees, therefore if we measure in clockwise direction it is 270

[viscid thistle]

It creates a triangle

[faint scroll]

Oh ok

my bad

we have to find the angle of the hypotenuse of that right triangle

from north ( clockwise)

am i right now?

[viscid thistle]

Sure why not

[faint scroll]

Ah is it 210.6 degrees?

[viscid thistle]

Jeez with how long I'm spending I don't think I'm fit for this

[faint scroll]

This is same as [180 + arctan(3/8)] degrees

[viscid thistle]

I think tan is sin/cos

[faint scroll]

arctan(3/8) = 20.6 degrees

oh sorry then the answer is 200.6 degrees

[viscid thistle]

Isn't it arctan(8/3)

[faint scroll]

No

draw it on paper you will get it

[viscid thistle]

Drawing on paper is inaccurate

[faint scroll]

Just draw inaccuarate one

You just have to find whether it is arctan(8/3) or arctan(3/8)

[viscid thistle]

You're right

I kept thinking it started from east

[faint scroll]

I calculated arctan(3/8) from this site

https://www.mathwarehouse.com/trigonometry-calculators/inverse-tangent-calculator-online.php

[viscid thistle]

The answer is 200.6 degrees yeah

[faint scroll]

Yep

[faint scroll]

here , the mistake I did was 180 + 20.6 = 210.6

haha, sometimes we do really silly mistakes

[formal forge]

If you were to use the complex definitions for sin x and cos x, how would you go about proving the > part of (sin(x))^2+cos2x >= 0, I guess it could be shown geometrically but idk if that's very valid

[fickle terrace]

how is the sereies r^n-1 + r^n-2 ... r + 1 a factor of (r^n -1)

and how did they get (r-1)

the proof makes sense but I don't know how you get the factor

[river jasper]

you dont understand why r^n-1=(r-1)(r^n-1 + r^n-2 ... r + 1)?

[fickle terrace]

@river jasper how do you figure that out series is a factor of r^n-1

[river jasper]

i think because previously you know that r^n-1=(r-1)(r^n-1 + r^n-2 ... r + 1)

[fickle terrace]

how can you previously know lol

[river jasper]

if i recall correctly it is seen in previous chapter

[fickle terrace]

ohh shoot

@river jasper thnx ill check it out

[kindred sluice]

Why is it that when we shrink the period of a trig function say tan(x) , are the points still undefined at the ends of the period? Like if we aren’t at those end points anymore shouldn’t the graph now be defined at those new shifted points? But this is not the case the new end points of the period are still undefined.

My textbook doesn’t go into any detail about it 💀

[vapid plaza]

Can you provide an example

[kindred sluice]

Sure like for example the function y=tan2(x-pi/3). The period get shrunk from pi -> pi/2. But when you go to graph it the end points are still undefined. Even though neither occur at -pi/2 and pi/2 which is tans normal period. Why is this?

[vapid plaza]

Well if the period of the function is shrunk then plausibly the points at which the function is undefined will shrink with it as well

For the function to be undefined you want the expression inside the tangent to be pi/2, 3pi/2 etc…

[kindred sluice]

Ah ok so the whole thing dynamically adjusts. For some reason I imagined more of a range like if something went out of the range or back in range it would now be defined

[vapid plaza]

It doesn’t lol

[kindred sluice]

Yea your explanation makes more sense lol

[low burrow]

i just finished trig and algebra 2, do you think it is necessary for me to take pre-calc before calc?

summed up: is pre-calc really necessary?

[tight compass]

not really precalc is usually trig and algebra 2, so just take calc.

[viscid thistle]

How do I do q63

[mild swan]

Solve the equation and look for complex solutions

[viscid thistle]

Quadratic formula? Isnt immediately obvious to me how to solve it

[mild swan]

Why/why not quadratic formula?

Any time you have a quadratic, you can use the QF

[viscid thistle]

I dont know how else to solve it

Complete the square? Idk

My algebra is rusty

[mild swan]

Either works

[viscid thistle]

Hm ok

[viscid thistle]

hey guys

i'm currently studying Precalculus, is anyone interested to be "precalc buddies" to help and talk each other about the subject?

[smoky kelp]

sure

I just started pre calc 3 days ago

[woven token]

Now I am studying calculas

[smoky kelp]

gamer

[candid iron]

hey rly quick what does it mean by f(4,3)? does it mean the values of f(3) and f(4)?

[hushed sphinx]

My first guess would be that it's a typo for f(4.3).

[candid iron]

ohh right, it is a translation so that makes sense

[hushed sphinx]

Especially if it's a translation from a language that uses a comma as the decimal separator.

[blissful stone]

I’m a math addict, I can talk about pre calculus for as long as I get more knowledge about it

[viscid thistle]

I don't rlly know much abt calculus but I'm rlly interested and wanna learn about it so where do I start, if it helps I've done trigo but idk if algebra 2 is still necessary since im still looking deeper into it and I don't know if there's any other areas in math that I should be good in for it

In general I just wanna know where to start with calculus

Oh shit wait do I have to be good at logarithms for calc

Forget it

[hushed sphinx]

You won't need logarithms to understand the basic definitions and concepts of calculus.

