help-26

[lusty ridge]

from the right its undefined and from the left its defined right?

[golden blade]

yea but that is not the reason, there i was just explaining the graph of g(x)

the reason is because the limits from both sides are different

so there is not definite limit

as x approaches 0

[lusty ridge]

oh i see

yeah right so because from the left itd be 3

and then from the right itd be 1..?

[golden blade]

ye

[lusty ridge]

the limit doesnt exist right

[golden blade]

yea

[lusty ridge]

and then in the case for (b) i wouldnt be able to solve it considering that

[golden blade]

yes

[lusty ridge]

ahh

thank you

[golden blade]

no issue

[lusty ridge]

.close

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[lusty ridge]

:333

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[spare monolith]

$f: A\to\mathbb{R}$

[thorny flame]

Good

[spare monolith]

Does this mean A is a subset of something, which is called domain, will give $x \in A$, a value in $\mathbb{R}$ with $f(x)$.

[thorny flame]

Good

[spare monolith]

Or does this just mean the set A is a subset of R?

And the result is a different thing to be discussed?

[vernal matrix]

Well, “all sets are subsets of themselves”, but A can be any set, at least in general (say e.g. A is a set of students and f measures their height/weight or returns their age or something)

[spare monolith]

So could I express like this $$f: D_f \to V_f$$ Where $D_f$ means domain, and $V_f$ means range?

[thorny flame]

Good

[vernal matrix]

I mean, you could

[spare monolith]

Is this certain, or under some circumstances?

Alright, I guess this means certain.

Thanks

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[hexed ravine]

help

[elfin sparrow]

post your question if you've got one

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[eternal nymph]

i ended up with,

$$ -4a - h + 2ah + 6 $$

[thorny flame]

Devil Wears Prada

[eternal nymph]

did i do something wrong?

[worthy storm]

show your work

[eternal nymph]

$$ \frac {(a + h)^2 - 2(a + h) + 3 - (a)^2 - 2(a) + 3} h $$

[thorny flame]

Devil Wears Prada

[eternal nymph]

then i just simplified it to,

$$ -4a - h + 2ah + 6 $$

[thorny flame]

Devil Wears Prada

[worthy storm]

wait let me double check

[regal grove]

yeah there is something wrong

[worthy storm]

for one thing, that second to last term should be +2a, not -2a

[regal grove]

at least, 6 should be divided by h

[worthy storm]

and the +3 at the end should be -3

[regal grove]

ah nvm

[eternal nymph]

why

[eternal nymph]

why

[worthy storm]

because you're supposed to subtract f(a)

and f(a) = a^2 - 2a + 3

so if you subtract it, it becomes -a^2 + 2a - 3

[eternal nymph]

so,

$$ 2ah - h $$

[thorny flame]

Devil Wears Prada

[eternal nymph]

is the solution

[worthy storm]

did you divide by h?

also there's a term missing

[eternal nymph]

i canceled the h out with a term?

$$ \frac {h^2} h $$

[thorny flame]

Devil Wears Prada

[eternal nymph]

makes it

$$ h $$

[thorny flame]

Devil Wears Prada

[worthy storm]

where did the 2ah come from

did you have a 2ah^2 in the numerator?

[eternal nymph]

$$from (a + h)^2$$

[thorny flame]

Devil Wears Prada

[worthy storm]

but you don't seem to have divided 2ah by h

[eternal nymph]

dont need to if it got canceled out

[worthy storm]

you said this is the answer

[eternal nymph]

refer to this

[worthy storm]

where did the 2ah come from

[eternal nymph]

i canceled it out

$$ \frac {(a + h)^2 - 2(a + h) + 3 - (a)^2 - 2(a) + 3} h $$

[thorny flame]

Devil Wears Prada

[eternal nymph]

its just 2ah on the top

[worthy storm]

but you're dividing everything by h

[eternal nymph]

when distributing (a + h)^2

[worthy storm]

including 2ah

[eternal nymph]

ok so then

[worthy storm]

so how can you have 2ah at the end

[eternal nymph]

i just told you i canceled H out

so how can i divide everuthing

[worthy storm]

wtf

show me your work, this makes zero sense

you can't just cancel the denominator with one term of the numerator

[eternal nymph]

$$ \frac {(a + h)^2 - 2(a + h) + 3 - (a)^2 + 2(a) - 3} h $$
$$ \frac {a^2 + 2ah + h^2 - 2a - 2h + 3 - a^2 + 2a - 3} h $$

[worthy storm]

ok

and what happens after that

first line is wrong btw

second one is ok

[eternal nymph]

how is first wrong?

[worthy storm]

you have -2a + 3 at the end, instead of +2a - 3

[thorny flame]

Devil Wears Prada

[eternal nymph]

ok so now

i divide everything by h?

[worthy storm]

now simplify the numerator as much as you can first

before dividing by h

[eternal nymph]

$$ \frac {(a + h)^2 - 2(a + h) + 3 - (a)^2 + 2(a) - 3} h $$
$$ \frac {a^2 + 2ah + h^2 - 2a - 2h + 3 - a^2 + 2a - 3} h $$
$$ \frac {2ah + h^2 - 2h} h $$

[thorny flame]

Devil Wears Prada

[worthy storm]

yes good

now you can do the division, what do you get?

