help-27

[umbral trench]

so here to get rid of the sqrt

[odd dew]

You square the whole equation and that's how you get the x/sqrt7?

[umbral trench]

you can sqrt the denominator and have x/sqrt7+sqrt1 which is 1

and it should be

6/sqrt7 arctan (x/sqrt7)

i think

if that helps

[odd dew]

Yess that's what I got!

[umbral trench]

for u sub problems i wouldnt worry too much about writing down every single step you kinda have to use intuition for a lot of it

[odd dew]

Oo okayy

[umbral trench]

what helped me before taking the apexam was practicing specifically arccos arcsin

[umbral trench]

okperfect!

[odd dew]

Ooo can I ask why those two?

[umbral trench]

because youre not gonna get an frq where you're asked to evaluate arctan

at least not as frequently

ok nvmd my friend is saying they do but i personally didnt study it

are you in bc or ab?

[odd dew]

I'm in ab rn

[umbral trench]

gotcha

ok wait so do you have any other questions about inversetrig functions?

[odd dew]

Uhh no I think it was just those, tysm for all your help!!!!

[umbral trench]

perfect

yeah no problem

[odd dew]

Genuinely appreciate it a TON

[umbral trench]

follow tallandjuav444 on tiktok for more awesome calculus tips ✏️

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[still cipher]

I have a couple questions involving series, but could someone explain why this answer is true ?

i dont understand why this wouldn't work like a normal p-series

[acoustic leaf]

there is an n in the numerator

which makes it behave in the limit as n/n^p

[still cipher]

i understand that but if i took the limit, wouldn't the dneominator still grow faster than the numerator ?

[acoustic leaf]

but then we can do a limit comparison with 1/n^(p - 1)

which converges when p - 1 > 1

[still cipher]

waitt i am confused, u can compare n/n^p to 1/n^(p-1) ?

[acoustic leaf]

n/n^p is exactly 1/n^(p-1)

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[tired kindle]

How do I do this

[pseudo basin]

@tired kindle do you want the slightly cheaty but intuitive(ish) way or do you want the formal but slightly obscured way

[tired kindle]

maybee whats easier to understand lol idk

[pseudo basin]

ok then let's go for the slightly cheaty way

imagine that 1000 forms come into the office and the 3 employees process them according to the percentages listed

how many forms does each of them process?

[tired kindle]

500, 200, 300

[pseudo basin]

james does 500, sophia does 200, oliver does 300...

let's keep it straight who does what, ok?

alright

now,

james' error rate is 0.06. of the 500 forms of his desk, how many forms does he fuck up?

[tired kindle]

30?

this is hard cause im not allowed to use a calculator

i need to look at some vids on how to multiply decimals lol

[pseudo basin]

uh oh

that is something quite necessary that you were missing indeed

but yes, james fucks up 30 forms.

now calculate how many forms are fucked up by each of the other two employees

(and do not just blurt out a pair of numbers. your answer should be a complete sentence)

@tired kindle

[devout snow]

@tired kindle Has your question been resolved?

[tired kindle]

wait am i able to do this with a tree diagram

I started this last night but idk if it’s how I meant to do it

[devout snow]

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[visual hazel]

would ba and ab be a single letter in Y with length 1

or are they length 2

[devout snow]

@visual hazel Has your question been resolved?

[visual hazel]

<@&286206848099549185>

[stone stump]

length 2

otherwise the whole setup is pointless if you have to differentiate between say ab a and a b a

then they also could have just called ab as y

[visual hazel]

yeah as i figured

ok thx

[visual hazel]

would (e) be just the set of X* that has length of 4 or less?

because i could just append a length 2 string from X and append it with Y

but its also the same if i just find X* and take the empty string for Y

<@&286206848099549185>

[visual hazel]

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[rare kernel]

9th one someone help pls

[craggy minnow]

I'll just tell you this

You can solve it using this

[pure flower]

whatd you fucking try

[craggy minnow]

TanA+Tan B +tan C=TanA.tanB.TanC

[rare kernel]

Yeah I remember that condition

When a+b+c = pi

[craggy minnow]

bruv tu kahan se hai?

[pure flower]

blr

you know everybody in a chat is jee when theres no latex and words are misused /lh

[craggy minnow]

Lolll

[pure flower]

$\tan(x)+\tan(y)+\tan(z)=\tan(x)\tan(y)\tan(z) \iff x+y+z=\pi$, yall.

[craggy minnow]

Add kar when x+y+z=pi

$\tan(x)+\tan(y)+\tan(z)=\tan(x)\tan(y)\tan(z) \iff x+y+z=\pi$

[woven radish]

_ehakastam_

Percy

[pure flower]

please slight typo

[craggy minnow]

😋

Typo karta hun toh sabh log mujhe marne chale aate hain

[devout snow]

@rare kernel Has your question been resolved?

[rare kernel]

bangalore

[craggy minnow]

assaaa

[rare kernel]

btw how will this ensure all angles are acute ?

what if x=pi,y=0,z=0?

