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[odd edge]

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[mystic saffron]

How am I supposed to find domain

[shut wedge]

of f(x)?

[mystic saffron]

jawohl

yes

[shut wedge]

you know what q tan graph looks like?

[mighty tundra]

tanx doesnt exist for x = pi/2

and then the period is pi

[mystic saffron]

No I dont

[mighty tundra]

so it doesnt exist for pi/2 + npi where n is an integer

[shut wedge]

maybe search that up someday

[mystic saffron]

Oh wait

[mighty tundra]

if u put tan90 degrees it doesnt exist

its infinity

[mystic saffron]

it has asymptotes

yeah

[mighty tundra]

yes

[shut wedge]

yea

[mystic saffron]

okay makes sense

thanks

So wait

is there a way to derive this

or are you just supposed to know the shape of the grpah

[mighty tundra]

its more helpful to know the shape but

[shut wedge]

its just a given, but you can say its cause sinx/cosx

[mighty tundra]

do you know your table of exact values?

[shut wedge]

cosx cannot equal 0

[mystic saffron]

what are those

[mystic saffron]

ohh

it equals 0 at the top and botton of the unit circle

so pi/2 and 3pi/2

[mighty tundra]

so its just for where theta is 0, 30, 45, 60 and 90 degrees

[shut wedge]

exact values are good to remember

[mighty tundra]

and u can write the exact values for each trig function at those specific points

[mystic saffron]

cos 90 is 0?

[mighty tundra]

yea

[shut wedge]

yep

[mighty tundra]

in radians thats pi/2

[mystic saffron]

not for 30 tho

[mighty tundra]

mhm

[mystic saffron]

30 degrees cos is root 3 /2

[mighty tundra]

yes

[mystic saffron]

these are exact values?

[mighty tundra]

no

[mystic saffron]

Oh

[mighty tundra]

the exact values are when you equate them

so like

sin30 is 1/2

1/2 is the exact value

sin60 is sqrt3/2

so sqrt3/2 is the exact value

[mystic saffron]

Oh

Can u help me with one more domain question

not trig related

[mighty tundra]

yep

[mystic saffron]

This one too

Like

I thought it wont be defined because

square roots cant have negative numbers

[mighty tundra]

yea

but

[shut wedge]

thats for even ones tho

[mighty tundra]

h(x) is a cube root

so think about it

if you have a negative number and you cube it

ur doing

• x - x -

oops

minus timesd by itself 3 times

which is minus

[mystic saffron]

-x*-x*-x

[mighty tundra]

so if u cube root that answer

u get a negative value

[mighty tundra]

yeh

[mystic saffron]

Ohh

Wait

I still dont get it

Why are we cubing

isnt it square root

of 3

[shut wedge]

basically

[mighty tundra]

its a cube root

[mystic saffron]

Oh cube root

[mighty tundra]

yeah

[mystic saffron]

Why are we cubing tho

instead of taking cube root

[mighty tundra]

well i just said that to explain why you can have a cube root of a negative number

in ur example you would just be cube rooting -1

which is -1

[mystic saffron]

so the cube root of -1 is -1?

[mighty tundra]

yes

[mystic saffron]

But then why doesnt this work for even

[mighty tundra]

well times -1 by itself 3 times

[mystic saffron]

the quad root of -1 is 1?

[mighty tundra]

you cant

if you times a negative number by a negative number what do you get?

@mystic saffron

[mystic saffron]

positive?

[mighty tundra]

mhm

so

when you times a positive number by a negative number what do you get?

[mystic saffron]

negative

[mighty tundra]

exactly

so

(-1) (-1) (-1) (-1)

[mystic saffron]

but we are doing this 4 times with a negative number

[mighty tundra]

can only be positive

[mystic saffron]

which will yield positive?

[mighty tundra]

yes

[mystic saffron]

So how wouldnt that work

[mighty tundra]

so basically you can never times a negative number by itself 4 times and expect a negative result

[mystic saffron]

Oh

So it isnt defined for negative numbers

OH

[mighty tundra]

exactly

[mystic saffron]

MY god

You are

SO hot

for telling me this

[shut wedge]

lol

[mighty tundra]

🥵

[mystic saffron]

/j but THANK YOU

[mighty tundra]

lmao

[mystic saffron]

thank you both

[mighty tundra]

all good

[mystic saffron]

WAIT WAIT

one more question

[mighty tundra]

yaeh

[mystic saffron]

So, does this have to do with the x^1/2 = square root of x

is the same concept being applied here?

