math-help

[left knoll]

just for the derivative?, then no

@gritty cloud

there

diff using chain rule

[supple island]

i think he's supposed to do it with the limit

[left knoll]

like using first principles?

that makes sense

@supple island do u want to explain it or should i

up to u

[gritty cloud]

Yes

[left knoll]

k

[gritty cloud]

Guys im stuck with it for 4 hours now

lol

[left knoll]

so basically, this is called first principles and sub in the values in to the limit function

so f'(x) = f(x+h)-f(x)/h

(x-4+h)-(x-4)/h

[gritty cloud]

Yes

[left knoll]

yea im just checking for mistakes then will continue

[gritty cloud]

Good i appreciate your effort

[left knoll]

ok

so then its h/h

[supple island]

there's a cubic root

[gritty cloud]

Yes

That is the problem for me

[left knoll]

i knew i missed something

ty

[supple island]

imagine u=x+4, then do f'(u)

[left knoll]

cant read smh

[supple island]

so you have f'(u)=crt(u+h)-crt(u)/h

now multiply and divide by (u+h)^2/3+(u)^2/3

there you go

then do the limit for h->0

[left knoll]

yea prty much

do u get it @gritty cloud

?

[gritty cloud]

To remove the root right?

[supple island]

that's the idea

[gritty cloud]

Yes sir thank you very much🌹🌹

[gritty cloud]

You too🌹

[supple island]

np

[gritty cloud]

Im a physics student but i hate math 😂😂

[gritty cloud]

Not so much i mean i love over subjects more

[left knoll]

i have a q for you guys

if we use t formula for cos2x or sin2x (lets take sin2x), and we let t = tanx, would sin2x = 2t/1+t^2 still?

i ask in regards to this q

[zenith dock]

i don't see why not

[left knoll]

can someone help me please

[left knoll]

can someone help me ?

for 6 balls we pay 48 dollars.
how many dollars would it be if there would be 15 of those balls ?

[ember kernel]

How many dollars is worth one ball ?

[left knoll]

um i have no idea o.o,
they didn't tell me that in the question and if you're asking me, i don't know

oh nvm, it's 8 dollars

[ember kernel]

No you have to answer my question, it's a step towards the answer

[ember kernel]

Yup, so how much are 15 of them (knowing that each one is 8 dollars)

[left knoll]

we will do 15 × 8 ? i suppose which will be 120 dollars o.o
is that correct ?

[ember kernel]

Yup it is

[left knoll]

<@&717391911132069929>

[high karma]

Help!!

[left knoll]

can anyone solve this pls

@left knoll

[vapid gorge]

can someone pls help

thanks

[left knoll]

@left knoll

F' means not face

@vapid gorge

there

also i just realised i spelt denominator incorrectly for the explanation at the bottom

my apologies

[zenith dock]

don't really have the time to do it now but i think it's solvable by using this property:

a lot of the stuff simplifies and i think you can take it from there : )

treat A from the above property as a in the task and B as (b-c) and then apply it

i might be wrong but i'm fairly confident it should do the trick

oh just noticed its solved already, nvm

[cinder heath]

infinite series

to find whether series is convergent or divergent

[sullen verge]

what is p?

[cinder heath]

have to solve in terms of p

[random flame]

Hey can someone help me with Q4? Ping me if you do and thanks in advance!!

[cyan night]

take the derivative and set it = 0, which is the extrema

and then plug x = -2 in and solve for a

[random flame]

So basically I have to find dy/dx then make it =0 cuz stationary point, then sub in x=-2?

[cyan night]

yes

[left knoll]

then isolate a @random flame

[random flame]

Ah okay thanks so much!!

Aight big thank

[cyan night]

then just solve for a

[random flame]

Lemme solve it and if I got problems I’ll come back

Thanks guys!!

[left knoll]

sorry for jumping in there my b

[cyan night]

gg

[random flame]

Issokay man HAHA

[left knoll]

my apologies @cyan night and @random flame

[cyan night]

uh lol np

[random flame]

Nah nah it’s fine

[left knoll]

gl man with ur q!

[cyan night]

also if you were wondering you set dy/dx to 0 because at a maximum point the slope of the tangent is 0

[random flame]

Woop now I’m stuck at Q5c qwq
I need to eat dinner now so gonna leave this here if anyone is available to help!! Ping me if you do, I’ll check later and thanks again :D

[supple island]

ok so, the question is very similar to q4 which you just done, i think you should study more the critical points of a function

because just giving you the method isn't enough for you to understand and do it alone during a test

[cyan night]

wait sorry @supple island but a cubic function if it has 2 extremas then is it a must that one is relative minimum one is relative maximum

intuitively i think that is the case

[supple island]

not necessarily

one could be an inflection point

[cyan night]

can you give me an example

[supple island]

y=x^3

[cyan night]

so like you are saying it can exist a cubic with 1 extrema and one point of inflexion?

im saying in the case it has 2 extremas

y = x^3 has no extremas

[left knoll]

i think under a defined domain it would have the extremas

but if u take it from -inf to inf then not really

i could be wrong tho

[cyan night]

oh yeah

so it has 2 extremas 1 point of inflexion

but

the 2 extremas must have different signs right

[left knoll]

not if the graph has been shifted up

then it could have same sign

same case if graph has been shifted down

[supple island]

i think he's saying that if there are 2 extremes, 1 must be a maximum and 1 must be a minimum

[cyan night]

yes

[left knoll]

i feel for these types of questions it is better to look at it from the perspective of the second derivative rather than looking at the graph wholistically

[supple island]

it depends, maybe the function isn't continuous

[cyan night]

cubics are continuous as they are polynomials

[supple island]

we can't just assume 2 critical points=a maximum and a minimum

[left knoll]

i think he is referring to cubics specifically

[supple island]

i don't think it's helpful to study cubics specifically

just study your function whatever it is

[left knoll]

neither do i which is why i proposed the second derivative method

[cyan night]

well we might be able to leverage it and use it in the problem

[supple island]

well even if you assume that there are a maximum and a minimum you ahve to say which is which

[cyan night]

we know from b)

[supple island]

so doing 2nd derivative is the correct way to do it

[cyan night]

yes i agree

[supple island]

well b) doesn't tell us, we have to find out

[cyan night]

i mean uh

after we find out we can determine the nature of the other

[supple island]

sure

[cyan night]

also

off topic but

[left knoll]

looking at the type of function has many flaws, if take the second derivative, no matter what we can find the nature of the stationary points no matter what. it is the most effective method

[left knoll]

go ahead

[cyan night]

how does root extraction when solving inequalities work

[left knoll]

what do you mean by root extraction?

[cyan night]

yesterday i was solving and i came up to 4 >= (x + sqrt 3*y)^2

i was required to find the min and max value of x + sqrt 3 y

(this isnt the problem but i arrived at it finally)

so how does taking the sqrt of both sides work

[left knoll]

as in with an inequalities problem?

[supple island]

can you send the whole text?

[cyan night]

you mean the entire problem?