[craggy minnow]

It won't be a triangle anymore

[craggy minnow]

Plus if a is obtuse

Tan(A)

Will be negative

You'll have to take the interior angle

[rare kernel]

why not? only condition defining a triangle is at sum of angles is 180

[craggy minnow]

So this is only applicable for acute

[rare kernel]

ohhhhh right okay

got it now

thanks a lot man

kis class me ho

[craggy minnow]

Dropper vai

😭

[rare kernel]

oh how was mains

[craggy minnow]

Kharab

I'll get 97-96

Percentile

[kindred mauve]

hmm

[rare kernel]

thats good only no ull clear cutoff

[kindred mauve]

Wat language are u speaking

[craggy minnow]

Barely

[craggy minnow]

hindi

[craggy minnow]

Ninga kannada barta?

[kindred mauve]

interesting

[rare kernel]

swalpa barathe saar

[craggy minnow]

I can speak kannada too 😔

[rare kernel]

no xutoff usually is 93 no

[craggy minnow]

Oh so you ain't one of those "SAAARRR"

Lmao

[craggy minnow]

Nah nah

[kindred mauve]

Hindi is similar to Urdu and punjab

[rare kernel]

😂

[craggy minnow]

This time the cutoff will be 95-96

[rare kernel]

shit

[rare kernel]

where are u from

[craggy minnow]

Because they are part of the proto indo european languages and predominantly inspired by sanskrit

[craggy minnow]

Telangana

[rare kernel]

ohh ok

hows advanced prep going

[craggy minnow]

About alright

Mocks mai iam scoring 160

10k rank aa jaye bas

That's my aim

[rare kernel]

out of 360?

[craggy minnow]

Yea

[rare kernel]

thats so good fir mains mai kkya hua bhai 😭

[craggy minnow]

Arey maine attempt toh 188 ke liye kiya tha

Par negatives chale gaye

Ek question mai toh-10+2 ko maine -12 samjh liya

[rare kernel]

stress ki vajah se

:(

[craggy minnow]

prolly

i hate doin this shi

Mummy papa gaand mar rahe hai meri

Roz

[rare kernel]

kyu bhai it takes courage to take a drop

[craggy minnow]

(drop leke kota gaya tha)

💀

[rare kernel]

SHIT

😭

kota kyu gaya

[craggy minnow]

Thought ki

Mujhe

Achi rank aayegi

Mere city mai meri rank was 1 to 3

[rare kernel]

chal ab padhai kro atb for advanced 👍🏿

[craggy minnow]

Thanmks

[rare kernel]

DAM

[craggy minnow]

Isliye I thought kota jaake khud ka level badhaunga ulta mai chud gaya

[rare kernel]

😭

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[shrewd nebula]

Via only a compass, given three arbitrary points, say A, B, and C, how should a point be constructed that lies both on line AB, and on the circle around A of radii AC?

[devout snow]

@shrewd nebula Has your question been resolved?

[glossy dew]

almost there

draw AB

and the intersection is your point

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[devout wave]

An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of
50.0 km (see Appendix F). To the dismay of scientists on earth, an electrical fault causes an on-board thruster to
fire, decreasing the speed of the spacecraft by 20.0 m/s. If nothing is done to correct its orbit, with what speed (in
km/h) will the spacecraft crash into the lunar surface?

[craggy minnow]

Oh btw

The ln(R+50/R)

That should have been ln(R+50*10^3/R). ...as it is in kms

I didn't notice sorry

[devout snow]

@devout wave Has your question been resolved?

[devout wave]

50*10^3 is the radius of moon right

what is this

[craggy minnow]

50*10^3 is altitude

R is the radius of the moon

[craggy minnow]

Gravity - centripetal force= net acceleration

[devout wave]

and for the next line why u integral like this

[devout snow]

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[rich temple]

I have a test in like 2 hours on trigonometry. I am struggling with how to figure out if an SSA triangle is 2 triangles or not i cannot seem to find a straight answer online

[rich temple]

this is a practice question for the test

and apparently this is 2 triangles but for the life of me i cannot figure out why and how to deal with that

so, hold up, you can do that with things that are declared as 1 triangle

you can subtract most answers from 180 so what makes that triangle so special

but in example 2 the only obtuse angle is the 93 yet we dont use it

97*

we use the 53

but that doesnt make sense since it is supposed to be the obtuse case

and 53 97 and 30 equal 180

so what is making this a double triangle

i dont understand how they are creating a second triable

yes i read that

but you can do that with any triangle

even though the correct answer is 1 triangle

its talking about an obtuse angle yet never uses it to justify the 2nd triangle

53 is an acute angle

am i not understanding something foundational here?

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[rare viper]

can i please get an explanation on how to solve these kinds of questions?

[polar chasm]

I'd start by giving things names and trying to get some equations

[fair juniper]

I would suggest dropping perpendiculars from F and E to RQ

[rare viper]

i have tried that, and decided on naming the smaller circle's radius x and the larger one's y. x + y = 4 correct?

but that's unfortunately where i am stuck at

[polar chasm]

thats one equation

[polar chasm]

try this

[rare viper]

not sure if i am on the right track, but i did get a = 4sin(60)

[polar chasm]

That works i guess, by comparing it with this, you can also get y - x btw

and thus both y and x

[craggy minnow]

If all the circles are equal

[polar chasm]

they arent tho

[craggy minnow]

oh then nvm

[polar chasm]

||they are 3 and 1 if i did the math correctly||

[rare viper]

hm? can u explain this a bit?