[mighty tundra]

ummm

what do you mean exactly

[mystic saffron]

Well look at this

[mighty tundra]

thats just a way to rewrite it

[mystic saffron]

This is the explanation they gave

[mighty tundra]

ok so you know how i said that you cant get a quad root of a negative number

[mystic saffron]

yeah

[mystic saffron]

bro get out

[mighty tundra]

basically, think of whatever is under the root sign as THE NUMBER

[mystic saffron]

ahh

[mighty tundra]

that would mean x+1 is the eventual number you are going to take the root of

right?

that just means that x+1 has to be larger than 0 in order for it to be positive

so you can write that as x+1>0

or

x>-1

[mystic saffron]

oh

i mean

I kinda get it

its hard for me to grasp

[mighty tundra]

thats fine

[mystic saffron]

would you mind writing it on paper rq

if thats cool with u

[mighty tundra]

alright alright

[mystic saffron]

thank you sm

[mystic saffron]

OhHH

duhh

[mighty tundra]

🤣

[mystic saffron]

makes sense now

yeah

[mighty tundra]

cool

[mystic saffron]

I got one more question

[mighty tundra]

go on

[mystic saffron]

give me 5 min to ask it

[mighty tundra]

lmao

[mystic saffron]

its just im tryna think of it mself

gimme 5 tho

brb

[mighty tundra]

ill just check back at 37

[mystic saffron]

alr sure

[mighty tundra]

ok

[mystic saffron]

It's 3 right?

cancel out the x's

[mighty tundra]

hm

gimme a moment

[mystic saffron]

alr

[mighty tundra]

oh yea yea

it is

lmao i had to understand the question

coz it said it was continuous

[mystic saffron]

yea

[mighty tundra]

you gotta understand tho

u cant just cancel out the x's

[mystic saffron]

Create a new function

and use it to compare the limit

[mighty tundra]

?

[mystic saffron]

ye khan academy explained

bc for 0 it would not work then

Unless im being stupid

yea just explain

im being dumm

[mighty tundra]

yea yea

ur right

[mystic saffron]

ayee

finally

what math lvl are u

taking rn

[mighty tundra]

oh

im from aus

and im doing year 12 ext1 math

for my hsc

so far

but im in year 11

wbu?

[mystic saffron]

wait

your year 11

Im going into year 12

[mighty tundra]

yep

r u in year 12 yet? or is ur school year starting

[mystic saffron]

not in year 12 yet

[mighty tundra]

oh ok ok

[mystic saffron]

in september starts

[mighty tundra]

thats cool

[mystic saffron]

why do aussies have school rn?

[mighty tundra]

we start school at the end of january

finish in mid december

[mystic saffron]

wtf

So u guys get no break

[mighty tundra]

hey i thought september was weird

[mystic saffron]

Just 2 week break

[mighty tundra]

4 week

[mystic saffron]

6 week*

[mighty tundra]

more like 4 week

[shut wedge]

AYO

[mystic saffron]

thats terrible\

[shut wedge]

AUSSIE?

[mighty tundra]

yeah

[mighty tundra]

nah its fine with me

[shut wedge]

its pre neat

[mighty tundra]

wbu

[shut wedge]

i am

very aussie

oo

same grade too

gl on your prelim finals coming up

gl on trials if you had accelerated subjects

[mystic saffron]

wow

u guys r good

[mighty tundra]

ayyy thanks bro

[shut wedge]

thanks, but if i were good, i wouldnt be waiting for an hour for my q to be answered lol

[mighty tundra]

i already did an accelerated course in year 10

band 6d it 😎

[shut wedge]

shEESH

[mystic saffron]

[mighty tundra]

lol

[shut wedge]

man, its easier for me to just remember graphs rather than actually solve them

[mystic saffron]

oh

[shut wedge]

Lmao

wait

im loopy

[mighty tundra]

fr tho

just remember the graph transformation

s

[mystic saffron]

can u snd a pic of it

thje transofmraitons

the ones i should know at leas

tr

[mighty tundra]

wait for which question

also graph transformations is like a concept

[mystic saffron]

this

[mighty tundra]

so like do you want me to send you the graph?

[mystic saffron]

ye

[mighty tundra]

i dont think you need to graph that

[shut wedge]

theres def an algebra way

im just loopy rn tho

[mystic saffron]

what does that mean

Ive never heard a single person in my life say that 😭

[shut wedge]

loopy?

[mystic saffron]

eyah

loopy

[shut wedge]

how would you describe loopy

uh

confused but in a mind blank way

[mystic saffron]

is that your favourite word or colour

Ah

makes sense

do u know where im from

guess

[shut wedge]

uh

i really dont know

[mystic saffron]

GUESSS

[mighty tundra]

america

[shut wedge]

idk you give off kiwi but not kiwi vibes

[mystic saffron]

what does kiwi mean

im american

[shut wedge]

nvm

[mystic saffron]

new york babyyy

[shut wedge]

i aint ever heard an american call australians aussies

ig its also too late for nz to be up tho

[mighty tundra]

lmao i knew it

[mighty tundra]

wait fr tho

[shut wedge]

yea that threw me off

[mighty tundra]

🤣

[odd edge]

@mystic saffron Has your question been resolved?

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[loud grotto]

i feel crazy for thinking its every option

[odd edge]

@loud grotto Has your question been resolved?

[loud grotto]

<@&286206848099549185> am i right?

[nimble blaze]

show your work

[lapis lynx]

lemme solve it for u

[nimble blaze]

!nosols

[odd edge]

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.