[eternal nymph]

$$ 2a - h $$

[thorny flame]

Devil Wears Prada

[worthy storm]

there should be 3 terms

[eternal nymph]

why

[worthy storm]

$$\frac{2ah + h^2 - 2h}{h} = \frac{2ah}{h} + \frac{h^2}{h} - \frac{2h}{h}$$

[thorny flame]

Bungo

[eternal nymph]

$$ \frac {h^2} h = h $$

[thorny flame]

Devil Wears Prada

[worthy storm]

yes

and 2ah/h = 2a

but you lost the -2h/h

[eternal nymph]

oh

$$ 2a + h - 2 $$

[thorny flame]

Devil Wears Prada

[worthy storm]

yep

that's the right answer

[eternal nymph]

oh thanks a lot

[worthy storm]

sure, cheers!

[eternal nymph]

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[solemn tinsel]

someone can help me i didnt know how to do this and by the way sorry my english is bad

[topaz sinew]

@solemn tinsel Has your question been resolved?

[sterile finch]

Use Integration by Parts (IBP).

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[left canyon]

What's the difference between f(x) and y?

[agile harness]

f(x) is just function notation

in your context they’re the same because the output of f will be a value of y

on the cartesian plane

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[young hemlock]

.reopen

[agile harness]

.reopen

[topaz sinew]

✅

[agile harness]

@young hemlock

this wasn’t your channel

[young hemlock]

yo

oh mb

[agile harness]

you can only reopen channels that were yours

[young hemlock]

I was just trying to reopen this channel

[agile harness]

to start a new channel just post a question

[young hemlock]

mb

I can't speak in there

I don't know how to do the command

[agile harness]

because the channel wasn’t available

[young hemlock]

I wasn't looking when I went to this channel mb

[agile harness]

just go to any of the unused channels

[young hemlock]

alr

[agile harness]

it says math help available

.close

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[wise tundra]

Help Me for #9

[wise tundra]

im just not sure on what to do from here?

[rose sierra]

what's it asking?

[wise tundra]

for the graph

im pretty sure

let me see if i can find it

@rose sierra

[rose sierra]

what have you tried so far

[wise tundra]

ive tried A = 2x * 2y

which is 4xy

then i find y and plug it in

@rose sierra so this was the work i have or atleast what my teacher wrote

but im confused on how he got = - A(X)

[rose sierra]

ok you don't want y

how can you express y in terms of x

[wise tundra]

yes so 4xy

[wise tundra]

then i put 4x and y (i isolated y) so 4x sqrt 4-x^2

and im just not sure which one to choose

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[still bough]

is x=0?

i dont understand this

[sweet shard]

!original

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[still bough]

one sec

Here we go

[dusky mango]

You wrote 5x-4 as 5x

Try with 5x-4

[strange monolith]

So we know that PQ+QR should be equal to PR right?

[still bough]

Yes

[strange monolith]

Try it then

[still bough]

1

is that it

.close

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[strange monolith]

Yep

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[lapis swallow]

This is more physics related but i really don't get b-d

b I used the formula but it is still wrong

[loud oasis]

what formula did you use?

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@lapis swallow Has your question been resolved?

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@lapis swallow Has your question been resolved?

[blazing trail]

(b) asks for 4.9 seconds after the maximum. So it wants you to find the time of the vertex, add 4.9 seconds to it, and then find the height.

for c, do you know something called a derivative?

for d, you should find when y(t) equals 0

[lapis swallow]

Yes lol

How do I set up the equation to find derivative here

[blazing trail]

plug in the initial values and then take the derivative

as well as -9.8 for gravity

[lapis swallow]

What is the equation for that? I searched up the problem and found the equation, but when I plugged it in, the answer was still wrong

[blazing trail]

x = -b/2a

for y=ax^2+bx+c

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[lapis swallow]

Ok ty

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[ripe stag]

Please check if my answers are correct. Calculus 1

[carmine marten]

Both are correct i think

Just a note on notation

You wrote $\lim_{v\to c^{-1}}$

[thorny flame]

Edward II

[carmine marten]

Instead of $\lim_{v\to c^{-}}$

[thorny flame]

Edward II

[carmine marten]

These are different things: the first would mean the (two sided) limit as v approaches 1/c, whereas the second what is desired here meaning the limit to c from below

[vestal sigil]

imagine a universe where $\lim_{v \to c^{-1}} L(v)=0$

how would we be 😂

[thorny flame]

Emily

[ripe stag]

Oh yeah thank you so much

[ripe stag]

Why are you not sure?

[carmine marten]

Not sure whether "physically meaningful" would be the correct justification for not having the square root of a negative

Since L isn't even defined for v > c

[ripe stag]

So what should I say instead?

[topaz sinew]

@ripe stag Has your question been resolved?

[vestal sigil]

ig you should simply say a lefthand limit is necessary because the Lorentz contraction formula is undefined for velocities beyond the speed of light

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[patent quest]

Hi everyone, I could use some advice. I'm currently taking Calculus 1 for Computer Science and I have only followed algebra 1, geometry and algebra 2 on Khan Academy.

Last week, we had a warm-up week covering these concepts:
1. Numbers and basic arithmetic operations
2. Powers
3. Fractions
4. Roots
5. Curves, functions and graphs
6. The function exp, ln and log
7. The functions sin, cos and tan
8. Equations, ineuqalities and system of equations
9. Differentiation
10. Antidifferentiation
11. Integration
12. Vectors

I feel pretty confident with topics 1–6 and 8, but I'm struggling with topics 7, 9, 10, and 11. We just started limits in class, and I didn’t understand much of it.