[polar chasm]

apply pythagorean theorem here

and youll get equation with x and y

and it should simplify to x - y = sth

[fair juniper]

i would follow this track

the small side of the triangle is x-y, but also by special triangles, half of 4

so x-y=2, x+y=4 and its a simple system of equations

[rare viper]

ah, i see

but, how would finding the radius of the circles help find the length of the triangle??

[fair juniper]

so we know that the partly red triangle in the middle is equilateral

the side lengths are 4 becuase one side is EF

thus, we can get the length from the center of the triangle to the edge (also known as the apothem)

[rare viper]

it's 4 + x, so 5

[fair juniper]

yes

if you need one more step: ||draw a line from the center to a corner, then use special triangles to find half the side length||

[rare viper]

5/tan(30)?

ah no half of EQ is 5tan(60)

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[elfin hull]

Hello guys I have a question regarding being efficient in finding the value of a matrix

[supple knot]

[pure flower]

good luck finding the 'value of a matrix'.

what does that even mean

the determinant?

[elfin hull]

So i meant a matrix game but thank you

particularly a 4x2 where there is no saddle point

[pure flower]

either this is stuff that's beyond me

or you need to give more context

which field is this from

[elfin hull]

Game Theory

Given a 4x2 Matrix, with probabilities x and 1-x for column 1 and 2, You get system of equations given the rows expected payoffs.

@pure flower Thank you for the help I know you tried but its ok 🙂

[wind mason]

1. Can you construct the matrix?
2. Can you calculate each expected value?

[elfin hull]

4x2 = {-3 5 , -1 3, 2 -2, 3 -6}

Expected Payoffs are : -8x+5 , -4x+3 , 4x-2, 9x-6

I have solved the whole problem already but am I really going to have to go through a system of equation and solve for x for each Exp. Val. ?

[wind mason]

Yeah.

[elfin hull]

Interesting

That sucks

[elfin hull]

What about this way?

[wind mason]

Can’t see it.

Also.

!ss

[devout snow]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[elfin hull]

Notice how the author Uses a 'focused' matrix instead of the whole 3x2

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@elfin hull Has your question been resolved?

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[vital island]

what is the fastest way to cancel this

[dire forge]

does that say
[\frac{100 \times 1744}{109} = h]

[woven radish]

amhERIC

[dire forge]

I can't read it

[vital island]

It does

My handwriting is ass sorry

[dire forge]

oh okay

so first we can bring the 100 over like this

[100 \times \frac{1744}{109}]

[woven radish]

amhERIC

[dire forge]

are you alright with that

[vital island]

Mhm

[dire forge]

alright and then how would you compute 1744/109?

[vital island]

uh

i cant wth 😭😭

109 x 16?

[dire forge]

yup!

so then you just get 16

and then what's 100 * 16

[vital island]

1600

[dire forge]

yup and then you're done

[vital island]

hmm yeah

Thanks mate

[dire forge]

you're welcome!

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[waxen steeple]

i was proving if a differentiable function $f : [a, b] \rightarrow \mathbb{R}$ is s.t. $f'(x) = 0 \forall x \in [a, b]$, then $\exists C \in \mathbb{R}$ s.t. $f(x) = C \forall x \in [a, b]$. I decided to use contradiction and MVT, so i said that suppose for a contradiction that $\exists x_1 \in [a, b]$ s.t. $f(x_1) = D$ and separated the case of when $x_1 \neq a$ and $x_1 \eq a$.

My question is that in the case $x_1 = a$, using MVT I get that $\exists c \in (a, b)$ s.t. $f'(c) = \frac{f(b) - f(x_1)}{b - x_1}$, however im unsure whether i can assume $x_1 \neq b$. [a, b] is an interval but does that mean I can automatically assume that b > a?$

[woven radish]

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

[waxen steeple]

(short form if u dont wanna read: im unsure whether i can assume that b > a in this proof)

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[vestal talon]

done b (x^N+1 - x + sqrt(x^2N+2 + 1) - sqrt(x^2 + 1), and ik that its only convergent when -1<x<1, just struggling w the last part

[devout snow]

@vestal talon Has your question been resolved?

[supple knot]

did you try ratio test?

[vestal talon]

idk what that is ibr

i got -x-sqrt(x^2+1) for c and apparently its 1 - x - sqrt(x^2+1)

just dont know how to get there

[supple knot]

did you try taking the limit as N goes to infinity of your expression in b)

for the range of x that you found

[vestal talon]

yeah

thats what i got my answer from

[supple knot]

show your work

[vestal talon]

wait nvm think i realised where i went wrong

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[prisma elm]

help with last one please

[acoustic leaf]

note the order of the bounds

,, \int_a^b f(x) \odif x = - \int_b^a f(x) \odif x

[woven radish]

cloud

[prisma elm]

so -64?

[river pebble]

yep

sorry i was high 😭

[prisma elm]

lol high and math?

[river pebble]

best combo

[prisma elm]

thank you

.close

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[gray monolith]

On a dice, two sides are yellow, two sides are red, and two sides are blue. The probability of landing on each color is therefore:
1/3 for each color.
You roll two such dice. What is the probability of getting. yellow on only one of the dice?

[lime plaza]

4/9?