[lapis lynx]

y = 4 cos x - cos x sin x

when u see questions with both sin and cos i like to look to factorise and square so that y= cosx(4-sinx) = 3, and squaring it would give 9= cos^2x( 16 -8sin(x) +sin^2(x)), now rewrite it using trig identity pythag so that 9= (1-sin^2x)(sin^2x-8sinx +16)

then expand it through to get sin^x -8sinx+16 -sin^4x -8sin^3x +16sin^2x = 9

simplify that to get -4sin^4x -8sin^3x +17sin^2x -8sinx +7=0

let sinx= u

so -4u^4 -8u^3 +17u^2 -8u +7 = 0

solve for u any way u like

then solve for x

[loud grotto]

oh

okay one sec let me try

5.132 ans 0.9 were wrong

[odd edge]

@loud grotto Has your question been resolved?

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[alpine jetty]

Just need help with these two

[lusty helm]

where are you facing difficulties here?

[lusty helm]

anyways to answer it, since it's a type jump discontinuities, it would DNE

[alpine jetty]

I just wanted to double check sorry

[lusty helm]

what answer are you getting though

[lusty helm]

DNE = Doesn't Exists

[alpine jetty]

For the first one 2 and second one 6'

[lusty helm]

wait

lemme help you conceptually

as you can see, the first graph is similar to it

[alpine jetty]

Ohhhh gotcha

[lusty helm]

btw isn't it x=4?

the points says otherwise?

[alpine jetty]

So would it be 4 or dne?

[lusty helm]

DNE

[alpine jetty]

Ok gotcha

.close

[odd edge]

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Use .reopen if this was a mistake.

[alpine jetty]

Thank you!

[wanton fossil]

First one ans is DNE but second question's ans is not the same

for limit to exist we have to see LHL(left hand limit) and RHL(Right hand limit) if they are equal then the limit exist

[alpine jetty]

Orginally I got 2 for that

[wanton fossil]

yea that is correct for second one👍

[alpine jetty]

Thank you!

[odd edge]

Available help channel!

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[mystic saffron]

why is product of 2 negative integers positive? interview question A-level science in top national school

[mystic saffron]

a interview question i got asked

[ember oar]

was it a job interview?

[mystic saffron]

A level admission interview (Science)

why is product of 2 negative integers positive?

[ember oar]

i was going to give you some sort of philosophical explanation, mb

[wooden hemlock]

I saw this funny explanantion in a vid
you turn around, you turn around again, OH I am facing the same way

[mystic saffron]

lol

[fervent hawk]

interesting interview question, what did you answer btw?

[ember oar]

i think that turning thing applies a lot to complex numbers and argand diagrams

[maiden inlet]

It is one of the laws of negative integers

[mystic saffron]

i just said i dont know

[ember oar]

its so over

[wooden hemlock]

how so?

[fervent hawk]

ah...

[mystic saffron]

they wouldnot accept this kind of answer

i was only suppsed to give proper reason

[maiden inlet]

So they are looking for a creative example

[wooden hemlock]

should have just became the inspirational speaker podcast

[wooden hemlock]

what is the proper answer ??/

[mystic saffron]

idk

[maiden inlet]

Have a bunch of interesting examples

[mystic saffron]

thats why i am asking

[maiden inlet]

For the interview

[wooden hemlock]

it's a property, what more do you WANT

[mystic saffron]

like?

[ember oar]

multiplying by -1 rotates something on an argand diagram by 180 degrees

[maiden inlet]

Examples of negative multiplied by negative becoming positive

[mystic saffron]

who and how did that person proved this property?????

[wooden hemlock]

ah, rotation, got it

[maiden inlet]

U can find many by googling I believe

Just get some interesting examples and explain it in a good way

[lusty helm]

you are basically multiplying positives with minus signs with them

[wooden hemlock]

oh god, now even I wanna know the history of -1💀

[maiden inlet]

Thats what they are looking for prob

[ember oar]

just pray your other responses were good boski

[mystic saffron]

interview question 💀

[maiden inlet]

U can use complex and interesting examples and simple ones that anyone can instantly understand

A mixture of both

[mystic saffron]

so which one is the best?

[maiden inlet]

Examples of easy can be a little nonsensical

[lusty helm]

uh, do you want mathematical proof?

[maiden inlet]

like a plus is made of 2 minus signs

joined together

[wooden hemlock]

nice-

[maiden inlet]

And when u rotate the plus

[mystic saffron]

that can work but short once cuz its interview

[maiden inlet]

Its a times

[fervent hawk]

well, there are quite a few explanations for this question,
the one i would use in such situation is "to treat - as opposite direction to +" approach

[maiden inlet]

lol

[wooden hemlock]

I don't think a complex number would cut it, we need an explanation that is simple for a normal person but complex enough for an interviewer

[mystic saffron]

true true

[wooden hemlock]

you can give an example of the english lanuage

language*

like in that picture

[mystic saffron]

like?

bro no

[wooden hemlock]

why tho

it is good-

[mystic saffron]

reasoning scientific or mathematical

[wooden hemlock]

simple enough

[wooden hemlock]

gosh-

[mystic saffron]

its just not any school its the one of best in hole nation

all teachers are expert

[wooden hemlock]

fair enough then

[maiden inlet]

Just testing ur creativity

[mystic saffron]

so i should tell like -1 rotates 180 again -1 rotates 180?