Could anyone suggest how I can catch up? Should I watch Professor Leonard's playlist, and if so, how far should I go?

https://www.youtube.com/watch?v=fYyARMqiaag&list=PLF797E961509B4EB5&index=2

[patent quest]

These are my course objectives:

[urban barn]

Hmm is your class coming to an end soon?

[patent quest]

No it just started

[urban barn]

Then isn't it normal to struggle on topics 9-12

because you're going to learn all of it in your current class

[patent quest]

Oh really, I had these topics in the warmup week

and I thought it was a must understand topic before going into calculus

[urban barn]

I mean i'm guessing "course objectives" means what you'll be expected to know by the end of the course

[patent quest]

yes

[urban barn]

that is topic 9-11

i don't see 12 but i'm guessing it kinda follows

[patent quest]

oh

[urban barn]

for 7) you can pick you trig yeah

its quite helpful for a computation based calculus class

helpful and important*

[patent quest]

Did you watch any professor leonard lectures?

[urban barn]

no...

u can just focus on doing some practice problems

after u learn from professor leonard or whatever

[patent quest]

Do you need to know differentiation and integration for limits?

[urban barn]

no

you have it backwards

[patent quest]

Oh so I had differentiation and integration in my warmup week, but the first calculus lesson is about limits

[urban barn]

yeah u generally start with limits

then differentiation and so on

[urban barn]

I guess that's just a diagnostic test or something?

Or you're not telling us something

[patent quest]

Oh cool so I can just start with a video like this:

[patent quest]

No it was like a warmup week for students who never had math before in high school

[urban barn]

But how is it a warmup week when they had you do everything you're expected to learn at the end of the course lol

[urban barn]

sounds good yeah

[patent quest]

I can show you some of the questions

[urban barn]

yeah u could show them i guess

[patent quest]

this is differentiation

maybe they picked really easy questions?

[urban barn]

okay so did you learn differentiation in class?

[patent quest]

not yet

only in the warmup week, but it was really difficult

[urban barn]

lol idk what's going in your class

but yes you can do these questions after yk what differentiation is

[patent quest]

alright so I can start with limits without knowing (anti)differentiation, integration right

[urban barn]

limits -> differentiation -> antidifferentiation

[urban barn]

u need to know things like: quotient rule, product rule, chain rule, etc. to do these questions

[patent quest]

I know these concepts average (red box), should I revise more topics before going into limits?

[patent quest]

ooh alright

[smoky sparrow]

yes you should do trig first

then you can do limits afterwards

[urban barn]

so did you receive any hw?

[patent quest]

so chapter 7?

[smoky sparrow]

yes

[urban barn]

yes

[patent quest]

yes I received limits homework for friday

but I need to catch up first

[urban barn]

oh then you're good i guess

[patent quest]

never had any math in high school related to calclus

[urban barn]

i thought u received smth like that for hw

[patent quest]

ooh

[urban barn]

anyway so yeah trig and then u can start off calculus

like south said

[patent quest]

Thanks for the advice @urban barn @smoky sparrow

any more advice

good source of information

[smoky sparrow]

ummm not for now

[urban barn]

Don't just watch professor leonard and expect to know everything

make sure to do practice problems

[patent quest]

yess thank you @urban barn and @smoky sparrow

< 3

.close

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[obsidian dew]

hello this is regarding x and y intercepts (rational function)
how do you find x^2 + 2 x + 1 / x

[neon iron]

What is meant by you when you say, "Find [expression]"?

[obsidian dew]

in finding the x - int

because you usually equate it to 0 right

[neon iron]

x^2 + 2x + 1/x = y?

[vestal totem]

!nosols lmao

[topaz sinew]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[neon iron]

So it is about finding the roots of f(x).

[obsidian dew]

yeah

[neon iron]

Put f(x) = 0

(x^2 + 2x + 1)/x = 0

It's quite clear now what you have to do now.

[obsidian dew]

x = 0

[neon iron]

No.

[obsidian dew]

wqaity sorry

[neon iron]

Wait

[vestal totem]

Also note that the numerator is just (x+1)^2 so even easier.

[neon iron]

x = 0 is indeterminate if I am not wrong

Idk

Just multiply by x both sides.

LHS and RHS.

[obsidian dew]

if x = 0 what will then x become

-1?

[neon iron]

What the heck you mean

I think you have confusion regarding the terms used here.

[obsidian dew]

yeah...

or i replied at the wrong mesg

[vestal totem]

patience broski patience

[obsidian dew]

nono it's fine

[neon iron]

😉

[obsidian dew]

i understand a bit better

thanks @neon iron @vestal totem

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[neon iron]

welcome

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[orchid agate]

So, for reference, I know my answers are correct, but I'm trying to understand how I do something like properly test the asymptote section

I know as x approaches the VA, h(x) is approaching infinity

and I did a little sketch

but why do I know that? I'm sorry if that question seems dumb or obvious

but I don't know how I can put into words or properly prove this is correct..