[gray monolith]

yeah

[lime plaza]

Ok so what did u get

[gray monolith]

but how do we get their

i havent tried anything

[lime plaza]

Ok so

To get yellow on only 1 die

We need probability of yellow of one die multiplied with probability of NOT yellow on other

[gray monolith]

okay how do we do that

[lime plaza]

uh what is probability of getting yellow?

[gray monolith]

1/3

[lime plaza]

and probability of not yellow

[gray monolith]

2/3

[lime plaza]

exactly

[gray monolith]

1/3 x 2/3?

so 2/9 and then where do we get the other 2/9

[lime plaza]

ok so

What u calculated right now is

YELLOW and NOT YELLOW

It can be NOT YELLOW and YELLOW also

Understood that?

[gray monolith]

okay

thanks

.close

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[hybrid snow]

In a very simple sense, f and inverse f just swap domain and range

[next star]

yeah but how does a quadratic not have an inverse

[acoustic leaf]

it won't have an inverse function if there are multiple distinct inputs which map to the same output

[next star]

that dosent happen on a quadratic?

[blazing jetty]

uhh it does

[hybrid snow]

Power in clutch

[blazing jetty]

for example, you have 2 roots of a quadratic

[next star]

wait i was thinking of the other way around

two outputs for the same input

[blazing jetty]

so 2 values of x has the same output, 0

[acoustic leaf]

then it just wouldn't be a function

[hybrid snow]

Unless you restrict the original function

But suppose you did restrict the original function

Where would pretty much every inverse lie in

[next star]

so its either (2, infinity) or (-infinity, 2)

or any subset of those

[blazing jetty]

yeah

[next star]

ok thanks

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[next star]

wait so if the domain of a quadratic isnt restricted then it cant have an inverse?

[blazing jetty]

not always true

there are quadratics which are always increasing

[next star]

but for a polynomial quadratic

[blazing jetty]

an inverse cant exist if the function is not one one

or onto

[next star]

oh okay

so a polynomial quadradic without a domain restriction dosent have an inverse

because its not one to one

[blazing jetty]

yes

[next star]

ok

thanks again

[undone chasm]

(you can type .close when ure done)

[devout snow]

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[brazen orbit]

could someone help me figure out part b?

[devout snow]

@brazen orbit Has your question been resolved?

[brazen orbit]

<@&286206848099549185>

[humble tundra]

use triangle similarity

[brazen orbit]

which triangles would i use?

[humble tundra]

have you done (a)?

[brazen orbit]

yes

but i dont understand why i cant put the pyramid on the yz plane, so that the "x" height is also the actual x coordinate

i was asking chatgpt but it doesnt give that solution

[humble tundra]

how do you do it?

should be using similar triangles too right?

or maybe not?

[brazen orbit]

yes but i have the vertext positioned at 0,0

i thought it would be more reasonable to have the center of the base at 0,0 for part b since then x is actually x

[humble tundra]

you can take the cross-section like this

where s is the one to prove

H is the total height

given in (a)

the 2 right triangles are similar

so you can make an equation and make s the subject to prove it

[devout snow]

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[slate glen]

Hihi I have a qn rolling right is due to red arrow the current flow right but doesn't current flow from green arrow to red which would lead to the force moving upwards instead so why do we take reference point of current at red arrow instead of green using Fleming rule

[devout snow]

@slate glen Has your question been resolved?

[slate glen]

<@&286206848099549185>

[devout snow]

@slate glen Has your question been resolved?

[slate glen]

Man

[devout snow]

@slate glen Has your question been resolved?

[devout snow]

@slate glen Has your question been resolved?

[restive river]

@slate glen This would be more suitable posting question in a server dedicated to physics. Btw, in my opinion we take that as a reference because we are considering the rod not the whole circuit as a whole. Also the electric rails are experiencing the magnetic field upward.

[acoustic leaf]

the rails at the top (whose current is the green arrow) do experience an upward force but are fixed in place. the thing which can move is the rod AB, and it has the red current

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[restive river]

.reopen

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[grave dune]

differential equations, Laplace transform

[wicked turtle]

1 + 9/s^2 is the same as (s^2 + 9)/s^2

just put everything over the common denominator s^2

[grave dune]

ohp

can you tell im exhausted

thanks

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[foggy dagger]

Let 𝑀 be the subset of 𝐶 marked by shading (the solid line belongs to the set). Which of the following statements is true?

[foggy dagger]

This is just really confusing, because it doesn't look like anything I've learned so far and I don't know what and how to interpret.

[polar chasm]

One way would be trying to identify those which are false

maybe plug in something like i and see if it rules out some of them

[foggy dagger]

Don't really know what I'm looking at really.

[polar chasm]

The graph shows all complex numbers which are part of the set M

so if 1 + i is in M, then it must also be part of that stripe e.g.

[graceful cosmos]

See "set builder notation" for a tutorial on these

[polar chasm]

these are then the conditions which tell you whether a given complex number is in these sets. E.g. for the first choice, the condition is |Im(z) + 1| <= 1

[foggy dagger]

I see...
So I have to somehow find a statement that is valid for this shading, right?

[polar chasm]

Yep

[foggy dagger]

I know that most of the time, the helpers don't show the solution to the problem, but would it be OK if I asked guidance towards a solution? Such as exemplary disproval of the first example.