[left knoll]

i agree, the q would be helpful

[cyan night]

its just a basic q but here:
Find the minimum and maximum value of A = x + (sqrt3)y known that x^2 + y^2 = 1

it was in a different language i just translated it

so uh i used bunyakovsky for the two sets (1, sqrt 3) and (x,y)

[left knoll]

what is bunyakovsky

[cyan night]

bunyakovsky inequality

cauchy-schwartz

[left knoll]

oh ok ok

my b

[cyan night]

so uh <=> (1^2 + sqrt3^2)(x^2+y^2)>= (x+ sqrt3 y)^2

which just means 4 >= (x+sqrt3 y)^2

im pretty sure the min is -2 and max is 2 after you extract the root

but im still uncertain

[left knoll]

i think ur correct

do u have a picture of ur working?

@cyan night

[cyan night]

uh not really

it was pretty short

but i can write it in paint

for u

is this what you need

[left knoll]

give me a second

to go through it

[cyan night]

kk

[left knoll]

i think ur right

unless i have missed something stupid

but min looks to be -2 and max to be 2

[cyan night]

but why

[left knoll]

because when u resolve the root on either side

[cyan night]

yeah

[left knoll]

it gives us +-2

[cyan night]

yes

[left knoll]

and the graph is positive

thus min is -2

and max +2

make sense?

[cyan night]

you took the 2nd derivative right

[left knoll]

yep

[cyan night]

so like

in my working

do i need to explain or elaborate on that

or can i just say

=> 2 >= x+ sqrt 3 y >= -2

[left knoll]

that statement should be sufficient

[cyan night]

i find it a bit not rigid enough

[left knoll]

but make sure to clearly show that u have taken 2nd derivative

[left knoll]

look u could always write a statement

[cyan night]

oh i cant do that im only in 8th grade they dont allow that 😅

[left knoll]

it doesnt hurt, but it depends on how much time u have in exam

[left knoll]

2nd derivative?

[cyan night]

yeah

[left knoll]

if ur doing bunyakovsky inequality

then 2nd derivative should be fine

?

[cyan night]

well bunyakovsky is in the extended curriculum of 8th grade in our country

but like the other countries calculus is only taught in high schol

[left knoll]

what country is it

if my asking is ok?

[cyan night]

i live in vietnam

[left knoll]

ok ok

well look

you could draw the graph

and prove it that way

but

do u really want to do that?

[cyan night]

uh not really

i think theres a general way i can use to justify it?

[left knoll]

go ahead

[cyan night]

hm can i make a table

the table of x+ sqrt 3y for -2 0 2

wait maybe not

[left knoll]

thats gonna take the same time as drawing the graph

no no u can

but

its inefficient

idk, 2nd derivative is the preferred method

just do it and maybe ur teacher will think ur a prodigy lmao

[supple island]

ok so this is a very cool method, unfortunately it doesn't actually tell you the extremes

[left knoll]

u understand it right?

[cyan night]

yes i do

[supple island]

also 2nd derivatives doesn't work here

[cyan night]

what do you mean

[left knoll]

how?

[cyan night]

it is 2 variables?

or do u do implicit

[left knoll]

u can do it with implicit

no?

i could be wrong

[cyan night]

im not sure

[left knoll]

that's how i did it

[supple island]

you are not required to find local extremes here

just extremes

[left knoll]

as in the global ones?

[supple island]

yep

but not actually global

[left knoll]

ahh ok ok that makes much more sense

yea yea i get what u mean

[cyan night]

[supple island]

you have to value the function in the circumference x^2+y^2=1

[left knoll]

mhmm

[supple island]

you have to think of it as the border of the intersection between the 2 functions

[cyan night]

uhh

[left knoll]

so we solve it by using the assumed intersection point correct?

which can be worked out by making them equal to each other?

tbh i have no clue why they are teaching an 8th grade student this

[cyan night]

x^2 + y^2 = x + sqrt 3 y?

[left knoll]

but @supple island go ahead

[cyan night]

its the extended program for more specialized students

[left knoll]

ahh so ur mr smarty pants

😁

im kidding

...

unless

U R

[cyan night]

uh

ok

[left knoll]

😯

i was curious since this is a big jump lmao

[cyan night]

what is smarty pants

[left knoll]

like ur smart

its an expression

[supple island]

no, not really, you have to think that you are using a=x+y^1/3 and you move along the circumference x²+y²=1

this is a problem that i could have been given in my 2nd year of university

[left knoll]

so we make them equal and find the intersection and use that to calculate the extremas?

[supple island]

uhh, you do a system

you should substitute

[left knoll]

?

[left knoll]

what i meant, my b. like we could sub in y after we solve for it correct?

or have i missed the mark completely

[supple island]

yeah but it is quite hard

perhaps there's a smarter method

[left knoll]

i figure, i thought we could just do it by implicit

but i was wrong

the hardest choices require the strongest wills

[cyan night]

ohh

@left knoll i just asked my teacher

so 4 >= (x+ sqrt3 y)^2

<=> 2 >= |x+sqrt 3y|

so x + sqrt3y is within the interval of -2 =< x + sqrt3 y =< 2

we can just say it like that

[left knoll]

ok ok i think i get it...

ty @cyan night

[random flame]

Oh- ;-;
I’m terrible at this and I’m having exam soon aaaaa-
It’s difficult to actually make time for revision cuz teachers give an extremely huge amount of hw every single day I just can’t sometimes-
But anyways thank you!!

[left knoll]

How can I get rid of maths anxiety? Do you guys have any tips?

[zenith dock]

what do you mean exactly by "maths anxiety"?

[left knoll]

I always get anxious when I try to study maths

[left knoll]

honestly, just starting always helps for me

countdown and just start doing something... just anything and the rest will follow

unless you get stuck on the first question you tackle which always sucks, but keep at it

the goal is to enjoy doing the difficult stuff so those moment after you get through the hard parts are always worth it

[zenith dock]

yeah, honestly starting is the hardest part, once you're doing it then it's easier

if you feel intimidated by long sessions, then you can try studying math in little increments, like 5-15 minutes, or less/more, as long as you feel comfortable

you can kinda trick your mind by doing these little increments to acknowledge that this isn't as scary as you might have thought

you also might be getting out of your comfort zone, and the only thing you can do to broaden the zone is to do stuff you're not comfortable with

i kinda get where you're coming from because i have chess anxiety and even though i like analyzing games, watching others play and doing puzzles my nerves get the best of me when i actually play

and if you get demotivated by being unable to tackle the first questions, then there are plenty of helpful people here that can explain it to you
if you understand the concept that drove the solution and are able to do the task by yourself after the explanation then you've just gained valuable experience that will help you once you encounter a similar assignment

it gets better, i used to completely suck at math in junior high but i studied tons (so now i suck less) and got a pretty nice exam score

[nova raft]

https://youtu.be/k6BpUmCY0D8

[minor sluice]

has anyone taken AP calculus BC?

if so whats the best way to prepare?