[wooden hemlock]

I guess

[maiden inlet]

Use more than one example

[mystic saffron]

this?

[late dust]

You can easily justify it by using multiplication as repeated addition...

[wooden hemlock]

english example, you said, it won't cut it

[mystic saffron]

...

[ember oar]

argand diagram rotation would probably be your best option

[mystic saffron]

probably

/stop

¯_(ツ)_/¯

[uneven osprey]

!done

[odd edge]

If you are done with this channel, please mark your problem as solved by typing .close

[mystic saffron]

.close

[odd edge]

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[odd edge]

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[digital cedar]

hi so i was solving this into REF form and I got stuck does that mean it is inconsistent?

how/what should tell me when im doing Gauss elimination that its inconsistent?

[late dust]

When you get something like 0 = not 0

[digital cedar]

so i should be able to put it into ref?

[late dust]

Yes you can always do that

[digital cedar]

ok

.close

[odd edge]

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[late dust]

(here it's fairly easy to see btw, add twice the first equation to the second, you get 4a + 8b +4c = 8, which is inconsistant with the third equation)

[odd edge]

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[alpine jetty]

Anyone know the answer to this?

[uneven osprey]

!noans

[odd edge]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[alpine jetty]

I keep getting a negative

[tacit wasp]

Do you know implicit differentiation?

[alpine jetty]

I keep getting -y/x-3y^2

[uneven osprey]

Through negative sign in denominator

[late dust]

You're correct, you just need to move the signs around

[alpine jetty]

in that case y/x-3y^2?

[late dust]

No

$\frac{-a}{b} = \frac{a}{-b}$

[clever fjord]

Nel

[alpine jetty]

so b?

[alpine jetty]

I just started this today and im doing practice problems

.close

[odd edge]

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[odd edge]

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• Show your work, and if possible, explain where you are stuck.
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[fresh sphinx]

can someone help me start this question please

[ivory dock]

Start by throwing a large brick at your teacher for posing a question like this

[fresh sphinx]

real

[ivory dock]

like, my guy wants you to find the sum of a series that may not converge

[fresh sphinx]

well i assume the first step is to turn it into a series

[leaden karma]

It does

[fresh sphinx]

is it supposed to be geometric

[leaden karma]

But yeah this sum looks not good

Try writing the general term first

[mystic saffron]

fr

[ivory dock]

Can you prove that it does?

[mystic saffron]

general term

[fresh sphinx]

i hate these assignments

[leaden karma]

||Alternating series test||

[fresh sphinx]

ok i will be right back

[fervent relic]

$\sum_{0}^{+\infty} \frac{1}{(2n+1)\sqrt{3}^{2n+1}}$ if you take $f(x) = \sum_{0}^{+\infty}x^{n}$ you may try to work on $f(x)+f(-x)$ and derivate

[clever fjord]

cjg#1618

[fresh sphinx]

what the hell

[fervent relic]

you can sum two derivatives of geometric series

[lusty helm]

that's the general form of series

[fresh sphinx]

oh

[leaden karma]

I think that isn’t necessary

[fresh sphinx]

i was just about to get there

[leaden karma]

just write each term as an integral

And bring the summation sign inside the integral

[lusty helm]

ps: it has alternate +-

[fervent relic]

Oh

[lusty helm]

wait I have better method

[leaden karma]

$\sum_{r=0}^\infty\frac{(-1)^r\left(\frac1{\sqrt{3}}\right)^{2r+1}}{(2r+1)}$

[lusty helm]

NVM won't work on this ques

[leaden karma]

Write the inner term as an integral

[fresh sphinx]

like the whole expression after the sigma?

[leaden karma]

Hint: notice the 2r+1 part common to the exponent and the denominator

[leaden karma]

Part of it

[fresh sphinx]

hmm what part shold i write

[leaden karma]

The (-1)^r doesn’t really matter that much, so you can keep it separate for now

[fresh sphinx]

alright

[fresh sphinx]

yesah

also how come you just moved the sqrt3 expression to the numerator

[leaden karma]

That was supposed to be 1/sqrt3

[fresh sphinx]

are you missing 3 in the denominator or

oh ok

[clever fjord]

kheerii

[fresh sphinx]

yeah

and then you just integrate it ?

[leaden karma]

Can you think of some integral relating to this?

[leaden karma]

Not exactly

You don’t integrate this, rather you write the inner function as an integral of some other function

[fresh sphinx]

not sure

[leaden karma]

What is $\int_0^x t^{2r}\dd{t}$

[clever fjord]

kheerii

[fresh sphinx]

holy ive forgotten the ftc

idk 💀

[leaden karma]

Hmm..

Do you remember the reverse power rule?