(To be frank, I'm not really sure what "good at logarithms" even means, but seeing some applications might easily be what you need to make it click, rather than trying to memorize random logarithm facts for no other reason than because).

[brittle talon]

I've some Calculus books and they all start either with the list of subjects of what you need to know in order to start with Calc or a test of those subjects, so i would recommend getting a Calc book and working from there.

[frank vine]

Rn in geometry gonna skip Algebra 2 and go into precalc next year so yes I accept as long as I get knowledge

[viscid thistle]

Having some trouble understanding this situation here, where I'm not given the period. Would it be safe for me to assume that the period is 360 and k-value as 1 ?

[storm lodge]

Algebra 2 is basically just trig

[proven marten]

yes

[hushed sphinx]

You're supposed to do something like compute the circumference of the wheel, then compute how many revolutions there are in 1000 m, then use trigonometry to figure out the vertical position of the stone after the last fractional revolution.

The actual answer, however, is that it's impossible to tell. It only takes a 1 mm difference in the measurement of the wheel diameter to add up to a whole revolution fewer or more over a distance of 1 km, and the rolling deformation of a motorcycle wheel is surely in at least that vicinity.

[viscid thistle]

Can anyone explain wtf is precalculus is about and what theorems and stuff it contains

[viscid thistle]

Ahh alright thank you, I'll definitely look into it and get myself some books

[viscid thistle]

I've got this so far. The circumference is 60pi. So I assume that 1m = 60pi (whole 1 revolution) so to find how many revs are there in 1000m I'm multiplied 60pi and got 60000pi. But, I not exactly sure what you mean by the last fractional revolution

[hushed sphinx]

So I assume that 1m = 60pi
What? Why? What's going on here?

[viscid thistle]

There is an answer to this (but I didn't exactly look at it )

[hushed sphinx]

60pi is about 188½. How do you get that to be 1m?

[viscid thistle]

I needed a reference point

[hushed sphinx]

You can't just make up stuff.

[viscid thistle]

Do you think I should divide the 60pi by 1000m instead?

[hushed sphinx]

I suppose you mean that the circumference is pi·60 cm, which is 188.5 cm. If you pretend that is equal to 100 cm, you get nonsense. Why would it equal one meter anyway?

[viscid thistle]

I think that 60pi is equal to 1 Rev, since we know that the wheel will continue to rotate up & down. What would 1 Rev would equal to exactly in terms of meters is what I am trying to figure out.

[hushed sphinx]

1.885 meter.

[viscid thistle]

What!?

[hushed sphinx]

What do YOU get when you multipy 60 cm by pi?

[viscid thistle]

188.5, you multiplied divide it by 100 to get that value in terms of meters.

[hushed sphinx]

Do you disagree that 188.5 divided by 100 is 1.885?

[viscid thistle]

No, I see how you got it, since 60mpi is 188.5cm, to convert that to meters you divided by 100, 1.885m would be 1 Rev.

[hushed sphinx]

Good. So how many of these revolutions does it take to drive 1000 m?

[viscid thistle]

So, then if 1rev = 1.885m, now I can figure out how many revs there would be in 1000m by multiple 1000m, which give me 1885rev

[hushed sphinx]

1885 times 1.885 is 3553.225 -- that's more than three kilometers.

Lets suppose you have giant wheel with a circumference of 100 meters instead. How many revolutions would that wheel make while it rolls 1000 meters? Surely not 100,000 of them.

[viscid thistle]

No, I wouldn't multiply it

That would be a bit too much, if I were to graph it.

I would instead divide this, because if the wheel rolls 1000m but with a circumference of 100m, not many rotate would be made. 1000÷100 = 10.

Wait

Nvm, @hushed sphinx

Okay from the question

I need to divide 1000 by 1.885, if that what was my circumference. 1885 is too much, if I were to graph it

[hushed sphinx]

Yes, you need to divide.

[viscid thistle]

1000m = 530.5 Rev

[hushed sphinx]

Right.

[viscid thistle]

Okay now all that's left is to find the vertical position (heigh) of the stone now that I know that 1km = 530.3 Rev

[hushed sphinx]

But you need more digits than that, because you need to find out how high the last 0.5 revolution of the wheel leaves the stone, and "about half a revolution" will not allow you a better answer than "it's somewhere near the top of the wheel".

[viscid thistle]

So I need the 530.5 Rev to be more precise

I'll use 530.50397 Rev. Is the 0.5 Rev, the last fractional revolution as you mentioned before?

[hushed sphinx]

Yes.

(Note that 530.50398 is 100/1.885 where you have already rounded the 1.885. If you divide by a more precise representation of 0.6·pi, you get 530.51648 instead).

(On the other hand, that makes a difference of only a few millimeters in the final height).

[viscid thistle]

Yes, I just check that could've been done as well if 60cm became 0.6m pi and divided by 1000 to give me 530.5164

[viscid thistle]

You mean like 530.5164 - 530.50397 =

[hushed sphinx]

Careful here! "0.6 pi divided by 1000" means something different from "1000 divided by 0.6 pi" -- the latter of these is what you did.

[hushed sphinx]

No, I went ahead and did the final trig step and compared the results with the two values.