I hope that explains my question.. because with other, simpler problems

I can just throw in a hypothetical test value and then plot it and go 'oh well look see that shows why it's like this'

or I guess I know that we cant have anything Less than 4/3 for an x value

I think I'll just use wolfram alpha or some program to graph a few of these functions, because it's really hard to picture in my head, or find words to explain how I know this

So just in general with a negative log function..

from the right side, h(x) approaches - infinity
and from the left it starts at infinity, right?

or well, the closer and closer it gets to the vertical asymptote, the closer it gets to infinity

infinitesimally close, right?

since it can't actually reach infinity..

[topaz sinew]

@orchid agate Has your question been resolved?

[topaz sinew]

@orchid agate Has your question been resolved?

[pseudo bone]

yes

you could say in the limit as x -> 0, y -> infinity

[orchid agate]

right

[pseudo bone]

it "cant" reach infinity in the sense that infinity is not a number part of the Reals

its """like""" saying that sqrt(-1) isnt i in the Reals since, well i is a complex number not part of R

sometimes when talking with limits you define a set $\bar{\mathbb{R}} = \mathbb{R}∪{\pm \infty}$ which is the closure of R, sometimes called the extended reals,

[orchid agate]

I think yoou're speaking a bit beyond my understanding, I'm sorry.. or I sorta understand, maybe?

[thorny flame]

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

[pseudo bone]

okay i give up

sorry i dont know latex ahgahaha

[orchid agate]

lol no worries

latex is cool

[pseudo bone]

basically sometimes you are trying to solve a limit and the answer is infinity

like in this case

the closer we get to the left, the bigger the number gets

[orchid agate]

yeah, intuitively I know that..

but like.. how do I know that?

[pseudo bone]

but saying that its equal to infinity doesnt really mean anything since infinity is not a number

[orchid agate]

like if we couldn't graph it

is there any way to prove iit?

or some way to reason out that's how it is?

[pseudo bone]

so we define a set R{infinity} thats basically R and the 2 infinities (plus/minus)

[pseudo bone]

Intuitively you can draw a vertical line at x = 0

and say the 2 never intersect

[orchid agate]

Sure

[pseudo bone]

to prove it you need to learn limits and thats a pretty complicated topic that if you havnt done yet you will eventually do

[pseudo bone]

that line being the asymptote

[orchid agate]

I used to know how to tell stuff like

as x approaches from the left and as x approaches from the right

but to prove it we need to learn limits?

Ii'll look into that then

because I want to be able to prove it beyond just

'look at this graph, boom, you see it? yeah? there you go'

or at least for some reason it bothers me? idk

[pseudo bone]

rigurously yes but currently you dont need to worry about it

[orchid agate]

with easier functions, yu know.. it's really easy

[pseudo bone]

If you want a better way

[orchid agate]

f(x) = x^2/(x-2)

we can just see the VA at 2

[pseudo bone]

just show that you can put smaller and smaller numbers instead of x and show that it grows larger and larger

[orchid agate]

Isn't it a lot harder with stuff like..

(-log(3x-4)+5)

too do stuff like that?

Like if we just say x is 1
(3-4) = (-1)
(-log(1)+5)

[pseudo bone]

You know how else you could do it

[orchid agate]

but isn't that still a bit awkward and complicated?

[pseudo bone]

y = -log(3x-4)+5

now invert this function

[orchid agate]

Sure, I learned how to invert things

interchange x and y and solve

[pseudo bone]

yes

do that and basically the vertical asymptote becomes the horizontal and vice versa

[orchid agate]

Thank you woomy

I'll close this ticket then?

[pseudo bone]

yw :)

go ahead!

[orchid agate]

.close

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[orchid agate]

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[patent quest]

can someone explain this step?

[thorny flame]

MæthIsAlwaysRight

[patent quest]

but why can you move the negative sign to under

[winged moat]

The negative can either be applied to the numerator or the denominator, and the result will be the same.

$\frac{-2}{4}$

[thorny flame]

USS-Enterprise

[winged moat]

This is -1/2, right

[patent quest]

yes

[winged moat]

If we wrote

$\frac{2}{-4}$

[thorny flame]

USS-Enterprise

[winged moat]

This is also -1/2

[patent quest]

ahhh

clear

[winged moat]

Dividing a positive by a negative number (or a negative by a positive number) both result in a negative quotient.

[patent quest]

thanks @winged moat @jaunty grove @prisma mesa

[winged moat]

Then just use the distributive and commutative properties

To distribute the -1 through the parenthesis and then rearrange the terms.

And that's how you get from the first to the second step 🙂

[patent quest]

is it wrong to have a negative quotient?

or bad practice

[winged moat]

It is not wrong

It's just bad practice usually, yes

[patent quest]

but the second step is more elegant

much nicher

nicer

thanks

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[patent quest]

Hey how can I solve this.

My first step is $$49^\frac{1}{ln7}$$ but after this I am clueless

[neon iron]

!context

[patent quest]

No context, but I am doing the chapter: "exp, ln and log"

[sweet shard]

,tex .exp rules

[thorny flame]

[torpid sparrow]

Use prime factor on 49

[thorny flame]

Frank

[patent quest]

$$(7^2)^\frac{1}{ln7}$$

[thorny flame]

Frank

[patent quest]

$$(7)^\frac{2}{ln7}$$

[thorny flame]

Frank

[sweet shard]

,tex .log rules

[thorny flame]

[torpid sparrow]

Now use exp rules to modify that

[patent quest]

I have no idea

[torpid sparrow]

Switch the exponents

[patent quest]

switch?