[dawn tiger]

am i tripping or is this just arctan

[fresh sphinx]

as in the power rule for integrateion?

[leaden karma]

It is yes

Shhh

[leaden karma]

Yes

[fresh sphinx]

yeah

[leaden karma]

So use it here

[fresh sphinx]

(t^2r+1)/2r+1?

or x instead of t?

[leaden karma]

Yes

[leaden karma]

Does that ring a bell here?

[fresh sphinx]

is that just the integral of (1/sqrt3)^2r

[leaden karma]

Not quite.

But close

Kind of

1/sqrt3 isn’t a variable remember

It’s a value

[fresh sphinx]

(1/3)^r?

[leaden karma]

Again, 1/3 isn’t a variable

[mystic saffron]

wont make any difference

[leaden karma]

You just rewrote the same expression

[fresh sphinx]

idk then

[leaden karma]

What value of x do you wish to place here?

To get the expression you have in your sum

[fresh sphinx]

dont know 😔

sorry

[leaden karma]

Try placing x=1/sqrt3

[fresh sphinx]

oh

[mystic saffron]

think bout def. int

[fresh sphinx]

so its just integrating x^2r?

[leaden karma]

Yes, but in what limits?

[fresh sphinx]

from 0 to inf? or 0 to 1/sqrt3 or something else

[leaden karma]

Tell me one answer.

Not multiple

Think about it

[fresh sphinx]

is it the first one

[leaden karma]

0 to infinity?

[fresh sphinx]

yeah

[leaden karma]

No

[leaden karma]

Think about this again

Placing what value of x lead you to the correct expression that you wanted

[mystic saffron]

are you familiar with def int ?

[fresh sphinx]

1/sqrt3?

[mystic saffron]

as of now, forget about sigma notations and its limits

[fresh sphinx]

like definition of an integral?

[leaden karma]

Yes

[leaden karma]

Definite integrals

[mystic saffron]

nvm, just listen to kheerii

[fresh sphinx]

yeah

[leaden karma]

Okay

Do you agree that $$\int_0^\frac1{\sqrt{3}}t^{2r}\dd{t}=\frac{\left(\frac1{\sqrt{3}}\right)^{2r+1}}{2r+1}$$

[clever fjord]

kheerii

[fresh sphinx]

yes

thats just evaluating the upper bound right and the bottom bound is just 0

[leaden karma]

Do you see that exact same expression here in the sum?

[fresh sphinx]

yeah

just with the alternating series

[leaden karma]

Yes

So can you place the integral inside the sum?

Replacing that expression with the integral

[fresh sphinx]

uhh im not sure if im familiar with placing an integral within the sigma?

we learned how to evlauate integrals with summations

if thats what youre referring to

[leaden karma]

You mean converting a summation to a definite integral?

[mystic saffron]

Riemann Sum as a Definite Integral ig

[fresh sphinx]

we did learn that yes though i did forget a little

[leaden karma]

No, that’s not what we’re doing here

[mystic saffron]

no limits tho

[fresh sphinx]

oh

[leaden karma]

Hmm, I don’t really know of another method of solving the question..

[fresh sphinx]

no, i think youre right with that being the method

[leaden karma]

Unless you’re given the series expansion of arctan(x) which this directly is

[fresh sphinx]

im just a little slow because i dont think weve covered this in class yet

it might be the next lesson or something

but if youre willing to help me still id be happy to work through it

theres another question in the assignment which tells you to do what youre saying i think

[leaden karma]

This is the reverse process of what I want you to do in the previous question

[mystic saffron]

@leaden karma can you tell in short what to do after placing the integral ?

[leaden karma]

Here you write out the series of arcran first and then integrate each term by term

Although if they’ve given you this question it means you should know the series of arctan(x) which makes the previous problem trivial..

[fresh sphinx]

wait we do lol

sorry it didnt occur to me

[leaden karma]

Take the summation inside the integral (this step needs to be justified using something called the Tonelli theorem I believe but it’s good enough here)
Then the sum you’ll get will be a simple GP which you can do
Then just integrate

[mystic saffron]

with expansion its quite clear, tan^-1 1/root3

[fresh sphinx]

so basically the sum is just arctanx just replace x with 1/sqrt3

so pi/6

[leaden karma]

Yes

I thought you were not given this

[fresh sphinx]

we werent given it in the assignment

[leaden karma]

The method I was describing is actually how you derive the series expansion of arctan(x)

[fresh sphinx]

but we did briefly cover the series of arctanx in a lecture

[leaden karma]

If you know the series you can recognise it immediately like Neil did here

[fresh sphinx]

yeah, this is all really new so i didnt recognize it

[leaden karma]

Don’t worry about it

[mystic saffron]

basically this only, found on internet

[fresh sphinx]

but the expectation is that you have important series like sin cos arctan and e^x memorized for exam

[mystic saffron]

thanks

[leaden karma]

Not sure why you made it 2x there at the end but yeah

[leaden karma]