[minor sluice]

for ap exam

[analog stirrup]

Anyone good at calculus 2?

[left knoll]

practise qs do as many as possible

[left knoll]

what do u need help in

[left knoll]

how long are your study sessions for?

[left knoll]

is this a general q for everyone

i assume so

mine are 60/10

no like how many hours ?

[left knoll]

should I understand this ?

pomodoro

60 mins work

10 break

ooo i understand now I don't use any wwbsite for studying so noob in that area..

[left knoll]

i dont use a website, i use an app

called flow

good

[gritty cloud]

Hi guys

I want to turn these equations into text but im bad at this

I need someone to do this for me and i wish if there is a tutorial about that in youtube.

[ember kernel]

If you really want it all converted to text :
y is the square of the tangent of the sum of 4x and the sine of 4x

But that's not very legible

So I'd just say : "y is the tangent square of sin3x plus 4x"

[thorny flicker]

need help with this stats question

this is the given answer but i cant seem to get why i need to divide the variance by 15

[thick crow]

Because there are 15 competitors

[thorny flicker]

but why did the variance get divided?

ok my phrasing is bad there but i just dont get why dividing variance is needed to find the mean race time of the random sample?

like why not do it somewhere else

nvm this question is not supposed to be in my syllabus at all

[floral jungle]

Does someone need help with your math problems? I am using Gauthmath, it has LIVE tutors who will give answers and step-by-step explanations 24/7 for FREE. Here's my invitation code: KCGGJY.
https://s.mathme.xyz/lp/invite?code=KCGGJY

[ember kernel]

That sounds pretty much like this channel

[jaunty monolith]

hi guys

can someone help me solve this simultaneous equation

[echo silo]

y = -1/3 +2x/3

use this y in the first eq

and you get the x

[jaunty monolith]

oh ok thanks ❤️

[left knoll]

We can do this by middle term spliting ✅

By taking +1 in LHS and the applying middle term spliting

[zinc charm]

guys i need help

if sin 90 is 1

why is sin 180 not 2?

oh my fault g i forgor it was a circle

[jaunty monolith]

Hey guys sorry to disturb agitation but I was wondering if someone could help me with this question

It says find the range of cakes of k for which the equation 4x^2+12x+k=0 has no real roots

*values

[novel relic]

I'm sure you know about the quadratic formula, so this formula has this part where there is a square root. This root is real only if (b^2 -4ac) > 0 so you have to find for which values of k, b^2-4ac (which is also called the discriminant) is negative so it will be a root of a negative number, a complex number.

[robust current]

is k<9? i just do for fun lol

[valid yoke]

how to find y? :((

[floral jungle]

Yes

[supple island]

use the intersecting chords theorem to find x

and the intersecting secant-tangent theorem to find y

[late axle]

need a quick help

consider f a bijective function, classed C(inf) on the interval I ( f : I -> J )

is (f^-1) classed C(inf) on J ? is it a property?

[supple island]

f-1 is just f lowered by 1?

in that case yeah, you are just adding a scalar, that changes nothing for derivability

[late axle]

no

(f-1)

the inverse function

[supple island]

f^-1

[late axle]

yes

lol

and look im not working on the same intervals

[supple island]

since f is bijective we know that it has an inverse function f^-1, so we can use the inverse function theorem

since we also know that f is continuous in the interval (since it's bijective) and it's differntiable, since it's C(inf)

[late axle]

ok ok ty!

[random flame]

Hey can someone help with Q4b? Any help is deeply appreciated!! Do ping me ^^

[left knoll]

I think the question is based on the principle known as Power Of a Point.

From the First theorem, we know that 3(14)=6(X) thus X=7

From Tangent-Secant Theorem we know, 8^2=(X+6)(Y)
Thus 64=(13)(Y) and thus Y=64/13

Do let me know if I am right or wrong, hopefully this was of help! :)

[supple island]

try to express the value of the area in terms of x and h

[random flame]

Yeah isn't that the question-

I'm not sure how to do it

Wait part a I'm done ady

I'm stuck at part b

[supple island]

ok so

there are 6 faces

right

[random flame]

Yeah

[supple island]

2 of them are 4x*x

2 of them 4x*h

and the other 2 are?

[random flame]

The other 2 is x*h

[supple island]

right

sum them and that is equal to 400

cuz that's the total area

[random flame]

Yeah

[supple island]

do that

then isolate h

[random flame]

Hmm

I did the same method earlier

But for some reason cancelled it

[supple island]

i just did it and it works

[random flame]

Ah okay

I'll go solve it

Thanks btw ^^

I went ahead to do V=4x * x * h instead x-x

[supple island]

you have to use that too

[random flame]

Oh wait rly

Ohhh-

[supple island]

yep

gotta substitute

[random flame]

Okay part a was rly misleading

Thank you ^^

[supple island]

kinda, yeh

[wintry fjord]

how to die

[supple island]

explain yourself better

[pulsar turret]

Can anyone explain why √x +2 = 5 is not a linear equation? Even though you have one variable?

[fast saffron]

Hi. Linear equation means that the power of the unknown variable(s) is 1. Here, the power of x is 0.5. Similarly, there can be linear equation in two or more variables, for example: x + y = 1, x + y + z = 1, etc.

[buoyant wedge]

hi, could someone please help me with plotting these two points? i think that part a is a shrinkage of 2 but....

[cyan night]

you want the proof of why d/dx a^x = lna * a^x?

[pulsar turret]

I get it. Thank you!

[thin portal]

part a while x is constant, y is doubled and for part b on x-axis graph should move one unit to right and on y-axis 2 units down

[south oracle]

hiii, could anyone help me with this? thank youu!!

[pulsar turret]

Any help with this one? answer is 2.7 mi

[supple island]

so saying that "x" is the distance, "t1" the time in the bike and "t2" the time on the car, we also know that space=speed* time
so we know that on the bike david has a speed "v", on the bike v* t1=x
on the car (v+4.5)* t2=x

you have 2 equations and you have to find x and v

[left knoll]

Hii, can someone please help me understand that how |3-a| converted to |a-3|. (ik that - was multiplied here, but dont know the steps or how it was done)

[harsh orchid]

Since the expression is in absolute value, it can be made into a-3 and vice versa.

[left knoll]

i didn't get it, sorry

@harsh orchid

[supple island]

(3-a)=-(a-3) right?

and |x|=|-x|

[left knoll]

Ohh okay got it. Thanks!

[left knoll]

@supple island @harsh orchid

[left knoll]

If you have a Categorical model, why is it the best to use Geometric distributions? With the mode: 0. If you have too choose between Poisson distribution, Geometric distribution or Binomial distribution

[left knoll]

Hi can someone please explain what is done here?

[left knoll]

what part do u not understand?