Because I don't know how and what to start working with.

Imaginary Part of z plus one is smaller or equal than 1 means really nothing to me when I look at it.

I'd be very glad.

OK I think I got it.

.close

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[pure flower]

The answer here involves finding the number of favourable cases as $9^7-8^7$ (selecting 9 coupons, removing the ones which don't have 9)

However, can I not assume I'm definitely selecting a coupon with 9 by default, and the rest can be selected in $9^6$ ways?

Prolly just brainfog idk.

[woven radish]

Percy

[pure flower]

(ping me)

[storm raptor]

Wrong screenshot @pure flower ?

[pure flower]

Shit yeah sorry

[polar chasm]

However, can I not assume I'm definitely selecting a coupon with 9 by default, and the rest can be selected in 9^6 ways?

This would likely lead to overcounting

just 9^6 would count the number of ways to select those coupons with 9 being the first one to select

1 * 9 * 9 * 9 * 9 * 9 * 9

[pure flower]

Yeah but why though

[polar chasm]

you could try to naively fix this by multiplying this by 7, which is the number of different positions the 9 coupon could be at

but that would lead to overcounting

[polar chasm]

Is it clear now or should i explain it further?

[polar chasm]

basically you would count choice such as
9, 9, 1, 1, 1, 1, 1 twice with 7 * 9^6

[pure flower]

I'm not sure I see why that leads to overcounting

[pure flower]

Ah.

[polar chasm]

you'd need to apply inclusion exclusion

and in theory that should give you the same result

[pure flower]

Okay yeah got it

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[tacit loom]

.close

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[silver canopy]

hi i am having a hard time finding the range, i believe domain is all real numbers but im stuck on range

[frozen aurora]

notice that this function is always increasing

[silver canopy]

yes

[frozen aurora]

so you just need to check limits to +infinity and -infinity

that will be your range

[silver canopy]

does (1,sqrt10) sound right?

[wraith lily]

You should check if 10^x increases faster than x^2 or viceversa

[frozen aurora]

yes

[silver canopy]

awesome thank you both for the help!

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[worldly sluice]

how can you factor this

by substituing x=1

[iron kindle]

do you know the quadratic formula?

[worldly sluice]

yes

[iron kindle]

why not use that

[meager willow]

He’s asking to factor

[iron kindle]

yeah, thats what you use the quadratic formula for lol

[meager willow]

3 and 1

3 multiplied by three plus one

(3m+1)(m+3)

[worldly sluice]

how can you factor this then?

@meager willow

[iron kindle]

!nosols

[devout snow]

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.

@worldly sluice Has your question been resolved?

[devout snow]

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[hasty ether]

What happened to the ! ? How are you able to substitute the (n+1)! to (n+1) n! ?

[sand dove]

k! is the product of all integers between 1 and k

so (n+1)! is 1 * 2 * .... * n * (n+1)

which is n! * (n+1)

[hasty ether]

O

wait i see it now

so wait

! = n! ?

like the variable value

[sand dove]

! makes no sense on its own

"the factorial" doesn't refer to any quantity on its own

we always refer to "the factorial OF a number"

n! is "the factorial of n"

like "+" isn't any quantity on its own

you need two numbers to add to each other for the "+" to make sense

so "2+5" is a quantity

while "+" on its own isn't

[hasty ether]

right, but how does it not affect the overal multiples ? like for sure (2+1) ! = 1 x 2 x 3 and (2+1)2! = 1 x 2 x3 x4 x 5 x 6 which is not the same? ...

[sand dove]

There is an order of operations to respect

factorials always come before multiplication

it's like exponents

so in (2+1)2!, the factorial only applies to 2

and not the product (2+1)2

so to be taken as (2+1) (2!)

different from [(2+1)2]! = 6!

[hasty ether]

what about the 3 ? would it multiply to the factorial of 2 after it is done?

[sand dove]

[hasty ether]

oh okay so it would be like 1 x 2 = 2 and then 2*3 =6

[sand dove]

so yes (2+1)2! = (2+1) * 2 = 3 * 2 = 6

if you meant to do multiplication before applying the factorial

only one way to reverse order of operations

parentheses/brackets

so [(2+1)2]! will do the multiplication first

and then apply factorial

[hasty ether]

ah so is this substitution/ like more indication... idk what this is, they are equal to each other... so it would just be another way of writing it? the (n+1)! = (n+1)n!

[sand dove]

(n+1)! = (n+1)n! is correct

[sand dove]

this is what we did here

so we are just rewriting (n+1)! a different way

but keeping it the same quantity

[hasty ether]

yah ik but im still a little confused how they just place the value of n there, what can i search it up to learn more about these rules?