They are all pretty easily identifiable if you notice the patterns in them

So shouldn’t be too bad

[fresh sphinx]

yeah i agree

[leaden karma]

also you need to make sure when this series even converges

[fresh sphinx]

we learned it yesterday so i dont know them too well yet

but this was really helpful so tysm

[mystic saffron]

[leaden karma]

You’ll get the hang of it

[fresh sphinx]

i think in my solution ill just convert it to this series and then show the similarities with the series of arctanx and replace x with 1/sqrt3

that should be enough i think

[leaden karma]

Yeah

That works

,w convergence of series of arctan(x)

[clever fjord]

Results provided by WolframAlpha

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

Requested by shikhargupta1207

[mystic saffron]

uh

[leaden karma]

This was not what I wanted

Thanks a lot wolframalpha

[mystic saffron]

tf

[leaden karma]

But I’m pretty sure it’ll converge for |x|<1

You’ll need to check x=1 and x=-1 separately and see if the series converge there

I think they would

[fresh sphinx]

hmm just check with ratio test or

[leaden karma]

And since 1/sqrt3 lies in between (-1,1) the series converges

[leaden karma]

Just alternating series test should be fine

[fresh sphinx]

oh right lol

ok tysm

.close

[odd edge]

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[leaden karma]

Honestly you should still try to do the sum with the integral

It’s a pretty cool method

[fresh sphinx]

like do that instead of direct comparison with arctan?

[leaden karma]

I’ll give you some hints: replace the expression we got with the corresponding integral, bring the summation and the (-1)^r part inside the integral, solve the series you get inside the integral (which should be much easier, as it should be a geometric series) and then integrate the final function you get from the series between the chosen bounds

[leaden karma]

Yes

Just for practice

[fresh sphinx]

ok i will try

[odd edge]

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[loud grotto]

is this correct?

[lusty helm]

yea

[loud grotto]

yayy

thanks

.close

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[plush nest]

I need help with this

[plush nest]

ive been having trouble with it since yesturday

i just cant do annuities

[royal herald]

whatve u tried

@plush nest

[plush nest]

someone suggested i use this formula but when i did the answer was wrong

[royal herald]

well thats for a singular cash flow

u have a series of level payments

the formula is this

the last line

then multiply that by ur payment amount to get ur accumulated value

[plush nest]

alright

[royal herald]

but notice its a monthly payment, that means u have to convert ur annual effective interest rate into a monthly effective interest rate

[plush nest]

i got 1547.66

[royal herald]

what was ur monthly effective rate

[plush nest]

uhh lemme see

0.004679?

[royal herald]

dont round

use the whole decimal

0.004669839

[plush nest]

ooh ok

now what

[royal herald]

well whatd u get

[plush nest]

1511.75

[royal herald]

im not getting the same answer

are u sure ur plugging it in correctly

[plush nest]

probably not

can you show me the steps you did

[royal herald]

i didnt do any steps i just plugged into calc

[plush nest]

ok im gonn redo

1514.13?

im gonna double check

ya im stuck

[royal herald]

type out exactly what ur putting into the calc

[plush nest]

i calculated (1 + I)n and got (1+0.004791667)12 = 1.057720

then i calculated the fraction

[royal herald]

0.004791667 is the issue

thats not exactly the monthly effective rate

[royal herald]

its this

[plush nest]

i got 1530.00 then

[royal herald]

$\frac {(1+0.004669839)^{12} - 1}{0.004669839}$

[royal herald]

,calc 1.004669839^12

[clever fjord]

Result:

1.0574999974733

[royal herald]

,calc 0.0574999974733/0.004669839

[clever fjord]

Result:

12.313057789209

[royal herald]

,calc 12.313057789209*125

[clever fjord]

Result:

1539.1322236511

[royal herald]

this is what im getting

idk how ur getting what ur getting

[plush nest]

i accidentally left my calculator at home, that's honestly mainly the reason why its just not working

im just using a online calculato

[royal herald]

ok

[plush nest]

is this meant to be the answer

[royal herald]

idk , u tell me

what do u think

[plush nest]

probably

idk

i wasnt built for math

[odd edge]

@plush nest Has your question been resolved?

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[odd edge]

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[silent jay]

is this correct for #9? I feel like i made a mistake somewhere

[mint mirage]

Didn't you get your answers checked in a different channel already?

[wraith torrent]

does the problem require you to give complex solutions?

[silent jay]

yes but the person helping said yes to my original answer which was wrong then also said yes to my updated answer so I just wanted to get it checked again just to make sure

[silent jay]

im not sure thats all the information i am given

[mint mirage]

You used an online calculator to get your answers, right?

[wraith torrent]

have you learned complex numbers

[mint mirage]

Those were the answers

[silent jay]

yes

[silent jay]

yea quadratic formula

[wraith torrent]

well then it's not easy to say whether you need to write complex solutions or not

[mint mirage]

#help-9 message
Those were correct, plus the original one solution you had

[silent jay]

idk tho cuz this is a new teacher I never met before

[wraith torrent]

maybe ask them? is that possible?