[torpid sparrow]

2/ln7 = 2 * 1/ln7 = 1/ln7 * 2

(7^(1/ln7))^2

[patent quest]

$$(7^\frac{1}{ln7})^2$$

[thorny flame]

Frank

[patent quest]

what is the difference

[torpid sparrow]

And now simplify inside the parenthesis

[patent quest]

the only thing I can think of is this right now but I don't think it is right

[torpid sparrow]

Think a bit more

How do you usually take exponents out?

[torpid sparrow]

Down

[torpid sparrow]

I want you to use the power rule

[patent quest]

I am not that advanced sorry

never heard of power rule

or do you mean multiply?

[torpid sparrow]

Do you know that ln(a^b) = blna?

[patent quest]

yes I know that one

[torpid sparrow]

Now our b is 1/ln7

We want to use another ln

[patent quest]

and why not the 2?

[torpid sparrow]

But to counter it we will ise the inverse function also

e^ln(7^(1/ln7))^2

[patent quest]

man... this is so difficult#

😦

[torpid sparrow]

Ok look ar this

You have x^(1/lnx), forget aboit the other 2 ok?

If we apply ln to that

We get

Ln(x^(1/lnx)) = 1/lnx * lnx

That is lnx/lnx = 1

Now we apply the inverse function

e^1

So we can deduce than x^(1/lnx) = e

And we have x as 7

And raised to 2

(7^(1/ln7))^2

e^2

[patent quest]

https://tenor.com/view/crying-crying-meme-gif-26327776

[little pine]

can I give another method?

[patent quest]

ofcourse my friend

[little pine]

you can express 7 as e^(ln7)

then I think you can figure out the rest using exponent rules

[patent quest]

the 7 from 7^2?

[little pine]

from the base of this

[patent quest]

alright I will try

and ask for help if I don't get it

thanks

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[lyric crypt]

It is asking for F`(x)

And since the antiderivative of F`(x) is F(x), i just took t^2/(t^2+4) and changed the t to x's

but i don't understand why the t's become x

[silent siren]

do you know the fundamental theorem of calculus?

[lyric crypt]

yeah

[craggy haven]

then this will make sense 😉

,tex .FTC2

[thorny flame]

[silent siren]

oooh, there's a command for it

[craggy haven]

there is, although I need to rewrite it to use d/dx notation throughout

[wispy pier]

Leibnitz rule

[craggy haven]

anyway in this case b(x) = x and a(x) = 4

[wispy pier]

Hey , how do you remember all this

[craggy haven]

like all the commands? i don't remember all of them but I have a few that I use all the time

[wispy pier]

NGL , you re great Hayley, nd all the moderators too !

[wispy pier]

Where can i learn them ?

[lyric crypt]

i no click in brain

can some1 explain this in really simple terms

Like I don't get why you can't just sub the t for x here just like in the previous one

[silent siren]

apply the ftoc

[lyric crypt]

idk how

[silent siren]

,tex .FTC2

[lyric crypt]

lol

[silent siren]

grrrrrrrr

[lyric crypt]

i see it, i just don't know how to apply it

[silent siren]

What's a(x) in your example?

[lyric crypt]

0?

[silent siren]

yes.

and b(x)?

[lyric crypt]

x^5

[silent siren]

yes. so a'(x) and b'(x)?

[lyric crypt]

0 and 5x^4

[silent siren]

and f(t)?

[lyric crypt]

no idea

[silent siren]

look at your problem, and compare it to the definition.

#help-26 message

[lyric crypt]

5x^9?

[silent siren]

no

[lyric crypt]

(x^5 * 5x^4) - (0 * 0)

i didn't set it up right?

[silent siren]

what's f(t) in the problem?

[lyric crypt]

i think i got it

(f(x^5) * 5x^4) - (f(0) * 0)

[silent siren]

yes

[lyric crypt]

f(t) is sin(t^4)

[silent siren]

yes

[lyric crypt]

and u plug in x^5 for t

[silent siren]

yes

[lyric crypt]

so its sin(x^5^4)

which = x^20

so it's x^20 * 5x^4

[silent siren]

no

[lyric crypt]

oh

sin

forgot the sin

[silent siren]

[lyric crypt]

sin(x^20) * 5x^4

[silent siren]

yep, there's your answer 🙂

[lyric crypt]

= 5x^4sin(x^20)

and the other part evaluates to 0 so its that - 0

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[thorny flame]

l'agit

l'agit

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[topaz sinew]

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[agile lark]

What do you call this step in the red text? Not sure where that came from

[glass maple]

multiplying by 1

[acoustic pecan]

multiplying by 1 in whatever form you choose, a common magic trick

[agile lark]

Is there more info about the "multiplying by 1" step? that's my first time hearing that

[acoustic pecan]

not much to really say
its often useful to multiply by something over itself
we do it when we rationalise denominators for a common example

1/sqrt(2)= 1/sqrt(2) * sqrt(2)/sqrt(2) = sqrt(2)/2

[agile lark]

yeah I remember the rationalizing denominators by the same kind

So you do that step to simplify it basically?

[acoustic pecan]

to get it into a more desirable form yeah

[agile lark]

Thanks!
did more research, it's very similar to multiplying by the conjugate (i think it is that lol)

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[topaz sinew]

Please don't occupy multiple help channels.