[spare ore]

the substitution you are seeing is part of the (recursive) definition of factorial

[sand dove]

if you define n! as the product of all integers between 1 and n

then there is a clear link between n! and (n+1)!

that is also its definition but in recursive

to get from n! to (n+1)! you just multiply by the next integer, n+1

I can repeat this as much as I want

for example

(n+2)! = (n+1)! * (n+2) = n! * (n+1) * (n+2)

so if you had to simplify an expression such as $\frac{(n+2)!}{n!}$

[woven radish]

rafilou is not not born in 2003

[sand dove]

the "recursion" formula is what helps us

[hasty ether]

ah

im now more confused T_T i never learned this at all...

give me a moment- ahh i understand it that yes once you put into practice and expand these to any value you wnat of n

you would get the same answer

but now im more confused how you were able to like expand that out-

so is the rule of that its like, ah lets say it is n + c ! so in the "recursion" you did it shows that you can just like decrease the value of c while also multiplying like every other valuue afterwards is that right?

so like n+0 ! * (n+1) * (n+2)

so what is happening in (n+1) ! = n! *(n+1).... :0

[sand dove]

the "one step recursion" is kinda the recursion definition of the factorial

the (n+1)! = n! * (n+1) (for ALL natural integers n)

that is one way to define it

[hasty ether]

O

[sand dove]

with 0! = 1

otherwise

you can use the product definition

n! = 1 * 2 * ... * n

and then regroup whatever amount of integers you want together

[hasty ether]

O

[sand dove]

so for example

(n+2)! = 1 * ... * (n+2)

but I could have decided to put all integers up to n in one box

and put all the others apart

so (n+2)! = 1 * ... * n * (n+1) * (n+2)

and boom (n+2)! = n! * (n+1) * (n+2)

[sand dove]

otherwise you use twice the "one step recursion" definition like done here

and you get the same thing

[hasty ether]

OMA thats pretty cool actually, okay so i just need to think like a pattern to which i can like expand on it

that makes this lim stuff with factorial easier than i thought

okie

i understand thank you so much!

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[azure sluice]

IM BACK after spending another 30 minutes on this grueling math problem, i have found a greater foe: pt 2 of this question! If anyone has a lot of free time could you please check my notes to see where I went wrong? Ty

[azure sluice]

I need to go to sleep

It’s 2:23am

wait nvm

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[chrome shuttle]

I'm not sure how to solve this limit - lhopital is way too messy it seems

[pseudo basin]

indeed it is

you would be a fool to do it with lhop

[lime plaza]

can we do the sin/x =1

[pseudo basin]

bad notation but yes we can.

[lime plaza]

I think thats how

cause tanx/x is also

[pseudo basin]

we can also use the log(1+t)/t -> 1 thing

[devout snow]

@chrome shuttle Has your question been resolved?

[spare ore]

i got 1/50, dont know if thats right

[chrome shuttle]

yeah thats really close the answer is apparently 50

howd u get there?

im still not sure what the first step would be lol

[spare ore]

oh wait

im stupid

of course its 50

i flipped everything the wrong way

[bold drift]

sin(x)/x =>1
tan(x)/x =>1
and same for the log
everything works out

[spare ore]

the previous ppl gave good hints. lim x-> 0 for sinx / x , tanx / x, and log (x + 1) / x are all equal to 1

yea

[chrome shuttle]

thank u very much i'll try that out

so we just divide all terms by x and simplify the limit and it should work out?

[spare ore]

well not just x you also need the constant raised to whatever power it is, for example sin^2 (5x) -> (5x)^2

[chrome shuttle]

ohh I think I got it yea

thanks i got 50

[spare ore]

forgot to put the x whoops

in this case all the x's cancel out anyways

[devout snow]

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[hushed arrow]

I need help

[hushed arrow]

arcsin[(n^(1/2)-(n-1)^(1/2))/(n(n+1))^(1/2)]

Sum it from 1 to infinity

[wispy oyster]

what do u wanna do with that sum

[hushed arrow]

My maths teacher gave this ques to me

In itf

I asked him for a hard ques

[errant depot]

Inverse trig huh

Why don't you convert it to tan

And sum it

[wispy oyster]

it telescopes once u convert it into arctans

[wispy oyster]

try showing that the expression is equal to arctan(√n) - arctan(√(n-1))

[hushed arrow]

It this arctan conversion right?

[errant depot]

Wait is your adjacent correct?

I mean denominator

Mujhe kuch aur aa raha hai

[hushed arrow]

Simplify krke kuch aur Asaan aa rha hoga

Mera simplify hogya

[hushed arrow]

Is reply ki wjh se ye cheez sochi meine

[errant depot]

Bhai agar tu jee ke sawal kar raha hai itf ke

Sab mai ham tan mai hi convert karte hain

[hushed arrow]

Hn meine tan me hi convert kia tha pr simplify krne ka tarika samajh nhi aa rha tha to yha aaya phir tareeka click krgya

[errant depot]

tan (√n) -tan ((√n-1)) hai

[hushed arrow]

Hn wo aagya

[errant depot]

Yupp

[hushed arrow]

Thanks 😊

. Close

[errant depot]

All the best 26 aspirant ho ig

[errant depot]

.close

[hushed arrow]

Hnn

[hushed arrow]

Thanks

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[turbid void]

Find AB

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@turbid void Has your question been resolved?

[fossil locust]

at least answer this

send a picture of your working, for example

hint: similar triangles

[humble tundra]

Hints:

1. Draw perpendicular lines
2. Use triangle similarity

[turbid void]

.close

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[rotund tangle]

is there any trustable website that can calculate ln(2) to ln(500) with 50 digits precision

[iron kindle]

,w ln(2)

[gray summit]

Ig you can use the Google calculator app

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by .bonk__

[gray summit]

Basically you can get how many ever digits you want

[rotund tangle]

but is that correct??