[viscid thistle]

Oh oh yes, that I what I mean. That that would equal to 530.516477

Trigonometry?

[hushed sphinx]

Yes.

Also yes, trigonometry, since now you need to find how high the stone is 0.516477 revolution after the last time it hit the ground.

[viscid thistle]

530.516477 is the revolution after it hit the ground.

[hushed sphinx]

But each time the wheel has completed one revolution, the stone hits the ground again.

So it's only the last .516477 we need to care about.

[viscid thistle]

Ooh so that why it needs to be exact

I think I should draw the circle to better visualize this

My radius is 30cm, would the angle be 0.516477?

My adjacent is 30cm

@hushed sphinx I have to go now, can we talk about this l8r?

[hushed sphinx]

Perhaps. Or perhaps someone else will be around.

The angle is 0.516477 of 360°, or 0.516477 of 2pi if you're working in radians.

[lean cove]

I have this extra credit assignment and I need to prove that both sides are equal working on one side at a time. I've tried a lot of ways to prove it working without a calculator but I havent been able to. How would I prove this?

[lean cove]

does this work as a proof

[neat zodiac]

help

[viscid thistle]

@hushed sphinx I got the right answer, instead of doing that trigonometry step you were using, my teacher told me to use a cosine function and have all my values in units of cm as mentioned in the question. The textbook answers was 59.8cm, but my teacher said 55.43cm was okay too.

[lunar forum]

I’m stuck

[viscid thistle]

Happy to help. Do you any calculus whatsoever?

[lunar forum]

no just basic limits and the derivative formula

[viscid thistle]

So I am assuming the problem is asking you to compute the derivative of 1/(2x+1) right?

Like plug the function into the derivative formula and solve the limit?

[lunar forum]

yes

i think i have an idea of what to do actually

well turns out i dont have to do this problem for homework actually i just didnt check what was actually assigned

[obsidian monolith]

Arr0w_04

[viscid thistle]

Done.

Does that make things clearer @lunar forum ?

[lunar forum]

yes thank you

although i dont have to do this tonight it does help

[viscid thistle]

or you could just use the quotient rule for derivatives and this could be done in two seconds but I digress

[lunar forum]

yea we have to use the derivative formula only for this

[viscid thistle]

Well best of luck in your course. If you have further questions feel free to ask.

[lunar forum]

thanks

[hushed sphinx]

Um, the cosine function is trigonometry.

[viscid thistle]

This unit I'm learing is called trigonometric functions

My last unit was trigonometry with the sohcahtoa stuff

[hushed sphinx]

Huh. In my world, "trigonometry" is the thing you do with trigonometric functions, and "trigonometric functions" are what you use in trigonometry.

[viscid thistle]

Okay, either ways I get it. I really really appreciate you for all the help. The final test is tomorrow so wish me good luck 💖@hushed sphinx

[viscid thistle]

Mhm mhm

i didnt learn shit in trigonometry so thats good to know

[sinful dome]

Can u help me

[faint prairie]

it's a harder algebra 2/trig class that prepares you for calculus basically + an introduction to matrices, vectors, and limits depending on what school you're in. i heard that they do

trig identities, graphs, and equations
matrices, vectors, limits, derivatives
harder complicated algebra 2

idk what theorems

so if you did good in trig and algebra 2 you'll be fine

[viscid thistle]

so its basically just reciting trig?

[faint prairie]

yea

[viscid thistle]

good

I didnt learn shit about trig

I dont blame myself since none of our batch did lmfao

[faint prairie]

same

[viscid thistle]

But u learned in precal?

[faint prairie]

kinda glad i'm also doing precal next year

my friend did it

and i looked at his shit

[viscid thistle]

U also graduatee?

Congrats bro

me too

Precal next ur

yr

[faint prairie]

yup did you graduate too?

[viscid thistle]

Yes

[faint prairie]

congrats

[viscid thistle]

mhm mhm

I do understand factorials

And the like

Sequence thing

Coz i was so interested in probabilities and statistics way before trigo

[faint prairie]

those are useful in calcbc i think if you're in the united states

[viscid thistle]

Not in the us sad

[faint prairie]

dam then everywhere else in the world would call it second semester calculus

[viscid thistle]

what

factorials?

[faint prairie]

like college

yeah they're useful then but not now

[viscid thistle]

wtf

[faint prairie]

factorials you aren't gonna use em for a while

[viscid thistle]

Well

Where r u from

[faint prairie]

US

[viscid thistle]

usa?

I see

how many years of high school do you take

[faint prairie]

4

[viscid thistle]

with college u take 8?

[faint prairie]

hell naw it depends what career choice you want to be

[viscid thistle]

Wtf

[faint prairie]

here go to #discussion i guess

[viscid thistle]

Alright come over there

[spiral locust]

K

[supple owl]

Precalculus

[restive berry]

hello

[stable yacht]

That quadratic has no excluded values. It is defined for all real x-values.

I am not sure which approach you were taking, but it factors to (x-9)(x+4).

[steel fern]

Can I just cancel out the x^2 ok in both then multiply

[willow bear]

no

you cannot cancel out addends in a fraction like you're suggesting.