[wraith acorn]

this particular step is confusing me

what property of the curl is being exploited here?

err cross product rather

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[upbeat saddle]

I dont understand where the +2 in the dominator comes from

[sweet shard]

Try writing it out for a few small m like 3,4,5

[upbeat saddle]

wdym

this is the original problem

im solving it with chatgpt help but im not getting from where does he get the
m(m+1) + 2 (m+1)/2

the 2 ^

[night imp]

Do you know arithmetic sequence?

[upbeat saddle]

no

[night imp]

Then it would be a bit difficult

[night imp]

First part means
1+2+3....+n

This is what we call an arithmetic sequence and it's sum is denoted by
n(n+1)/2

[upbeat saddle]

ohh okay yh i think i know what you mean

[night imp]

Cool then it should be ok

Main question is you need to find sum of

1+2....+m+m+1
1+2....+m = m(m+1)/2

So total sum becomes 
m(m+1)/2 + (m+1)```

[upbeat saddle]

yeah i get that

but like then it becomes m(m+1) + 2(m+1)/ 2
but this "2(m+1)" is the thing i dont understand

[night imp]

m(m+1)/2 + (m+1) , you understood this ?

[upbeat saddle]

bro i just realized im braindead

XD

[night imp]

They just multiplied 2 in numerator and denominator

[upbeat saddle]

i read once again everyhintg

[night imp]

For 2nd part

[upbeat saddle]

and understood

thanks

[night imp]

Cool

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[sweet shard]

Yea don't use chat gpt for math

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[upbeat musk]

1. How did they remove X? Did they factor X into X to remove it? And, if so, how does that work? What operation did they do (division, subtraction, etc).

2. I am generally confused about what operations they did exactly across the problem.```

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bruh it boke

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[still swan]

Any ideas how i would solve (implicit differentiation) of a: $$ \frac{x-y}{x+y} = \frac{x^{2}}{y} + 1. I have tried this, but this is not correct: Please ping me on response :)

[thorny flame]

Pandora

[covert juniper]

Why does everytime I do calculation mistakes ahh

[still swan]

No, it should be $$ y' = -\frac{3x^{2}+2xy}{x^2+4y} $$

[thorny flame]

Pandora

[covert juniper]

Yap that’s the answer

Start by simplifying the equation

Then its easy

[still swan]

simplifying before differntiation?

imma try that rq

[covert juniper]

Subtract denominator by nominator in both sides

[still swan]

I definitely fucked up somewhere, but I'm getting closer

[covert juniper]

👍

[still swan]

thank you sir

[covert juniper]

[still swan]

sometimes i wonder why i havent gone to an optician

ait, how do i close this bad boy

.close

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[normal urchin]

I have two separate but related questions:

1. I am trying to find out if the complexified lie algebra of the Lorentz Group, which has commutator relations $[A_i, A_j] = i\epsilon_{ijk} A_k$, $[B_i, B_j] = i\epsilon_{ijk} B_k$ and $[A_i, B_j] =0$, has two ideals (subalgebras closed under the lie bracket) given by $\mathfrak{a} = \text{span}(A_i, A_j, A_k)$ and $\mathfrak{b} = \text{span}(B_i, B_j, B_k)$ as $A_i$ and $B_i$ commute and zero belongs to both the subalgebras. I'm not sure if this is correct, please help me if I'm missing something.
2. Is there a way to calculate all the ideals of a given lie algebra? Like for example, for this complexified Lorentz lie algebra?

[thorny flame]

tensegrity

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[normal urchin]

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[neon iron]

I’ve been keep getting wrong answer

[neon iron]

What did I do wrong?

[versed elm]

Step 2 to step 3

When you write that as (x-2)^2

Look at the constant term. It’s not the same as the previous step

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[neon iron]

Where?

[neon iron]

Yeah but converted it to 8/4 after that

[gray ridge]

the answer is right, but the step is not correct

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[snow reef]

What does the probability of independence of event mean? how could one interpret the fact that it becomes P(A)*P(B)? if A and B represent rolling different dices, then what does P(A intercept B) mean?

[ripe basin]

i think you are talking aboutconditional probability

[snow reef]

yes

I just dont know how to interpret the last formula

[ripe basin]

this one?

[snow reef]

no P(A intercept B) = P(A) * P(B)

like if A and B represent rolling different dices, then P(A intercept B) = (6/36) * (6/36)?

[ripe basin]

yeap its the same see if by doing one event no changes on event B so we will see whats the probability of event 1 and then event 2 (it just becuase of independency) so the ways(probability ) multiplies

[rich owl]

YALL PLS HELP

[snow reef]

it feels like mixing apples with pears

[snow reef]

like A is the outcomes of rolling a dice

[rich owl]

BRO I HAVE TO DEAL WITH THIS

[hearty turret]

2 events are independent if intuitively "knowing about 1 doesn't affect knowing the other"

so for example, if i roll a dice and flip a coin

[snow reef]

and 36 is a two dimensional outcome, no?