[iron kindle]

yes ofc

[rotund tangle]

ln(2) is quite famous. so I think WA store them

I doubt about the other ln()

[pseudo basin]

why do you need to have such precision

i mean, fifty decimal places?

also, do we understand correctly that you plain and simple don't trust the values for ln(3), ln(4) etc. that WA gives you?

[rotund tangle]

Long story tbh... I can tell the story but not now , because if I tell now it might become another question

[pseudo basin]

ok sure yes tell it

[iron kindle]

why does it matter?

if its giving you 50 digits

and theyre correct

why does it matter if its calculates them or stores them

[gray summit]

Basically, ln 2 value is stored in calculators

[rotund tangle]

because it mean the other ln(x) such as ln(407) might not be correct up to 50 digits

[gray summit]

And almost every calculation is done based on it

[pseudo basin]

so you think this output is untrustworthy?

[pure flower]

also damn would you look at that it works for anything

[iron kindle]

and i think it calculates it

cuz when i tell it to do exponentially more digits it takes longer

[pseudo basin]

again, what im wondering about is what FOR do you need 50 decimal digits of precision?

[rotund tangle]

aight thx all, I think I will trust y'all

[pure flower]

[pseudo basin]

[pure flower]

what are you doing though

[iron kindle]

[gray summit]

Dude just compare multiple sources

And if they're the same, it's correct

[iron kindle]

!xy

[devout snow]

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.

[rotund tangle]

I need 50 digits precision to check if my coding right. currently I'm making a 36 digits precision float type of my own, I have my reason as to why I don't use already available c++ library

it mostly for performance reason tho

[pseudo basin]

oh so you are making your own floating point numbers and need some benchmarks.

[pure flower]

pfft 50 decisions precision for floats is kinda insane

[rotund tangle]

yes

[pseudo basin]

right

id say WA is a good source then

[rotund tangle]

I see... thx

[pure flower]

float cant handle 0.001 + 0.002

also yeah i recall something else about floats from you

[rotund tangle]

fixed

it's 36 digits not 50

[pure flower]

ah

[rotund tangle]

but I want 50 from source just to be sure

Anyway thx all

[pure flower]

you can prolly get a wa api

make life a bit easier

[rotund tangle]

might look at that

[devout snow]

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[rustic venture]

Can someone explain what Sal is doing here in this video? It makes zero sense to me based on the prior information in the course. If someone could also send an article breaking down what property is being applied here I’d greatly appreciate it.

https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-5a/v/limits-of-composite-functions-external-limit-doesn-t-exist

[rustic venture]

Specifically the section on how he approaches from the left twice confuses me

[devout snow]

@rustic venture Has your question been resolved?

[supple trench]

!showowrk

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Show your work, and if possible, explain where you are stuck.

[supple trench]

to provide context for your own question, you may recall the relevant definitions and results learnt in your course

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[gray summit]

I kinda don't understand what's going on here?

I understood the maxima and minima part but how to tell if the point is a point of inflection or not

[wispy oyster]

you look if the sign changes around c for f''(c) = 0

[gray summit]

I know that

[gray summit]

But what is going on here?

Let's take x⁵

double diff is 20x³

y'''' = 120x

y''''''= 0

Then it's always gonna be 0

[wispy oyster]

why are you taking further derivatives

oh the image

[gray summit]

At x = 0

Yes

[pure flower]

further derivative thing is kinda wonky

[versed juniper]

is this your teachers notes?

[gray summit]

No, my friend's

Probably it's a direct copy of the board, so yeah

[gray summit]

So I can't 100% rely on it?

[versed juniper]

i think ur friend copied it wrong

[pure flower]

https://en.wikipedia.org/wiki/Derivative_test#Higher-order_derivative_test

[wispy oyster]

if the second derivative test is inconclusive, try the first derivative test but essentially higher derivative tests are s.t

if f^n(c)> 0 where f^n is the nth derivative and n is even then c is a local minima
if f^n(c) < 0 then c is a local maxima
if n is odd then i forgot

f^n is the first nonzero derivative

at x=c

[wispy oyster]

yeah just read this

[gray summit]

Thanks everyone

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[gray summit]

I vaguely remember now learning this. Thank you

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[prisma elm]

I dont understand this part can anyone send youtube for this?

[pure flower]

what part

[prisma elm]

Eveything

[supple knot]

https://www.youtube.com/watch?v=QcHz3h81U-s

[prisma elm]

Thank you

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[grave acorn]

can someone pls help me solve 23 d)

[grave acorn]

i get to -1/2 < x < 1/2 ?? and then it gets confusing from there

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[fierce ember]

can you send the table in appendix B

[devout snow]

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[quaint ether]

how to write the dv expression for this

[quaint ether]

spherical coordinates but it made it worse

i don't think i'm meant to use spherical coor

[pseudo basin]

the volume element is a disk with thickness dx and radius y

and x^2+y^2=1

[quaint ether]

y pi dx

right?? like this

x^2+y^2=1 1 is the radius

so

i think i get it

y = sqrt(1 - x^2)

and 1 is the radius

that means that dv = sqrt(r - x^2) pi dx

right??

[proven ore]

Take the area of the disk and multiply it with dx

That will be your differential volume element

[quaint ether]

yeah but what i wrote was right ??