[left knoll]

That how to identify this needs factor theorem and the last step

[left knoll]

ok

so for factor theorem

if f(k)=0 then (x-k) is a factor of f(x)

so in this case 1 is a factor of f(x)

thats how you also get the last step

using the factor theorem

[left knoll]

Right but what did they do in the last step tho? As in what does it mean?

if (x-1) is a factor

we can factor it out @left knoll

just as we can factor out x from an expression such as x-x^2

@left knoll get it?

[left knoll]

Ohh okayy understood! Thank you so much!

[left knoll]

all good, have a good one!!!

[atomic dagger]

anyone knows good resources to practice vector projection? I study with this a lot in physics

[supple island]

can you be more specific? projection on what?

[atomic dagger]

sorry, on an axis in a 3d plan

[supple island]

what's the problem projecting on an axis? it seems quite easy

[atomic dagger]

i don't know if i'm saying it properly, but i'm talking about this type of projection, where one of the axis (example Oy) is in a 3d plan and we use trigonometry

[fervent tide]

A four-digit number-lock combination (where each digit is in [0-8], ie. each digit has 8 possible values) is chosen at random. How many combinations contain exactly two unique numbers (eg. 7477 or 0808)?

I tried myself, and got 888 111, but I wonder if it's correct

E: I wrote a python script to brute-force it, and it seems to be 392. How do I do it mathematically?

[dark sorrel]

[0-8] is 9 possible values though

[solemn sphinx]

There are two possible cases here :

1. 3-1 combinations, where one number is occupied at one of 4 spots and the other number occupies the remaining 3 spots. So we get (9C1 * 4) * 8C1
2. 2-2 combinations, where one number occupies 2 spots and the other one occupies the leftover two spots. So from this we get (9C1 * 4C2) * 8C1
   Edit: Step two will be divided by two since cases like AABB and BBAA, are both counted
   This gives a total of 720 504 cases

9C1 - Choose 1 number out 9
8C1 - Choose 1 number out of 8 remaining numbers after one is taken out of the possibility
4C2 - Choose 2 spots out of 4 possible ones

[edgy crag]

can someone help me understand what to do? I don't know how to set the equation up

[dark sorrel]

Correft me if im wrong, but i believe you counted doube in your second step

You said 9C1 * 4C2 * 8C1, shouldnt you devide by two

[solemn sphinx]

Yess, sorry, my bad

[dark sorrel]

Np

If you then use 8 values in stead of 9, you get exactly 392

[solemn sphinx]

Was about to try that as well

[dark sorrel]

Nice, otherwise my solution was the same

[solemn sphinx]

Thanks for that correction!

[dark sorrel]

You are welcome

[fervent tide]

Wow, thank you a tonne! And yes, my bad, i should have written [0-7], but I just replaced 9->8, 8->7 and got the right answer, which indeed was 392

[fervent tide]

Good eye, 0-indexing isn't all it's cracked up to be lol

Is the formula for finding every single combination that could be made with maximum 2 numbers difficult? (So that would include 0000, as a valid combination for instance)

This would presumably equal 400

[solemn sphinx]

Most welcome. Feel free to ping me for such doubts. It's part of my syllabus I need to complete over the next year

[solemn sphinx]

This would include only 8 more possible combinations (AAAA form)
So to the previous case, just add 8 (392+8=400)

There are only 8 such 4 digit numbers possible with the given conditions. We already found out what to do for 2 numbers' combinations

[fervent tide]

Thank you!

[vapid geode]

hi guys, can I ask how to do this? I've tried to change it to quadratic equation form and use z1+z2 = b/a and I've also tried to change them in form of (a+ib) but no result

[ember kernel]

Express z in its cartesian form (z = x +iy) and solve for x and y

Remember, a + bi = c + di implies a = c and b = d (two equations)

[vapid geode]

thank you, i'll try it

so, x will be 1 or -1 and y will be 1, right?

[left knoll]

Guys I need your help ? Please

[delicate cave]

yes

[grave sierra]

How am I wrong? Why is there a g next to the s?

They didn’t simply?

Or dumb? Or am I dumb?

[ember kernel]

Both are right, it just depends on if you want the denominator to be a rational or not

Because 1/sqrt(x) = sqrt(x)/x afterall

[dry cypress]

Can someone please explain me the graph of |x|/x function?

[ember kernel]

Just analyse the resulting functions when x >= 0 and x < 0

So that in each case you can get rid of the absolute value

[dry cypress]

I solved the math but idk why i can't understand the graph

[ember kernel]

If you did the math you would understand right away I think

Use geogebra

You'll see 😉

[dry cypress]

I know I'm missing something

But brain stopped 😥

1st one is correct but why?

Okay got it

[teal karma]

Does anyone have a sheet with all the trigonometric identities and hyperbolic functions and identities

[zenith sparrow]

Is this right ?

[left knoll]

ye its correct whats the problem

[zenith sparrow]

in the answer key it says the answer is e

maybe the key is wrong

[left knoll]

did u try it with

[zenith sparrow]

anyways thanks

[left knoll]

tree man method

[zenith sparrow]

idk that method

[left knoll]

its basically we take function of e with the raised to the equation and then we apply lh rule on it

and subtract 1 from it

[zenith sparrow]

ohh zamn idk how to do that

anyways thanks

ill ask sir to teach me that method

[left knoll]

i can give u video link tho

[zenith sparrow]

ye that would be helpful

[left knoll]

https://youtu.be/cNbmhuhnWDg?t=2599 video will automatically start from that concept

[zenith sparrow]

will check this out thanks for the help

[floral jungle]

Does someone need help with your math problems? I am using Gauthmath, it has LIVE tutors who will give answers and step-by-step explanations 24/7 for FREE. Here's my invitation code: KCGGJY.
https://s.mathme.xyz/lp/invite?code=KCGGJY

[left knoll]

answer is e. I did tried it check it out ping me if i did wrong hehe.

[zenith sparrow]

nah it think its right thanks man
imma have to work on my derivation tho

[zenith sparrow]

man seems very sketchy and seems like a promotion please delete

[floral jungle]

I dont think its a promotion-

This is also not my app :/

[zenith sparrow]

alright idk

[ember kernel]

Pls stop with that. This is promotion btw

[floral jungle]

Uhm… this is not btw

The app is really useful too. Im not good at math but it helped me a lot. So, why cant i just let others know that we can use app to get help in math? Maybe someone need the answer ASAP n not everyone have time to reply their message 24/7 🗿

[ember kernel]

The mere fact that you included your invite code (so that you get access to more tickets) makes it a promotion. You're actually promoting your invite code 🤨

Talking about the app without mentioning your code is totally fine tho (even though I don't like its business model, where you're forced to get people to use your code so that you get to use the app more. That just reminds me of pyramid schemes but with money replaced by accounts and data)

[floral jungle]

Uh-

If u dont like maybe u can just ignore my message n help others in math instead-

[ember kernel]

Well, that's what I've been doing for the past 8 months

"[Maths help]"

But just like you I'm an undergrad so I answer when I've got time and there are no pending questions

[floral jungle]

Ok thts good 😄👍🏻 keep it up

[left knoll]

seems we have quite the kerfuffle here

[storm ginkgo]

Guys can you help me?