[hearty turret]

intuitively those are independent since knowing what happens about 1 doesn't affect what happens with the other

[hearty turret]

!occupied

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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[hearty turret]

create a new post here in one of the non-taken ones

[hearty turret]

then if i ask what's the probability of flipping a head and rolling a 6

that should be 1/12

cus flipping a head and rolling a 6 have no impact on each other

[hearty turret]

it turns out that the better way of expressing this idea formally is to use that P(A)*P(B) = P(A and B) cus if A has probability 0 of occuring, then it is independent to everything

[snow reef]

I think I get it. I was struggling because I was thinking about 'rolling a dice' instead of an specific event. So, they are multiplied because the sample space becomes the mapping of both event's sample space

thank youu

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[snow reef]

Hello, I don't understand this concept of conditional independence. What does P(A|C) and P(B|C) even mean in the example? the probability of rolling a dice given the sum of A and B's outcomes add up to 7?

[snow reef]

or even like if A and B are both rolling a dice, then what does A intercept B mean in the conditional independence formula?

[ripe basin]

in simple words now you have the restriction that let say you rolled 1st dice and it showed 1 so the second dice must be 6 (se its now bounded to be 7-showed on dice 1)

[snow reef]

ok, I think I get what you mean, but then when finding P(A|C) we have to calculate P(A intercept C) what does that mean?

all the outcomes of A involved in C?

also, without thinking in terms of probability, what does A intercept B mean when they are independent?

[topaz sinew]

@snow reef Has your question been resolved?

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@snow reef Has your question been resolved?

[snow reef]

Also, what I dont understand is that is P(A intercept B | C) is defined as P(A and B and C)/P(C) isnt this 1?

isnt P(A and B and C) the same as P(C) in the example?

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hellooo

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[summer saddle]

can someone please explain this question?

[summer saddle]

i get how to do i, i just dont understand ii at all

[plain depot]

Find HS

I don't understand the statement of the example above myself but ii is pretty clear

Then round to once decimal place

Like 25.73 becomes 25.7

63.48 becomes 63.5 etc

[summer saddle]

but i dont get how to find HS

[plain depot]

Did you draw a diagram?

Can you share it

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[viral anchor]

I have to show that this is true, how?

[hallow depot]

$\leftarrow$ it is due to the continuity of $f(x)=|x|$

[thorny flame]

everg

[opal vault]

(what's your definition of lim(...) = 0 when n-> +infinity, it should be pretty obvious)

[hallow depot]

for the other direction you can do it by using the limit definition

[viral anchor]

can i get a bit more detailed explanation?

[hallow depot]

about which implication ?

[viral anchor]

of how i can prove it, like i understand it, but i don't know how i show it mathemataicly

[hallow depot]

now that you have the idea try to figure the proof out by yoursefl

we will be glad to read it and (perhaps) correct it

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[mossy spindle]

So the question I'm doing has two parts. There are two series, c_n and a_n and then the "p-numbers". The first part is to prove that a_n converging towards A implies that c_n also converges towards A. The second part is to explore if that implication is just an implication or an equivalence, and i'm stuck on that part.

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[ivory sorrel]

So I feel this should just be $\neg(P \land Q \implies \neg P \land \neg Q)$

which feels wrong

very wrong

[thorny flame]

Veni, vidi, perii

[vernal matrix]

May help to remember that the statement "if $A$, then $B$" is the implication $A \implies B$

[thorny flame]

@vernal matrix

[ivory sorrel]

yes, I know that

[agile harness]

but it’s not what you wrote

[ivory sorrel]

if not P or not Q, then , that doesn't imply that P or Q

right

oops

I messed up the negation of \implies

[vernal matrix]

There really shouldn't be any negation of implications, really...

[agile harness]

your assumption should be $\lnot P \lor \lnot Q$ yes?

[thorny flame]

knief

[ivory sorrel]

yes

which is $\neg ( P \land Q)$

[thorny flame]

Veni, vidi, perii

[agile harness]

sure

but why did you negate the entire implication

[ivory sorrel]

oops

well

the question says then it is NOT the case

[vernal matrix]

Also this is not what your statement says - it says "...then not [...]", not "...that doesn't imply..."

[ivory sorrel]

so that doesn't imply

[coral fable]

It implies it is false

Not that it does not imply it is true

Which can occur if unrelated

[ivory sorrel]

oops

Why am I struggling over such trivial things?

😭

thanks

so $\neg(P \land Q) \implies \neg (P \vee Q)$

[agile harness]

chartbit who would you be without your emojis?

[vernal matrix]

I know right

[ivory sorrel]

What's wrong with this

[vernal matrix]

Check the right hand side, and the original statement

[ivory sorrel]

it is not the case that P or Q

[coral fable]

So where’s the not

Can’t drop that

[thorny flame]

Veni, vidi, perii

[ivory sorrel]

This feels so wrong

it is not the the case that P or Q

that intutively doesn't mean this, does it

either that or it's just my bad english

[vernal matrix]

"it's not the case that I'm either the fastest, or the best"

[coral fable]

It does

Btw you’ll notice this is the contrapositive

[ivory sorrel]

yeah, it is

that's fine

just worried that I'm struggling with the translation

[coral fable]

Contrapositives look nasty with the negations

[coral fable]

Just read the stuff more

Get familiar with it

Gaslight yourself into thinking it makes sense

It’s just a dictionary translation, the actual ability to manipulate the expressions is what counts

Rather than making precise statements out of natural language

[ivory sorrel]

That's easy enough, I mostly struggle with the english to logic translations

Thanks

This would just be $[P \implies (Q \implies R)] \implies [ (P \land Q) \implies R]$

right

[coral fable]