[viscid thistle]

Factorials are used everywhere in higher math…

[hollow cosmos]

Only use i can see is combinatorics , binomial coefficient

[viscid thistle]

There are so many more applications than what you just mentioned. They are used for (1) calculus (power series) (2) combinatorics (literally everywhere) (3) algebra (symmetric groups) (4) probability theory (poisson distributions) (5) number theory (legendre's formula, wilson's theorem) and I could go on and on

[hollow cosmos]

So basically 99% combinatorics 1% rest
(Not real %)

[viscid thistle]

What math have you done yet, out of curiosity?

[hollow cosmos]

Calculus , Algebra , Combinatorics , Number Theory , Geometry

And you can put lil bit of linear algebra to the list ig

[viscid thistle]

So AoPS/contest math basically?

[hollow cosmos]

Well basically competition math is all i do

And a lil calculus / analysis just because its interesting to me

[viscid thistle]

OK, yeah that explains things. To keep it short, there are a lot more applications to factorials besides introductory combinatorics and the math that you are used to. They come up everywhere in weird places not just in combi.

[hollow cosmos]

Well i mean power series and binomial coefficient are like id say biggest places where you see it right? Not including combinatorics

I mean sure there are bunch of theories that use it

[obsidian monolith]

Arr0w_04

[hollow cosmos]

Thats group theory?

[viscid thistle]

Yeah.

[hollow cosmos]

Well i said alot of theories use it

[viscid thistle]

You also said 99% combinatorics 1% rest, which you now know is false.

So now ya'll know

[hollow cosmos]

That was not really supposed to be true but more like pointing out that combinatorics is biggest use case

But yea i get you

[viscid thistle]

Are you on AoPS Pluton? I'm assuming yes because you do competition math?

[hollow cosmos]

What is AoPS?

Art of problem solving?

[viscid thistle]

ye

[hollow cosmos]

Not really

Thats like a website?

[viscid thistle]

Yeah they have forums on there and stuff

[shrewd prawn]

hiiii

[hollow cosmos]

Didnt use it

Is it good?

[viscid thistle]

Yeah, most contest people use AoPS nowadays in some form.

Like the entire US IMO team uses it, most USAMO quals use it, etc.

You should check it out. I think it'd be a good resource for you.

[hollow cosmos]

Their whole website looks like it just wants to sell you books and courses lol

[viscid thistle]

Yeah

It's a business/company that sells textbooks and courses

I'm not sure if you are from the US or not, but most of the top math students in the US (ranked via competitions) use art of problem solving.

I use it.

[hollow cosmos]

Ye im not from usa. But if i may ask you what do you use it for?

[viscid thistle]

Books, problems, they also have contest collections from every olympiad/contest in the world.

[opal tree]

That is just false

Ain't no way you just said that

[tight compass]

Just let Posato daydream for a bit.

[faint prairie]

i mean i'm not doing anything with higher math so my bad

[faint prairie]

for a while bruhhh

he's in pre cal not calc 2 or 3

[opal tree]

They appear in Calc 1

[faint prairie]

oh yeahhhh

i remember seeing that once from proving the power rule i think

[opal tree]

Nth derivative definition

[faint prairie]

yeah yeah

hella rare

except probably in higher maths i don't know

[opal tree]

I mean just a general rule of thumb

They like to ask problems like "what is the 16th derivate of x^(16)"

At least, for me, that's what I ask constantly asked

[faint prairie]

wait so the definition
"nth derivative of x raised to the nth power is n!"

so that'll just be 16!

[opal tree]

Yeah

It's like getting us ready for Taylors ... even though like

That doesn't appear until late Calc 2

Series tho

[faint prairie]

is it anywhere else in calc 1 or is that just all for now

factorials

[opal tree]

Not really

Maybe for like

Finding a term in a derivative of like (x+7)^6

Then that's just binomial theorem

[primal harbor]

Hello
IF f(x)=2g(x-1)
and g(x)=m(x-1)+n(x)
does that mean that f(x)=2[m(x-1-1)+n(x-1)] ?

[frank vine]

yes

[deep plaza]

can anyone help derive the function. passes through points (-3,0),(1,0),(4,0) and (-1,40)

[viscid thistle]

Well you have the x-intercepts so you can set up an equation in factored form

You also have the graph so you can get a basic image of the factors’ exponents

The graph touches at (1,0), meaning the factor will most likely be (x - 1)^2

The rest are assumed to just be their normal factors

Now you have an equation

y = a(x + 3) (x - 1)^2 (x - 4)

(Spaces for clarity)

And since you’re given a point and you have an equation (input/output), just plug in the sample point

40 = a(-1 + 3) (-1 - 1)^2 (-1 - 4)

Now just solve for a

40 = a(2)(4)(-5), thus a = -1

And your equation is complete

y = -(x + 3) (x - 1)^2 (x - 4)

[burnt lodge]

Find what?

[viscid thistle]

Can anyone smart help me in #help-7｜zen1thxyz

[viscid thistle]

sorry

partial frac decomp

[viscid thistle]

is there a quick way to find the y or x intercept in general form?

or does it only work in standard form (c/a or c/b)

[viscid thistle]

nevermind, i got it

[hot reef]

Help

[fierce violet]

same help

[celest nacelle]

for the first question you just aply Pythagoras: |AC| = sqrt(260^2 + 195^2) km
idk rly understand what bearing is suposed to mean here (not native in english) but is it's the angle BÂC its arctan(195/260)

*if it's

[fierce violet]

so divie the 2 angles

[celest nacelle]

is that a question?