[proven ore]

I think you gotta square the radius

[quaint ether]

yeah

[proven ore]

Then it'll be fine

dV = pi y^2 dx

[quaint ether]

yeah thank youu everyone

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[quick dirge]

what do i even do here?

[iron kindle]

quadratic formula

if you take u=x-[x] then you get -3u^2+2u+a^2=0

[quick dirge]

how do i find the condition for

non integral solutions

after this?

[iron kindle]

do you know how to use the discriminant?

[quick dirge]

no i do not we havent reached it yet

is it not possible to do without it?

[iron kindle]

i dont think so

at least, it will be much much harder

[quick dirge]

i saw a solution but i cant understand it

leme send

[iron kindle]

since with the discriminant you can determine whether it has 0, 1 or 2 solutions

[quick dirge]

wut are they doing here?

[quick dirge]

oh ic

[iron kindle]

yeah they used t=x-[x]

[iron kindle]

if you rewrite this to a^2=... you get that

[quick dirge]

yes how did they find thre range of a with that tho

[iron kindle]

and then they graph it ig

[quick dirge]

how did they find the x intercept without constant term lmao

[iron kindle]

3t^2-2t is pretty easy to factor

t(3t-2)

[quick dirge]

yes

but

for that a=0

how did they determine it is zero

[iron kindle]

they dont

firstly, they use the fact that a^2 is always nonnegative

[quick dirge]

ok

[iron kindle]

thus every positive solution has an equal negative solution

secondly, if 3t^2-2t is negative, then there is no real solution for a

[quick dirge]

ok

[iron kindle]

(since a^2 is nonnegative)

[quick dirge]

oh

so if

a^2 is negative

[iron kindle]

(which it cant be)

[quick dirge]

then t lies between (0,2/3)

[iron kindle]

yup

[quick dirge]

but how does that

nvm

can you just say how they concluded this

[iron kindle]

hmm

idk think itd be 0<a^2<2/3

,w -3(x-floor(x))^2+2(x-floor(x))+1/2=0

[woven radish]

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Requested by .bonk__

[iron kindle]

huh?

i dont get it either

sorry

[quick dirge]

ah no worries

this prolly aint even coming for the exam lmao

ty for helping tho

cya

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[summer summit]

im stuck on what to do with this. do the absolute values mean anything? if so, what?

[iron kindle]

$|x|=\begin{cases}x\text{ for } x\geq 0\-x\text{ for } x<0\end{cases}$

[woven radish]

Bonk

[summer summit]

but how does that change the integral?

is the evaluation still $\frac{-x^3}{3} + x^2 -2x$ from -2 to 2?

[woven radish]

Krish

[iron kindle]

no

you can break it up into two cases

[summer summit]

-2 to 0 and 0 to 2?

[iron kindle]

where x(2-x)>=0 and x(2-x)<0

[iron kindle]

yes

[summer summit]

so if i see absolute values in an integral from a negative bound to a positive bound, will it always be split at 0?

[iron kindle]

not necessarily

[summer summit]

how do i figure out where to split it?

[iron kindle]

counterexample: $\int_0^2 |x-1|\dd{x}$

[woven radish]

Bonk

[iron kindle]

you have to find where the thing inside the absolute value is 0

because then you know whether itll go positive or negative

[summer summit]

so i just set it to 0 and then, therefore, i split from 0 to 1 and 1 to 2?

[iron kindle]

in the example i showed, yes

[summer summit]

and for my example since y=0 at x=0, i split it at 0

[iron kindle]

yup

[summer summit]

okay that makes sense thank you

[iron kindle]

well, you also have at x=2

but thats on the boundary, so doesnt matter

[summer summit]

yeah so i only use the solution that is within bounds, exclusive right?

[iron kindle]

if you have the integral $\int_{-4}^4|x(2-x)|-2\dd{x}$ then you need to split it in 3

[woven radish]

Bonk

[iron kindle]

sure

[summer summit]

would it be -4 to 0, 0 to 2, and 2 to 4?

[iron kindle]

ye

[summer summit]

ok ok this is makin sense now

wait so why is one of them +x^2 and one is -x^2?

[iron kindle]

for x>0, |x(2-x)|=x(2-x)

for x<0, |x(2-x)|=-x(2-x)

[summer summit]

i see

[summer summit]

in that case this would be 2x-x^2 though

[iron kindle]

yeah

and second case would be -2x+x^2

[summer summit]

the solution shows that the 2x is negative on both of them

and the x^3/3 is different

[iron kindle]

thats the -2

if you take the integral of -2

you get -2x

[summer summit]

so howd you get a positive 2x on the other one im confused

[iron kindle]

are you forgetting how to do integration or smth?

$\int_{-2}^2|x(2-x)|-2\dd{x}=\int_{-2}^0 (-2x+x^2-2)\dd{x}+\int_0^2 (2x-x^2-2)\dd{x}$

[woven radish]

Bonk

[summer summit]

ah i was mixing up the 2x in the evaluated integral with the 2x in the integral itself

my bad

[summer summit]

is the answer -16??

i tried it like 4 times and got -16 as the answer but the answer key says 0

[iron kindle]

,w int |x(2-x)|-2 dx from -2 to 2