[silent jay]

okay thanks

[silent jay]

ig i could send an email

i think ill just do it with complex solutions though

[mint mirage]

It does say solve the equations by factoring so complex solutions are valid

[silent jay]

Also is this correct for #10? I feel like I made another mistake here 😭

[odd edge]

@silent jay Has your question been resolved?

[odd edge]

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[polar hazel]

how would you solve for X here

[hardy panther]

Use a substitution

w = ln(x)

[ln(x)]^3 = ln(x^3)
[ln(x)]^3 = 3ln(x)
[ln(x)]^3 - 3ln(x) = 0
w^3 - 3w = 0
w(w^2 - 3) = 0
w = 0 or w = +-sqrt(3)
--> ln(x) = 0 or ln(x) = +- sqrt(3)
So then
x = 1 or x = e^sqrt(3) or e^[-sqrt(3)]

Hmm, I'm missing one

Oh

Got it

[odd edge]

@polar hazel Has your question been resolved?

[polar hazel]

how did you get 1

ln(x) = 0 is 1?

[odd edge]

@polar hazel Has your question been resolved?

[strange epoch]

Yes because ln(1) =0

[odd edge]

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[calm cobalt]

is this correct

[minor crypt]

yups

[odd edge]

@calm cobalt Has your question been resolved?

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[fervent oar]

Need help with this

[fervent oar]

I got to a final series which is the sum from 1 to infinity of (1 + 12 + 123 + 1234 + 12345... + n^2/2 - n/2 + 1)/11^n but not sure how to compute it as the 1 + 12 + 123... part is recursive and I'm not entirely sure if it's right. Thanks.

[tepid acorn]

Is that Mathdash :0

[fervent oar]

yep

[fervent oar]

yoo wait youre in the comp too, did you get this one?

[tepid acorn]

Probably not…

[fervent oar]

yeah thats okay nobody in the standings did lmao

[tepid acorn]

But how do you know this…

[fervent oar]

we have the server in common

[tepid acorn]

I don’t see it in our mutual servers list for whatever reason

[fervent oar]

shows up for me

[fervent oar]

<@&286206848099549185>

[uneven osprey]

btw, here why did you wrote that nth term like that?

ig it doesn't work

[fervent oar]

for what? the quadratic seq?

or a_n entirely

[uneven osprey]

here n^2/2 - n/2 + 1

[fervent oar]

yea thats cuz the number of times 1 is being added in each string increases 1, 2, 4, 7, 11 like a quad seq

[tepid acorn]

Is this from considering ending strings of ‘1’ of length n

[fervent oar]

and thats being added to a pattern of 1 + 1, 11 + 1, 111 + 11 + 1, 1111 + 111 + 11 + 1

[fervent oar]

so i seperated both these sequences, this one being rescursive and the other being quadratic

[fervent oar]

yup

[tepid acorn]

I mean you could write 111..1 = (10^n-1)/9 and try to bash out an answer

[fervent oar]

idk to what extent that wld work tbh, did cross my mind but didnt think it'd work

cuz idk how youd sum that for this pattern

[tepid acorn]

It would be easier to sum over each 11…1 individually

Like the sum of [all ‘1’ in the series] + sum of [all ‘11’ in the series] + …

[fervent oar]

dont quite get this because the sum itself would diverge

[tepid acorn]

So it becomes an arithmetic geometric series, I think, then should be solvable

[fervent oar]

so we need to find a general a_n to divide by 11^n

no?

[tepid acorn]

I mean 1/11 + (1+1)/121 + (1+1+1)/1331… + 11/121 + (11+11)/1331 +…

Splitting up a_n as 1n + 11(n-1) + … and summing each of the ‘1’, ‘11’, etc. individually

[fervent oar]

hmm but the strings of 1 would just keep going

so how would you evaluate the sum

1, 11, 111, 1111, 11111...

[tepid acorn]

Yeah but find a closed form for n-long strings of 1

[fervent oar]

is there where this could come in maybe

[tepid acorn]

Yes

[fervent oar]

hmmm

ight lemme try it thanks @tepid acorn

[tepid acorn]

Also there’s probably a genfunc solution

[fervent oar]

yea thats what i was tryna do

[tepid acorn]

Yeah but then I realized it’s probably really hard 😭

[fervent oar]

yea i tried this and im not getting the ans, everything i do leads to a divergent sum so im probably doing something wrong, can you try?

i keep getting S = 0.11 * sum from n=0 to infinity of (11^(n + 1) - 1)/10

[tepid acorn]

Ok, I also noticed that a_n = a_n-1 + 10(a_n-1 - a_n-2) + n

For the complicated expression

So you should be able to get a relatively simple closed form from that

[tepid acorn]

I’m literally in bed on mobile (12:52 ET), I’m sleeping right after this bye

[fervent oar]

yea that was my original question

its recursive

so how would you find the sum

[fervent oar]

i expressed the 1 + 12 + 123... part recursively

and the rest as a quadratic

[tepid acorn]

Get the explicit formula

Then, just use that

I’m gonna sleep now bye

[fervent oar]

<@&286206848099549185> hey can anybody available help please?