[fierce violet]

so bearing is the angle in degrees measured clockwise from north.

ok waite i got it but this i left out cus i have no clue what it means

[celest nacelle]

in that case arctan(195/260) should be right

for the 3th one you do besicly the same

[fierce violet]

thx alot man

[lofty sage]

bro the only thing that i though is use l'hospital 4 times

hahsah

or maybe taylor series

[hot reef]

It'd make it even more worse right

[hot reef]

Probably might work

[celest yacht]

@hot reef i gotchu bro

i think taylor series could have been applied at the beginning but this route simplifies that portion into a simpler step

[proven marten]

why are these the domain restrictions?

[hot reef]

Aww, thank you so much! Really means a lot homie! ❤️❤️

[celest yacht]

👍

[proven marten]

<@&286206848099549185>

[stuck lark]

theyre the x values where the equalities hold, graph each side to see

[proven marten]

right but how would you deduce that normally

just by graphing it?

also why cant the x value take the value of lets say 2

za zombie

Christina

[gentle vale]

I'm confused on how one differentiates some Tan functions
Like $y = Tan^{4}x$. It should be $4Tan^{3} Sec^{2}x$ but I don't understand why the Sec's power is 2 not 8

[obsidian monolith]

Scott 🌙

[stuck lark]

plug in 2 into each side, u get different values

[stuck lark]

late reply but maybe i'd try drawing an appropriate right triangle

[stuck lark]

tan'=sec^2

[gentle vale]

Why is Tan^2 = Sec^2 then?

Unless maybe the book is wrong

[stuck lark]

where did u get this

[gentle vale]

My textbook example

The one in the picture

[stuck lark]

nowhere does it say that

[gentle vale]

It does? The second line of the red box, they multiply by sec^2 3x which is the derivative of tan^2 3x

apparently

I'm guessing it's an error?

[stuck lark]

actually the derivative of tan^2 3x is 3 sec^2 3x

but thats very different from what u said, tan^2=sec^2

anyway i think u messed up using the chain rule for the first one

write $y=(\tan x)^4$ so the use of chain rule is easier to see

[obsidian monolith]

RokabeJintaro

[stuck lark]

by chain rule, $y'=4(\tan x)^3(\tan x)'$

[obsidian monolith]

RokabeJintaro

[stuck lark]

now tan'=sec^2

$y'=4\tan^3x\sec^2x$

[obsidian monolith]

RokabeJintaro

[gentle vale]

Okay I did the chain method and yeah I got it this time
There's this other kind of quick method you use without substituting and I think I make some slip-ups with that if the function has a Tan in it

[ivory urchin]

Hey guys can someone help me out with this ones, this are the answer for F
a) a = 2, b = −3;
b) a = 1/2 + 1/π, b = 1/2 − π/4;
c) a = −3/2, b = 1

I don't really know how to start F

E i think i got it, but just wanted to check if i did it right

[lofty sage]

u want a little hand?

[ivory urchin]

yes pls

i know i have to do lioke this

but idk how to evaluate at X = -3

if i don't take the limits

because on the first one i will end up withj

-9 + 6a

second one will be -9a -7b

[lofty sage]

no

[ivory urchin]

idk what to do after that

[lofty sage]

x is lower than -3

not -3

[ivory urchin]

so this is wrong?

[ivory urchin]

oh right

i'm thinking as if it was limit

so i can just make X=2?

[lofty sage]

you can think this, to know if limit exist u can see the left and right limits, so for the left the f(x) is 3x+6a and right is 3ax-7b, now you can sub x to -3 and set -9 + 6a = -9a - 7b bc in the question f(x) must be continous

and you do the same for x = 3

but now for 3, the 3ax-7b is for the left and for the right f(x) is x-12b

[ivory urchin]

so this is right?

[lofty sage]

you'll get
15a + 7b = 9
9a + 5b = 3
now you solve this system

[lofty sage]

yeah its the idea its right but with this explanation you cant get anything from limits by left and by right

and its important to see how this works

u need help on E?

[ivory urchin]

Just wanted to check if my conclusion was right

i just ignored the first one bc i though:

F(x) -3 <= X^2 - 3

If X =1

f(1) = 7

7 -3 = 4

1^2 - 3 = -2

4 <= -2 ( do not exist )

So it's discontinuous

is it right to think like this?

[lofty sage]

no

[ivory urchin]

rip

[lofty sage]

bc after this inequation the question said, x different than 1

u need to put f(x) only in the middle of this inequation, and then you have to get the limits by left and right

then you'll see they are different

limit not exists

and functions is discontinuous

u get?

@ivory urchin

[ivory urchin]

hmm

[lofty sage]

u speak portuguese?

[ivory urchin]

yes sir

but i get what u are saying

i just don't know why you would to that

X different than 1

But if X-> 1

it wouldn't be 1 right

[lofty sage]

by right yes

but try to use x = 1 on the left

[ivory urchin]

by right you mean 1+

?