Yes but uh

For reasons of non-associativity, you’d wanna say P -> (Q -> R) for this class

[ivory sorrel]

ah, so that it's more readable

right

[coral fable]

Once you get further it’s assumed to be bracketed like that usually, but the order of doing it matters

[thorny flame]

Veni, vidi, perii

[coral fable]

Compare P -> (Q -> R) to (P -> Q) -> R

[ivory sorrel]

yeah, they are completely different

[coral fable]

Yeah so just watch out there

[ivory sorrel]

5(d)

so to start, I compared it with a natural sentance

"I'll be fine only if you'll be fine"

but that's obviously not the case here

Like this should be $P \implies R$ but that's obviously false

[thorny flame]

Veni, vidi, perii

[coral fable]

“Only if” is stupid, don’t worry too much about it

[coral fable]

It’s false, but that is a well formed formula

[ivory sorrel]

Is that the right answere here

[coral fable]

By stupid I mean no actual mathematician says it outside of it and only if

[coral fable]

Dawg it’s been so long since I’ve seen “only if” used unironically idk, but I believe so yes

It’s the converse in iff I think

[ivory sorrel]

Thanks

The discriminant is negative only if the quadratic equation has no real solutions.

so this would be if the quadratic equation has no real solutions, then the discriminant us negative

right

[ivory sorrel]

Well, it's confusing at first glance, so I'm very likely to be tested on it

[coral fable]

I think

[coral fable]

Literally real, but only to never be useful

I have my qualms with logic pedagogy and PR

[ivory sorrel]

I mean I literally was yesterday

[coral fable]

Classic

Anyway, just replace it with iff and consider the converse

:3

[ivory sorrel]

cool, thanks

So this would be

" if the angles of a triangle are congruent, then it is equilateral "

[ivory sorrel]

My classmates say it's the other way round, as did my teacher, I'm really confused now

*said yesterday

[coral fable]

Yes

[coral fable]

Look dawg I dunno, it’s probably the most worthless convention out there in logic

[ivory sorrel]

Like they say it's of the form P only if Q

[coral fable]

Once you get past the intro stuff it’ll never show up again

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[thorny flame]

Aya

[limber prairie]

Maybe find the average in integral form

you can use feynman's trick to integrate this

I'mma try

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@strong sable Has your question been resolved?

[strong sable]

Lemme try

Uhh this is weird

[limber prairie]

Idk bro

that might not be the way

$$ frac{e^(-a)}{ a^2 + 1} $$

Wth

Fq

[strong sable]

I'm cooked again I don't even have a clue how to analyze it

[thorny flame]

Aya

[limber prairie]

yeah that

How'd I integrate this

[strong sable]

What's this..

[limber prairie]

and there was another

it was same but multiplied with a

[limber prairie]

Tried feynman for the avg in 0 to 1

Idk man this seems like out of my capabilites

<@&286206848099549185> Help him pls

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!15min

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[limber prairie]

it's been 15 min?

Oh you mean like no one answers in 15 min THEN

?

hllo?

[strong sable]

What's wrong with you? We already discussed for more than 15 mins?!

[bleak widget]

yes but idt u asked or something
anyways if u did my bad

[strong sable]

Your message is unhelpful, just stop.

[limber prairie]

Anyways

If someone helps

Pls ping me

[strong sable]

Sure

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[torn osprey]

ok has anyone solved this yet? I tried

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[strong sable]

What did you get

[torn osprey]

I sent you a dm

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[ancient cloud]

proof that (cos2alpha+cos2beta)/(1+cos2(alpha+beta))=cos(alpha-beta)/cos(alpha+beta)

[ancient cloud]

im kinda stuck

[neon iron]

for anyone who wants to help ^^^

[ancient cloud]

ty

wait no

u did it wrong

its cos2alpha not cos^2alpha

@neon iron

$\frac{cos2 \alpha + cos2 \beta}{1 + cos2 (\alpha + \beta)} = \frac{cos(\alpha - \beta)}{cos(\alpha + \beta)}$

[thorny flame]

Sleepy

[neon iron]

^^

[ancient cloud]

i did L.H.S=$\frac{cos^2 \alpha - sin^2 \alpha + cos^2\beta - sin^2\beta}{1 + cos^2 (\alpha + \beta) - sin^2(\alpha + \beta}$

[thorny flame]

Sleepy

[ancient cloud]

and im stuck now

<@&286206848099549185>

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@ancient cloud Has your question been resolved?

[ancient cloud]

<@&286206848099549185>

anyone?

[flint stump]

Use this on numerator and for denominator, use cos2A = 2cos^2A - 1

then its a 1 step answer

[ancient cloud]

can you try approaching the answer from this?

[flint stump]

|| retrace your step to arrive at original problem and use my method || /s But honestly, if I see cos^2 x - sin^2 x I convert it to cos2x

tbf you have reduced it to primitives which doesnt go anywhere. I would try to reduce the right hand side to similar form if possible

[ancient cloud]

so start from the rhs?

[flint stump]

If you are hell bent on using this, then that would be my approach, yes

[ancient cloud]

lemme try

ive been stuck on this question since yesterday

and i thought sleeping would help

uh

@flint stump

R.H.S= $\frac{cos\alpha * cos\beta + sin\alpha * sin\beta}{cos\alpha * cos\beta - sin\alpha * sin\beta}$