[odd edge]

@fervent oar Has your question been resolved?

[fervent oar]

<@&286206848099549185>

[odd edge]

@fervent oar Has your question been resolved?

[odd edge]

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[sharp crane]

Can someone help me with the following problem ?

[sharp crane]

I have tried the trigonometric identity

$1+tan(\theta)^2=frac{1}{cos(\theta)^2}$

[clever fjord]

Kidpreneur

[minor crypt]

i love frac1cos^2

anyways

what do u think of 1+cot^2x

[sharp crane]

What do you mean ?

[minor crypt]

what is it equal to

there is one clever lil identity

[sharp crane]

1/sin^2 ?

[minor crypt]

nopes

yes actually

u r correct

[sharp crane]

Ok.

[minor crypt]

now put that thru a square root

what is it

[sharp crane]

sqrt(1+cot^2)=sqrt(cosec^2)

[sharp crane]

But we need cos not cosec ?

[minor crypt]

think about it real hard

cot A = ?

in terms of cos and sin

[sharp crane]

cos/sin

[minor crypt]

now cot A / csc A

what is that

[sharp crane]

cos

[minor crypt]

good job

which option corresponds to that

[sharp crane]

2nd ?

[minor crypt]

yups

[sharp crane]

bruh

Is their another way of solving

[minor crypt]

no

u use identities

[sharp crane]

So whats the working out ?

[minor crypt]

first use this identity

[sharp crane]

ok

[minor crypt]

then √(csc^2x) = cscx

correct?

[sharp crane]

ok

[minor crypt]

then we get cotx/cscx

then we simplify

[sharp crane]

so we get cos ?

then after that ?

[minor crypt]

yes

cotx/cscx = (cosx/sinx) * sinx

correct?

sinx cancels out

[sharp crane]

yup

ook

.close

[odd edge]

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[odd edge]

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[quick needle]

tips on how to approach this Q?

for DSA comp sci class

[leaden karma]

2^ log log n and log n! should be easy to compare

So are log log n and 2^log log n

The only problem is the n^(1/log n)

[long tinsel]

you can just kind of guess tbh

[leaden karma]

Take the log of all of them

Then it should be much clearer

[long tinsel]

also n^(1/log n) is just e?

[leaden karma]

Yeah lol

[long tinsel]

then it's done

[leaden karma]

First one is just O(1)

[quick needle]

wot

so just guess and checking?

is there no more systematic wya?

[leaden karma]

I told you, take the log

Of all of them

[sharp oak]

We didn't guess and check. Are there any two comparisons you are confused about?

[quick needle]

isn't double expionential n^n the fastest growibng

faster than n!

[leaden karma]

$\log\log\log n, \log\log n!, \log 2\log\log n, 1$

[clever fjord]

kheerii

[leaden karma]

These are the things you get after taking the log

comparison should be pretty easy from this

[leaden karma]

It should be yeah

[quick needle]

typo here?

[leaden karma]

That’s just the question right

What’s the answer

[quick needle]

yeah ur ruight

omg im trolilng

xD

[leaden karma]

$\sqrt{n}, n, n\log n, n^3, 2^n, \frac{3^n}{n^2}, n!, n^n$

[quick needle]

so take log again here it seems?

[clever fjord]

kheerii

[leaden karma]

Yeah nice

[quick needle]

since i can take adcvantage of log laws

[leaden karma]

You can

But again

A lot of these are pretty obvious

[quick needle]

yeah

[leaden karma]

the polynomial functions are obviously less than the exponential ones

nlogn < n^3

because

log n < n < n^2

2^n < 3^n/n^2 because the latter is basically just 3^n

[quick needle]

yuss

thanks!

[leaden karma]

and factorial is larger than exponentials

the only one you need to worry about is n! < n^n

[quick needle]

huh?

by L'Hpopital's?

[odd edge]

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[elfin bear]

whats [k]

[low locust]

{1,...,k}

I would guess

but the notation as a whole doesnt make a lot of sense

the a_k at the end being all alone

its weird to require that lambda * i is in [k], that is probably a mistake

[elfin bear]

thank you, i understand now

they made an inverseable function

.close

[odd edge]

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[odd edge]

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[rough grail]

Help

[rough grail]

How do i do polyonomial interpolation

polynomial

like this

and maybe some help on linear algebra

and maybe some examples on what polynomial interpolation can be used for

<@&286206848099549185>

[odd edge]

@rough grail Has your question been resolved?

[rough grail]

No

[runic swift]

what help do you need with this

[rough grail]

How i can solve/ use

polynomial interpolation

[runic swift]

use it when you have a table of x and y values and you want to find another y value given another x value not in the tables

[rough grail]

also

how could i use linear algebra

[runic swift]

for?

[odd edge]

@rough grail Has your question been resolved?

[rough grail]

anything

[runic swift]

i mean you can use it for a lot of things

solve linear equations

vector spaces and many more

[rough grail]

do you know game development

math?

[runic swift]

not really

only messed around in unity for like 3 days

[odd edge]

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