[lofty sage]

you'll get division by zero

[ivory urchin]

or this

[ivory urchin]

yeah

[lofty sage]

yeah

[ivory urchin]

but i have to tweak it right?

i would

hmm

[lofty sage]

actually this is not the function by right, bc you have to sum 3 on both sides

so you have lim x to 1+ x²

[lofty sage]

what means tweak

[ivory urchin]

change it

simplify it, if you will

[lofty sage]

yeah

[ivory urchin]

modernize it, if you so incline

evolve, if you fancy

[lofty sage]

u get?

[ivory urchin]

nah

wait a sec

@lofty sage

tem como a gente fazer o passo-a-passo do pensamento?

[lofty sage]

sim

[ivory urchin]

k

[stuck lark]

@pulsar turret help on the test itself?

[serene cradle]

Imagine you draw a card from a shuffled pack of 52 playing cards. It is the Jack of spades. You set it to one side. Now imagine you draw a second card from what is left of the pack. What is the probability, expressed as the simplest possible fraction, that this new card will be the Queen of spades?

I think it is 1/51 right? Reason is that we removed 1 card from the deck and so the probability of drawing queen of spades become 1/51?

[gentle vale]

Yep

I don't see any error in that

[tight creek]

The following question is from pg. 17 of the student guide for Marsden and Weinstien Calculus I

I found to equation of the line to be 5x + 3y - 5 = 0 however the answer in the book has the equation as 5x + 3y +5 = 0. Have I made a mistake or is the student guide in error?

[granite holly]

please help

[noble trench]

can u clarify wut a decay constant is

[granite holly]

inverse of lifetime

[midnight timber]

hi

pls

im in need of urgent help

is anyone good at logs

[kindred sluice]

Hey guys I’m trying to figure out what exactly the trigonometric addition and subtraction formulas represent. Like I know how to use them, but I don’t know what the result means. My book is mentioning the distance formula. But it doesn’t really explain it any deeper than showing how to prove cos(s+t).
So we are multiplying and adding the cosines and sines of two angles but what does that give me at the end and why is it important?

[lofty sage]

just send the question

[lofty sage]

idk if i get your ask but think in sin(75) for example, how you can calculate this? sin(45+30), now why this is important? idk, i just learn and use this to manipulate some trigonometric equations

[kindred sluice]

Lol 😂 good to know. I guess maybe that’s all it’s really good for.

[lofty sage]

some relations you can use to be easier to solve some integrals on calc 2, i dont know other things rn

[kindred sluice]

Good to know. I am kind of relieved when I realize something I thought was going to be important turns out to not be

[midnight timber]

hi

are you still there

[lofty sage]

yes

[midnight timber]

can u help with that question

[lofty sage]

do the difference in left then you get
2log 2a = log(11a+3)
now put the 2 inside the log:
log (2a)² = log(11a+3)
now you can remove the log:
4a² = 11a + 3
4a² - 11a - 3 = 0
the answer will be the roots of this quadratic equation

[lofty sage]

if you want to check, answer is letter A

[midnight timber]

omg tysm

[midnight timber]

wait but it cant be -1/4 tho right

[lofty sage]

yeah, srr i forgot this

a > 0

[steel fern]

i need to convert this from interval to set builder. I am not sure why the correct answer here is [-2,0)

[celest yacht]

@steel fern the intersection means that only the shared elements are included
visually:

[steel fern]

i figured that out. yeah

[celest yacht]

Ah sweet

[dreamy marsh]

Helloo, I need help with maths, I have a test soon of the domain of functions and logarithmic functions so if you wanna help me I’ll be more than thankful

[dreamy marsh]

So do you have similar exercises ? I wanna practice

[stable yacht]

Factoring each quadratic would help if you are looking for the domain.

[placid folio]

guys i need help

what information can u obtain from the

• f(x) graph
• f'(x) graph
• f''(x) graph

[opal tree]

f(x) is the function itself (so domain and range)

f'(x) is the "slope" of f(x), (can determine where extrema exist)

f"(x) is the "slope of the slope" (tells concavity and can confirm existence of maxima and minima, and sometimes saddle points)

All of which can be used to determine the behavior of f(x)

[placid folio]

thx

[viscid thistle]

i need help on this pls

[supple owl]

I can help

But what does it mean perpendicular

[viscid thistle]

a line that is 90 degrees that crosses both line

[supple owl]

Oh

First

If c is perpendicular to both A and B which mean A and B never touch

And A is just B but shifted by a constant k to its new place

[viscid thistle]

can you explain the second part more pls

[supple owl]

Imagine A and B in single line

[viscid thistle]

yes

[supple owl]

They both on 1 line

But

We shifted A from b

By some number k

So it's now have a different position

But A will never to B in any point

[viscid thistle]

the some number k is the perpendicular?

[supple owl]

No....

[viscid thistle]

wait now i get it

[supple owl]

So reminds you of femilier equation ?

[viscid thistle]

yea i think

[supple owl]

Nice . Now write it Infront of you

[viscid thistle]

Ax + by = c ?