Solve without a calculator

[ember kernel]

Let's treat the real numbers first :

You can pretty easily identify them : these are 1; 3i^2 = -3; 5i^4 = 5; 7i^6 = -7; ...

So the total sum of the real numbers is 1 - 3 + 5 - 7 + ... + 41
There are many tricks and techniques you can use to calculate this without having to go through every term. I'll leave it up to you.

Then, you can apply the same reasoning to the imaginary numbers, but this time there will be an i in the final answer
Just sum the two results you have at this point (the total sum of the real and imaginary numbers), and there you go

[cinder yacht]

-2*9+41 right?

wanted to see if I'd get it wrong if I don't take my sweet time

oh

-2*10

[ember kernel]

honestly idk

Haven't done the calculations yet

I just know there are many tricks to get the answer quickly

I just want to point the main steps

[cinder yacht]

yea makes sense

I just can't stop myself from trying to guess an answer when I see a question lol

21-20i is my guess

sorry continue ur explanation xD

and since I'm stupid, I just wasted 5 min looking for a second (much more complicated) method. for the guy asking ignore the following please lol
let f(x) = 1+ x+x^2+... x^41
= (1-x^42)/(1-x) for x not equal to 1
so f'(x) = 1 + 2x + 3x^2 +.. +41x^40
= (-42x^41+ 41x^42 + 1) / (1-x)^2
so by replacing x by i
1+...+41i^40 = (- 42 i - 41+1) / (1-i)^2
= (-40-42i) / (-2i)
= - 20i + 21

[ember kernel]

oh wow

I'm actually impressed, I wouldn't even have considered thinking that the = (1-x^42)/(1-x) could maybe have been a way to solve it

[cinder yacht]

i got used to seeing that sum of n x^(n-1) as a derivative, because of other math chapters

like

séries entières (idk in English)

or to compute the infinite sum of that (with |x|<1)

[ember kernel]

Yeah, but I didn't know there was an equivalent for finite sums

is "finite" actual vocabulary ? You know what I meant

[cinder yacht]

ehmm i think so

partial sum works too ig

[cinder yacht]

i didn't have it in mind either until i just tried now xD

and stuff like this (derivatives/antiderivatives) also work to compute a sum like : the sum of k * (n choose k) for k = 1 to k = n

using the derivative of f(x) = (x+1)^n, evaluated at x=1

[cosmic harbor]

The following data refer to questions 1-2
It is known that the average blood counts in a healthy population is 240 and in patients 230. It is also known that the distribution is normal with a variance of 225.
Two researchers wanted to test the effect of drugs on the average blood counts while fearing that among drug users this average had dropped.
36 people were sampled taking drugs and a blood count was performed. What is the null hypothesis?
One answer must be chosen:

1-Effect of drugs on average blood counts is greater than the effect of candies

2-No answer is correct

3-No effect of drugs on average blood counts

4-The two answers are correct

Yossi claims that a possible mistake is: to determine that the average decreases due to drug use, even though in practice there is no effect
Sima claims that a possible mistake is: to determine that the average does not decrease due to drug use, even though in practice it does decrease due to drug use
One answer must be chosen:

1-Yossi and Sima are right

2-Only Sima is right

3-No answer is correct

4-Only Yossi is right

answers pls?

[floral marlin]

Hi, can anyone help me with this?

[void gazelle]

hi, did you try to solve it?

[floral marlin]

Yes, but i cant get rid of the ln

[void gazelle]

can you post here what you wrote to try to solve it pls?

[floral marlin]

I think this was the closest i've gotten

[cinder yacht]

u sure u have to find X?

complicated version :
f(x) = 2lnx - xlnx - 1
f'(x) = 2/x - 1 - lnx
f''(x) = -2/x^2 - 1/x
f''<0 so f' is decreasing, so there's a point c>0 such that f'(x) goes from positive to negative (f'(c) = 0 so ln(c) = 2/c - 1. we could prove 1<c<2)
so f is increasing until x=c, then decreasing
and f(c) = [4/c - 2 - 2 + c - 1] = [4/c + c - 5]
= 1/c [c^2 - 5c + 4]
= 1/c [c-1] [c-4]
which is negative cause 1<c<2
so actually f never reaches 0,it always stays negative
so there is no solution

**another version (still complicated) **
Let us assume the equation is true for some solution x. Then
ln(x) = 1/(2-x)
if x<=1 : ln(x) <=0 and 1/(2-x)>0 so it can't be true
if x>2 : ln(x) >0 and 1/(2-x)<0 so it can't be true
for 1<x<2 : ln(x) <= x-1 so 1/(2-x)<=x-1
so 1<= -x^2+3x-2
so x^2-3x+3<=0
so (x-3/2)^2 <= - 3/4 : that's absurd. So the equation can't be true
=> In conclusion : there is no solution

there must be an easier way to prove there is no solution though

third method (simplest one i found so far)
if we put t = ln(x), meaning x = e^t, then the equation is
2t-e^t * t - 1=0
using the fact that e^t>=t+1, that means thzt :
2t - e^t * t - 1 <= 2t - (t+1) * t - 1 = - (t^2 - t + 1) = - [(t-1/2)^2 + 3/4]
since (t-1/2)^2 >=0 and 3/4>0, that means [(t-1/2)^2 + 3/4]>0
so -[(t-1/2)^2 + 3/4] < 0
and since 2t - e^t * t - 1 < -[(t-1/2)^2 + 3/4]
that means 2t - e^t * t - 1<0
so 2t - e^t * t - 1 can't be equal to 0,for any value t>0
so no solution

[floral marlin]

Thank you so much for ur help! It's indeed a bit complicated haha but thank you again

[balmy spoke]

Guys anyone know any good channel on yt for engineering maths?!

[spice basin]

How do i solve it? Maybe there’s a better substitution but I haven’t been able to find any

[spice basin]

Bruh I forgot about +5 after 2lnx sorry

[cinder yacht]

t = u+3

now

you'll like that

(because u^2+6u+10 = u^2 + 2 * u * 3 + 3^2 + 1 = (u+3)^2 +1)

then u'll find some ln(1+t^2) and some arctan(t) in the antiderivative

[fiery widget]

Does anyone know how to do 3b?

the answer to 3a is P -> s=2.8t+0.06t^2

Q -> s=2.4(t-3) + 0.1(t-3)^2

[weary arrow]

someone's had a field day with the emojis

[tulip knot]

d

[robust oak]

can anyone help me with this?

[vapid geode]

I think you can move the right hand's denominator to left hand and place the gamma sign(?) to right hand, and then simply square both sides

[left knoll]

There ya go mate

[vapid geode]

anyone can help me with this?

[left knoll]

There ya go mate

[balmy star]

I deleted the reaction spamming

[gritty palm]

would this be correct?

[ember kernel]

Yup

[gritty palm]

thanks!