[supple owl]

The z component

BC it has I j k mean it's 3d space so it's X y w

Make A and B as a vector form

[viscid thistle]

how

i was writitng it then i deleted cause i think i was wrong

[supple owl]

Lemme see it

[viscid thistle]

(8,9)x + (0,6)y = 6

[supple owl]

The 2d

That 2d

[viscid thistle]

i thought it was 3d cause u said its 3d space

how do i do the 3d one

[supple owl]

In colom

Do up to down

X then y them z

Which is from your question X=I y=j z=k

[viscid thistle]

what is the equation then

i dont get it ;-;

[supple owl]

I think you should ask another on

$\overrightarrow{v}\langle x,y,z \rangle$

[obsidian monolith]

MRme001

[supple owl]

Like this

[fiery saffron]

The right term doesn't have x^2, the left term doesn't have 5, so 5x^2 isn't a CF

I guess technically you could factor $5x^2$ out, and have $$5x^2(\frac{x+7}{5}-\frac{x+7}{x^2})$$

[deft meteor]

.

.

[obsidian monolith]

seth.delacroix

[deft meteor]

.

.

[fiery saffron]

See my note in algebra channel

Well on problem two, you already have $5x^2$ out front the parentheses already, so you can just factor that trinomial

[obsidian monolith]

seth.delacroix

[deft meteor]

.

.

[fiery saffron]

At point you have one term with three factors, so there is nothing to factor out

Factoring is just the distributive property in reverse

[deft meteor]

.

[fiery saffron]

Problem 2 is fine

[deft meteor]

.

[fiery saffron]

Problem 1 is fine

[deft meteor]

.

.

[fiery saffron]

If you had 5x^2(x-2)+(x-2), you could take out x-2 to have (x-2)(5x^2+1)

[deft meteor]

.

[fiery saffron]

If you had 5x^2(x-2)+1×(x-2), you could take out x-2 to have (x-2)(5x^2+1)

Is it more obvious now?

[deft meteor]

.

[fiery saffron]

There is no need

Because that's factored form all ready

It's 5abc

Where a=x^2

b=(x-2)

c=(x-2) also

Btw you could say 5x^2(x-2)^2

Now if you had 5ab+2b

You'd factor out over that addition

To get b(5a+2)

Yes

Factoring is something you do on terms separated by addition or subtraction

Just like multiplication is an operation that distributes over addition

Factoring is the distributive property backwards

You see, if you use the distributive property on the factored form you are back where you started

No

That top you could say is 3×3×5

You can always multiply by 1 and nothing changes

Does it make more sense now how they're different?

[iron gulch]

AROC and IROC

Derivative

[frank vine]

Alight can any explain what this means f(x) is the function itself (so domain and range)

f'(x) is the "slope" of f(x), (can determine where extrema exist)

f"(x) is the "slope of the slope" (tells concavity and can confirm existence of maxima and minima, and sometimes saddle points)

All of which can be used to determine the behavior of f(x)

Like what extrema concavity saddle points mean?

[mild swan]

yup, they are all correct

[mild swan]

These are things you can look up

But: extrema - maxes or mins

Concavity, whether the graph "faces" up or down

Saddle point: this is used in multivariable calculus

[frank vine]

Hmm ok yeah I was gonna soon

[frank vine]

And what significance do they have

[mild swan]

You'll figure that out if you ever take a multivar calc course

Oh

In this context, it's where concavity changes

[frank vine]

Oh ok I see

So if f(x) =x^2 then f’(x)=2x and f’’(x)=2 right?

I can see the slope but not the concavity

[hasty belfry]

yo

i need help

The integer n for which
x→0
lim
​

x
n

(cosx−1)(cosx−e
x
)
​
is finite non zero number is

[rocky wind]

you can use LaTeX to typeset math?

if not you can try any online WYSIWYG $\LaTeX{}$ editor, say

https://latexeditor.lagrida.com/

[obsidian monolith]

vin100

[hasty belfry]

bro i cant

lim
x→0

​

(cosx−1)(cosx−e
x
)
/ x^n
​

WYSIWYG $\LaTeX{}$ lim
x→0

​

(cosx−1)(cosx−e
x
)
/ x^n

[obsidian monolith]

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

[rocky wind]

you're on 📱 / 💻 ? there's #latex-help on #resources

[hasty belfry]

laptop

[hasty belfry]

this is the question bro

[willow bear]

@hasty belfry do you have a picture

as-is this is incomprehensible

[hasty belfry]

its e^x

[rocky wind]

to start with you can write an equation with two commas

[willow bear]

do you have a picture

[rocky wind]

,,e^x

[obsidian monolith]

vin100

[hasty belfry]

lim x tends to 0 , (cosx-1)(cosx - e^x) upon x^n

[rocky wind]

that's not an answer to his problem

[hasty belfry]

okay

[willow bear]

and he is not answering my question of whether he has a picture of the problem

okay, so you have here

[hasty belfry]

no

i dont

its a question online

[willow bear]

screenshots are a thing...

$\lim_{x \to 0} \frac{(\cos(x) - 1)(\cos(x) - e^x)}{x^n}$

[obsidian monolith]

Ann

[willow bear]

so you have this limit

what are you asked to do with it

[hasty belfry]

yup

this is the question

[hasty belfry]

find n

[willow bear]

find n such that what

[hasty belfry]

so that the limit is finite

[willow bear]

ok

find all such n?

or only the smallest?

[rocky wind]

sorry that's not a #precalculus problem

[hasty belfry]

limit should be finite non zero

[rocky wind]

better asked in #calculus

[hasty belfry]

bruh its limits

[willow bear]

thanks for not answering my question again

[hasty belfry]

there is only one n

not a set

just a single value

[willow bear]

a set can consist of one element only

also do you have access to things such as taylor expansions?

might be of use here

[hasty belfry]

you mean the sinx series?

yeah ik

[willow bear]

not the taylor series of sin(x) in particular

you would want the ones for cos and exp here instead

[hasty belfry]

sinx = x- x^3/3! + x^5/5! ...... right?

[hasty belfry]

yup

i do

how to use it tho?

[willow bear]

no, sin(x) is not x - x^3/3!. you cannot just clip off all but two terms of the INFINITE taylor series and claim equality stull

still*

but well ok

[rocky wind]

i don't think you reli need tayloy series of trigo funct

just bound them by 1

that won't change the problem

[hasty belfry]

i cant understand bro

[willow bear]

neither can i

how does bounding anything help us here

[hasty belfry]

wdym bound them by 1?

[willow bear]

$\cos(x) - 1 = -\frac{1}{2} x^2 + O(x^4)$ and $\cos(x) - e^x = 1 - \frac{1}{2}x^2 - 1 - x + O(x^3)$

[hasty belfry]

like limit the values of y?

[obsidian monolith]

Ann

[willow bear]

this is what i was going for

[hasty belfry]

oh yeah

[willow bear]

you have that cos(x) - 1 behaves as x^2 and cos(x) - e^x behaves as x

up to multiplicative constants

all as x goes to zero obviously

[hasty belfry]

fair

[rocky wind]

oops i misread the limit as $x \to \infty$

[obsidian monolith]

vin100

[willow bear]

so num behaves as x^3

this should make it transparent

[hasty belfry]

n=3?

yeah its the correct answer

[willow bear]

yes exactly

[hasty belfry]

we just had to use the series?

damn bro i was trying to convert it into standard limit lmao

[willow bear]

taylor series helped us but i would not go so far as to say it was necessary to do it this way

[hasty belfry]

yeah it was prolly the shortest one thanks

[willow bear]

if you're a masochist you can spend like a year or two doing this with l'hôpital (or attempting to)

[hasty belfry]

LMAO

I TRIED

lh rule is just too easy to NOT use

@willow bear which series do i need to memorise ?

e^x , sinx , cosx , tanx , ln(x+1) ?

[willow bear]

you can go without tan(x)

you might also want to commit (1+x)^p to memory

[hasty belfry]

yeah its complex but somehow ik the first 3 terms

[hasty belfry]

whats that?

[willow bear]

(1+x)^p

[hasty belfry]

wait ill google

[willow bear]

a function whose taylor series i am suggesting you memorize

p is an arbitrary real number

[hasty belfry]

oh yeah ik that

its 1+ nx

nC2 x^2

and so on

[willow bear]

yes, except your n is my p

[hasty belfry]

its binomial right?

[hasty belfry]

...

that sounds so wrong

but yeah

your p is my n

just these ?

and sinx cosx tanx are enough?

[willow bear]

wym by "that sounds so wrong"

[hasty belfry]

leave it

also

[willow bear]

e^x, sin(x), cos(x), log(1+x), binomial

also 1/(1-x)

as a somewhat special case

but it's a geometric series

and good to know still

[hasty belfry]

what conceps would you suggest to solve questions related to relation and functions? @willow bear

like ik domain range

[willow bear]

too vague for me to make any meaningful suggestions

[hasty belfry]

but odd , even , peridocity etc

[hasty belfry]

mainly just like solving questions related to weather the function is odd/even and finding period of composite functions

[hasty belfry]

this is ,,(1+(-x)) ^ -1

wait how tf do i use latex

,,(1+(-x)) ^-1

[obsidian monolith]

Zyzzbrah

[willow bear]

this is $(1 + (-x))^{-1}$

[obsidian monolith]

Ann

[willow bear]

and yes i did say it was a special case of binomimal

binomial*

but it is still good to know separately

[hasty belfry]

aight cool

[hasty belfry]

okay thx

[pallid jewel]

56

[quick temple]

Hello

I am learning precalculus but I am in grade 8

Precalculus is really fun to learn actually

but it is hard

[hasty belfry]

\begin{array}{l}\underset{x\to 0}{\mathop{\lim }},\left[ \frac{x}{{{\tan }^{-1}}2x} \right]\end{array}

[obsidian monolith]

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

[hasty belfry]

nvm its 1/2

[gritty flax]

https://tenor.com/view/well-yes-but-actually-no-well-yes-no-yes-yes-no-gif-13736934

[fiery saffron]

@pallid jewel did you try writing cos(2x) as 1-2sin^2(x)

[steel fern]

What did i mess up here

[void thorn]

looks like you have 15+4 = 11 when you probably meant 15-4 = 11

[gritty flax]

In step 4 it should be 15xy - 4xy

[hasty belfry]

hey

$$ If 2sin^2θ−5sinθ+2>0,θ∈(0,2π), then θ∈ $$