[ember kernel]

Use the quadratic formula to get alpha and beta

Once you know their value, computing the expression with the squares and cubics is a piece a cake

[fossil kite]

ohkk cool

[unkempt sleet]

How to do (b)ii ？🥲

[tiny tiger]

20.000 * (1.05^n)

[tough elk]

how do i approach this

[winter dove]

calculate the standard deviation of the following set of data. birth weight of ten babies

2.977
3.155
3.920
3.412
4.236
2.593
3.270
3.813
4.042
3.387

[frozen meadow]

use the equation of standard equation

[gritty palm]

@winter dove @frozen meadow damn that looks complex tho

[frozen meadow]

this is a raw data equation. N is the number of data. u would be the mean .

and xi is the data given

[winter dove]

can someone help me with histogram?

like the chart

[left knoll]

Histogram is frequency (how many of the same thing do u have) on y axis and x (the numbers themselves) on the x axis

[fervent tide]

you might want to experiment a bit with bin size, in order to have the histogram communicate the data in a meaningful way

[novel folio]

Anyone can help me with this please?

[ember kernel]

This question can be split into two sub questions.
a) Find the expression of the values of A (in terms of n)
b) Find the sum of all the elements of A

Have you managed to solve the first part yet ?

[atomic dagger]

Hi! I’m trying to understand how to project a vector on a straight line.
I want to project a on the line d. The angle separating the vector a and the line d is the angle is pi-teta. So the projection:
| a |• | u | • sin (pi-teta).
My question is why sinus ?

(Just realised I made a mistake and vector a should be on the dotted line )

[ember kernel]

I don't see why theta has to be 90°, and not the angle between u and a

Like it's pretty much useless here, unless I misunderstook something

[full quiver]

hey, I need help with this limit bc no matter how hard I try I can't figure it out, should I use l'hopital? looks like a very long derivative tho

[supple island]

just use some if the basic limits

like for x->0 sinx=x

same for log(1+x)

[full quiver]

oooh thank you so much i don't know why i thought that when x->0 sin(x)=0

my bad

[supple island]

yeah i mean it's not wrong

sin(0)=0

[left knoll]

Log(1+x)/x ->1

sinx/x->1

1-cosx/x^2 -> 1/2

Hence cosx-1/x^2 -> -1/2

Final answer is -1/2

[left knoll]

This is a standard result, you can derive by converting to sin^2(x/2) if you want for understanding

Or by applying LH rule too

[sullen verge]

anyone has exercices for complex numbers please?

[supple island]

you gotta be a little more specific than that

[full quiver]

thank u so much!! < 3

[sullen verge]

idkk like basic stuff 😅

[sullen verge]

for example this exercise posted by someone here was a good one

[left knoll]

Hi, so R is a relationship, and our teacher explained it to be a symmetric relationship. However, I feel along with symmetric it's also Reflexive as (1,1),(2,2) & (3,3) value defines the same.

[left knoll]

Can someone pls help me with the same?

[solemn sphinx]

Yes, it is reflexive as well✅

(And transitive, hence an equivalence relation, if you wanna dig deeper)

[spare shale]

Can somebody help me with this please

would be absolutely great if worked solutions can be sent

[whole wind]

Hii

I am new to this server

I am from India

And you all

??

[ember kernel]

There is a formula that helps you compute the n first terms of an arithmetic sequence using the first term and the common difference (the 2 unknowns)

And you have access to two equations (one with the 110, and one with the 320)

That leaves you with a system of two unknows and two equations, it should not be too much of a problem to solve once you know what the equations are

[cinder yacht]

that's not the formula of a projection, it would be the formula of the dot product if it was cos(theta) instead of sin(pi-theta)

a projection is a vector btw, while the formula is a scalar

if ur still curious abt this u can send the correct drawing and ill try to correct/explain

[silver pier]

Can anyone check this and let me know if I made any errors

[silver pier]

cant i just say that <P and <Q are subtended by the same arc hence they're equal and the points ABQP ar concyclic?

instead of proving all these?

[sullen verge]

no one?

[silver pier]

you can look for a book on complex numbers with exercises

[sullen verge]

do you have any recommendations?

[silver pier]

i dont have complex numbers this year

i would give them to you if i had em 😓

[sullen verge]

thanks for the list anyways!

[limpid harness]

can anyone help me wit

with this question

[whole wind]

0.9

[cloud sky]

helpp

[ember kernel]

I'm very interested in having the answer as well

[left knoll]

What did I do wrong

nvm

im an idiot lol

ignore it

[supple island]

we know that OBM is a right triangle, we know that OB=r and OM=LM-r, also MB=AB/2, so we know that OB²=OM²+MB² which is r²=(18-r)^2+12²

now you just have to find r

[silver pier]

can anyone help me solve a and b

[silver pier]

i was able to solve

[kind fossil]

I forgot about this channel

And had math hw for today :(

[dire glen]

Okay

[subtle sluice]

Hi. Can anyone help me find the value of D if this equation 4x^2+y^2-4x-Dy=-2 was an ellipse?

[left knoll]

ye its correct, what is the problem?

[silver pier]

i just wanted it checked by someone to make sure i didnt make any errors

thanks

[left knoll]

no problem

[left knoll]

Can anyone help me to find the first derivative?

[supple island]

you can do a little trick by saying t=sin(u)

so you have u=arcsin(t) and du=sqrt(1-t^2)dt

but t=sin(u)

so du=cos(u)dt

so in the end you just have to do the integral of cos²(u)du

[left knoll]

is this trick applicable to all this type of questions?

[supple island]

i mean, you can do whatever substitution you like for integrals, as long as it works

here it's ok since you have sqrt(1-t²) so with the substitution you know that that is cos(u)

[left knoll]

okk, means we need to first analyze the question first and then we can substitute ...thanks man for helping me too

[left knoll]

ah i get it

[silver pier]

Can one check this

Ques:
Given,
X = sinA
Y = cosA
If X+Y=2^1/2 then A=?

[supple island]

to do this more quickly 2sin(a)cos(a)=sin(2a)

so you get sin(2a)=-1, so 2a=3/2pi, so a= 3/4pi

[supple island]

the second page is overall not super correct, because you can't just say that given cos(a)sin(a)=-1/2, these are all the solutions

ah wait i didn't read completely the secondo page

it is absolutely incorrect and very wrong

A can't be 120° and 90° at the same time

even considering all the cases, A can have a single value

[silver pier]

can solve this one for me? i cant figure this out spent about 45min figuring this out

[supple island]

i'm writing it out

do you know radiants?

[silver pier]

thats great, and thanks

[subtle sluice]

Hi. Can anyone help me find the value of D if this equation 4x^2+y^2-4x-Dy=-2 was an ellipse?

[supple island]

in terms of x and y?

cuz if not we need more info

[subtle sluice]

I thought so too

But it's all there is that's why i couldnt solve it

[supple island]

can you provide the text?

[subtle sluice]

Determine the value/s of 𝐷 if the graph of the equation 4𝑥^2 + 𝑦^2 − 4𝑥 + 𝐷𝑦 = −2 is

1. an ellipse;
2. an empty set;
3. a single point

I got D=2 for nos. 2 and 3

[supple island]

maybe @ember kernel could help more than me, rn i have no clue

[subtle sluice]

Alright thanks anyway

[ember kernel]

Wait, are you saying you managed to get two different results using only one value for D ?

Also, can't help either for question 1, geometry's not my fav

[subtle sluice]

i managed to get one result

from 2 different solutions

[subtle sluice]

okay thank you

[dreamy ember]

does anyone know mathematical induction?

Im stuck on a question

[silver pier]

thanks a lot

[supple island]

post the question, someone will help

[silver pier]

i think you made an error when writing the ques

its

root over 2

not only 2

[supple island]

it's 2 after you square everything

[silver pier]

why is it -1 here

[silver pier]

interesting

[supple island]

i mean it's literally what you did

it was the second page that was wrong

the first page is alright

[silver pier]

oh

i thought my whole sum was incorrect

[supple island]

the first part was good

[silver pier]

my badd 😓

[silver pier]

umm soo me have another ques,
what happened to cos(A) and 2

sorry, if im bothering you

[supple island]

as i said sin(2x)=2sin(x)cos(x)

[dreamy ember]

im stuck at n=k+1

[supple island]

because sin(a+b)=sin(a)cos(b)+sin(b)cos(a), apply the same to sin(x+x)

[silver pier]

interesting, thanks for pointing this out

[atomic dagger]

thank you! i need to do my exercise again i think 😅

[cyan night]

i got the answer

do u still need the help

it was a bit complicated and the key was applying the inductive hypothesis

ok ill still write you the proof

[cyan night]

hey

done

dang the quality is a bit bad

i emphasized at a few spots that were the key

@dreamy ember

[cinder yacht]

it's cool if you see it as :
(2n+0) + (2n+1) + ... + (2n+n ) = (2n + 2n + ... + 2n) + (0+1+...+n) = 2n * (n+1) + (1 + 2 + .. + n)
so you need to prove 2n(n+1) + (1 + 2 + .. + n) = 5n(n+1)/2
meaning 1+2+..+n = 5/2 * n(n+1) - 2 * n(n+1)
meaning 1 + 2 + .. + n = n(n+1)/2
and that is much easier to prove by induction

[quartz sparrow]

Hey guys, i usually get very good marks in every lesson. But math is always the lowest among them, any advices to fix that?

[fallow jetty]

practice problems

[dreamy ember]

thank you so much

[dreamy ember]

thanks for this point of view, it actually helps me understand the question better

hmm I dont understand this part still

[timid delta]

aah its been ajes

[dreamy ember]

nvm I got it

[clever light]

@worldly jacinth daje korki 100zł tanio i szybko

[worldly jacinth]

taak

polecam

[paper pecan]

How do you remember the equations?

[cyan night]

its just following the pattern of consecutive numbers

k-1,k,k+1 are consecutive numbers

[astral quartz]

hi, I don't know if some of you read french, but if you understand, i would need help with this probleme

it' a law of poisson but in don't know how to deal with the intersection that appear after the application of the conditionnelle
i m not sure of the terms in english
hope you understand

[fallow jetty]

generally, learning math comes down to learning the intuition and doing practice problems

you'll memorize equations better through application instead of just repeating it to yourself a thousand times

learning the intuition = understanding how a certain equation or formula is made and the meaning of it

not necessarily going and reading a formal proof

[left knoll]

How do I do part a

[sharp ferry]

is the answer tan-1(2-root3) or 15 degrees ?

[left knoll]

yes

[sharp ferry]

just open sin(x+pi/3) using the formula of sin(a+b) then rearrange the terms so that you get sinx=(2-sqrt(3)) cosx

then tanx =2-sqrt(3)

then take inverse tangent on both sides or if you remember the value of tan15 degree then you can directly say 15 degrees

[left knoll]

How do i go from that to that

@sharp ferry

[sharp ferry]

multiply both sides by 2

and take root3 cosx to the other side

sinx+√3cosx=2cosx
sinx=2cosx-√3cosx=(2-√3)cosx

[left knoll]

ohhhhh

ok ok

ty

@sharp ferry

[sharp ferry]

youre welcome

[atomic dagger]

I must've made a mistake somewhere then 😭 i'll read it again and do the correct drawing then. Thank you for your answer

[valid comet]

How do i solve with the sine rule

OH WAIT IM SO DUMB

[cinder yacht]

tan(x) = tan(x+pi)
so there are two solutions in [0;2pi]
which are pi/12 (15°) and pi+pi/12 = 13pi/12 (195°)

[silver pier]

how do i simplify this

[left knoll]

how do i even do this

[solemn sphinx]

Let me try

It should be first to find tan theta and use it for cos theta and sin theta

[left knoll]

?

[solemn sphinx]

Give me some timw

[left knoll]

kk

[solemn sphinx]

I used L'hospital repeatedly and the answer came out to be -2/7

cos(theta)=(1-t^2)/(1+t^2)
sin(theta) = 2t/(1+t^2)

Rest substitute it in the equation and find the limits

[left knoll]

there is acc another way

just ignore the limits and expand to god

and u get the answer

[undone peak]

Aaa

[solemn sphinx]

I didn't completely understand. Can you share it? It would be good to know alternate ways to approach these problems

PhysStudent, I think you cleared your doubt? I don't know the right tag

[pulsar turret]

To solve this cubic equation by factorization, how did they get to the second step?

[left knoll]

According to me : 1. find out the root or the zero of the first equation using Hit-and trial method. For example : X should be equal to -2 to make the actual equation 0

[summer laurel]

can someone please help me with this ,how does that work

wait lemme send the whole solution for context

question

[left knoll]

then 2. when we found out the first root (x-2) divide this by actual equation x^3+8=0 imo. Then we reach second step Correct me if i am wrong ok

[summer laurel]

i got it all the way till they got tan(theta)

after that im lost

[left knoll]

I will show u tomorrow since I have to go rn but remind me

[sharp ferry]

oh yes youre right thanks

[sharp ferry]

can we not just take theeta =pi? coz for tan pi/2 t tends to infinity so we get (2k-1)cos(pi)-5sin(pi)=5k+3
ie (1-2k)=5k+3 or 7k=-2 and k=-2/7

[sharp ferry]

they just took the square root right mg/kq^2 all are constants ie their value wont vary so they just let all that mess=C(say) then from the diagram you can find out tan theeta

[summer laurel]

nah bro , iwas confused about how they got that proportional relation of 'r' with 'y'

[left knoll]

anyone can help me w derivatives

[sharp ferry]

hm maybe i can help send the question

[left knoll]

alr

it's not giving me the result it's supossed to give

[sharp ferry]

hmm wym

you want to differentiate that?

[left knoll]

i want to find the derivative

[sharp ferry]

yes so just use the power rule right?

[left knoll]

i use a derivative table my teacher gave to me

[sharp ferry]

hmm so is there something like derivative of x^n =nx^(n-1) or something?

[left knoll]

yes

[sharp ferry]

use that

[left knoll]

i did

[sharp ferry]

then what result did you get?

[left knoll]

2x - 3/4

[sharp ferry]

yes but you need to multiply by the 4/3 which is outside as well

but otherwise it is correct

[left knoll]

how do i solve that part bc i did 4/3= (0×3-4×0)÷3^2

i searched up how to solve it on google

i think i'm doing it wrong

[sharp ferry]

nonono you just multiply 4/3(2x-3/4)

[left knoll]

ohhh

[sharp ferry]

because when you take the derivative if there is only a number which is outside without x then you can just take that number out

for example when you take the derivative of 2x^2 then you can do 2* derivative of x^2

similarly if you have 4/3(x^2-3x/4+2) you can do 4/3 * derivative of (x^2-3x/4+2) which you just calculated and is equal to 2x-3/4

[left knoll]

thank sm for the help i aprecciate it

So after studying maths for 9hrs and now i am feeling burnout .and tired .I need suggestions so that I overcome this and study more.

[supple island]

take a break, eat something, get some air

[left knoll]

I am doing this for 1hr now. Ah i can't concentrate anymore. I am having I hate maths feeling when I am doing questions now

Plus I have maths exam in 2days now😭

[sharp night]

Working out helps me overcome this

or any other physical exercises

something you enjoy

[left knoll]

Thnks i am feeling okayish now

I am doing one more session:))

[summer laurel]

BROO ,THANK YOU SO MUCH

[onyx hollow]

Anyone here have any knowledge about Support vector machines, hinge loss and subgradients?

[left knoll]

yes that way actually also works

[willow basin]

hey

please can someone tell me why my answers are wrong?

i feel like pulling my hair out lol

[winged spindle]

hello , please ineed a simple help on math if anyone can please send msg

[left knoll]

im trying to solve this but i'm doing something wrong bc it's not giving me the answer it's supposed to give

[onyx hollow]

write the denominator in the numerator (with negative exponent) and add the x exponent terms together

[winged spindle]

how did we get 1/2*3x ?

[teal karma]

Help on #14

[left knoll]

so it'd be √3 × -x^3/2 and then i solve it?

[onyx hollow]

yes

[left knoll]

alr thank u

[supple island]

what's your problem?

[supple island]

i'm assuming for x->0?

[winged spindle]

yes its like Y= infnity , so Y = 1/x

[supple island]

can you post the whole text?

[winged spindle]

yes

thats all

its limited development

[supple island]

but basically lim x->0 of (1+x)^c -1=cx

[winged spindle]

its about limited development *

[supple island]

oh so X=1/x i guess

[winged spindle]

yup

[supple island]

this is what you need to know btw

X² is included in o(X)

[winged spindle]

ahaaa isee

here we are

[left knoll]

it didn't work

[onyx hollow]

Sorry, read your answer too quickly it's sqrt(3)*x^(-3/2)

[left knoll]

alr thanks

[winged spindle]

thank you so much

[supple island]

np

[teal karma]

I’m not sure how to find the area

[left knoll]

hey can anyone help me out with this question i am kinda confused ish

[left knoll]

astaghfirullah

[left knoll]

how is it -1 bruh

also bottom one i got the same one i used the AC method i think thats what its called

[storm ginkgo]

Top part multiplied by - 1

[left knoll]

ohhh i get what u mean

thanks sm for the help

[winged spindle]

Haha what ?

[left knoll]

I said that cuz I pray that I will never get this in my exams 💀💀💀💀

[worn skiff]

Hi can anyone help me with this question?

[left knoll]

idk how to solve this i tried

[supple island]

that's a function, there's nothing to solve about this, what's the question?

[left knoll]

i need to get the derivative

[supple island]

ok so sqrt(x³)=x^3/2 right?

[left knoll]

yes

[supple island]

and do you agree that (x^3/2)/x^4 = x^3/2-4?

[left knoll]

yea

[supple island]

so we have 3/2 x^(-5/2)

so you just have to do the derivative of x^n where n=-5/2

simple as that

[left knoll]

ohhhh

alr thank sm!!

[supple island]

np

[left knoll]

when i have a sqrt of a random number in a function n i have to solve the derivative do i just remove the sqrt? i'm confused

[supple island]

can you give an example? i'm not quite sure of what you're asking

[left knoll]

sure

here

[supple island]

and you have to find the derivative?

sqrt(5) is just a number, its derivative is 0

[left knoll]

alr thanks

[vapid geode]

Hi can anyone help me to solve this?

[ember kernel]

Draw different values of z for different values of theta

Then try to find a pattern for the argument of z that matches what you drew

[vapid geode]

umm sorry I don't understand..

[cinder yacht]

or see z as :
z = 1 + exp(i * (theta-pi) )
draw z in the complex plane (for some theta between 0 and pi) by summing the two corresponding vectors (1 and exp(- i * theta))
notice what the argument of z is

a third method (which is way more complicated lol, and which more generally works) is to

1. compute |z| = sqrt( (1-cos theta) ^2 + sin^2(theta) )
   =sqrt[ 1 - 2 cos(theta) + cos^2(theta) + sin^2(theta)]
   = sqrt[ 1 - 2cos(theta) + 1]
   = sqrt(2 - 2cos(theta))
   = sqrt[ 2 ( 1 - cos theta)]
   = sqrt(2) * sqrt(1-cos theta)
   = sqrt(2) * sqrt[2sin^2(theta/2)]
   = 2 * sin(theta/2)
2. compute z/|z| = (1-cos theta) / [ sqrt(2) * sqrt(1 - cos theta)] - i sin(theta) / [2 * sin(theta/2)]
   = sqrt[(1-cos theta) /2] - i * 2 * sin(theta/2) * cos(theta/2) / [2 * sin(theta/2)]
   = sin(theta/2) - i cos(theta/2)
   = cos(theta/2 - pi/2)+ i sin(theta/2 - pi/2)
   so it's 1/2(theta-pi)

[lucid hollow]

Guys when the exponential function is raised to 0 what value is it? example = e^0

is it always 1?

[graceful mesa]

yes

[lucid hollow]

thanks

[supple island]

any number raised to 0 will always give 1

[lucid hollow]

Does that apply for everything? even functions?

[supple island]

well, the function may do something strange, but generally speaking yes

[vapid geode]

alright thanks a lot

[lucid hollow]

roger that, thanks.

[willow basin]

hi i need help with this please i tried

[left knoll]

i didnt get this answer

[left knoll]

i think im doing it wrong again i can't get the answer (i have to solve the derivative)

[magic stag]

this is a trigonometric exuation right?

equation*

[left knoll]

nvm i got it i think

[magic stag]

I got the first X right pi/2, but the second one doesnt match

[supple island]

do you know how to calculate the volum of a cylinder?

[left knoll]

we want to find y

what happens from the marked steps here

why does 3 become 3 log2(2)

[left knoll]

360-90-95-112