help-28

[onyx glen]

like this

[pure basin]

u type fast latex

[onyx glen]

to be clear this is just an ALGEBRAIC thing

[torn jolt]

x² cos x are connected
2x sin x are connected

I should know where to simplify it.

[onyx glen]

do you understand this here

[pure basin]

they both have a common x

[torn jolt]

x² and 2x are different

[pure basin]

uh

yes

but you can write it as

x(x+2)

x^2+2x

[torn jolt]

but it'll just be the same we are just canceling down 1 x.

[pure basin]

that is further simplification

[torn jolt]

All it is telling me is to differentiate.

Not simplify

[pure basin]

Yes then leave it

[onyx glen]

yes true

[onyx glen]

simplifying is still a good idea

[pure basin]

but you might lose marks if simplification is necessary

[onyx glen]

like in general

also makes your life easier

[torn jolt]

Trigonometry is making my life hard than it already is

But I'll use that advice thank you

[full forum]

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

[torn jolt]

Next is logarithmic-

I added 3 photos

Let me work on it

[pure basin]

oh ok

ping me once u finish log ig

[torn jolt]

Wait a min

In number 5

Is the answer only
cos² x - sin² x

Like scrap the ½ sin (2x)?

@pure basin

[pure basin]

Yes

dy/dx is not 1/2 sin(2x)

y= 1/2 sin(2x)

@torn jolt

[torn jolt]

But can I add that or no??

[pure basin]

no

[torn jolt]

Ah I see

[pure basin]

1/2 sin(2x) is not dy/dx

[torn jolt]

Okayy

[pure basin]

u can write cos^2x-sin^2x as cos2x

[torn jolt]

Thank you

[pure basin]

now do log

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[silent quest]

Interesting question:
There are two curve, y = a^x and y = log_a (x). There exists an 'a' such that the curve touches each other at a point. Find a.

[silent quest]

From what I know that a = e^(1/e), but why?

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[rapid rain]

those functions are gonna touch each other at a single point, right?

Which means that not only at that point $x_0$, you will have the functions equal to each other

[glossy valve]

rafilou is not not born in 2003

[rapid rain]

but the curves being differentiable at that point must also be tangent to each other there (otherwise they will cross, forcing a second point of intersection, if you can prove why)

which means that the derivatives at that point are also equal...

2 equations, with two unknowns, "a" and "x_0"

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[sharp hatch]

can anyone help with question c and d?

[covert heath]

question 4 sub parts c and d?

[sharp hatch]

question 1 part e

i solved c and d

it;s an integer do i just use every number possible?

[devout nova]

yes in the given domain

[sharp hatch]

lemme send a screenshot of my answerr

hold on

this correct?

can you help me with 2. too?

[devout nova]

for c it says negative integer not negative numbers

[sharp hatch]

i rthought it included 2 too?

[devout nova]

for d "N" is the notation for natural numbers

[sharp hatch]

so 0 shouldn;t be included?

and the negative numbers too shouldnt be included?

[devout nova]

yes

[sharp hatch]

why does it include -2 in the interval

[devout nova]

for d it says both x and y are natural numbers

[sharp hatch]

oh

we're talking about c

[devout nova]

oh

c only asks for negative integers

[sharp hatch]

so it's correct?

[devout nova]

negative integers don't include decimals and fractions

[sharp hatch]

i see

so it should only nbe {-1, -2, -3, ...}?

[devout nova]

yes

[sharp hatch]

got it

can ya help me with number 2 a b and c

i'm confused

[devout nova]

for a and b just simply list out the possible x values

[sharp hatch]

wouldn;t that be too much work?

[devout nova]

like how you usually solve equations

[devout nova]

it's not much

[sharp hatch]

so i use 1, 2,3 and so on

?

[devout nova]

for example a

how do you usually solve quadratic equations?

[sharp hatch]

factorization

like this?

so the elements are 2 and -1?

fyi i'm autistic so it's a little bit hard for me to understand sorry

[slate violet]

cool that's correct

[slate violet]

yes so you'd just write {2, -1}

the x = is implied so you don't need to write that

[sharp hatch]

would the other matter?

like

if i write {-1, 2} would it matter

[slate violet]

nope!

the order does not matter

[sharp hatch]

thank you!

[slate violet]

npnp

[sharp hatch]

how about b}?

[slate violet]

ah no

they want the same value of x for both equations

so that's the empty set

[sharp hatch]

what do you mean

[slate violet]

they want an x such that

x^2 = 9 and x - 3 = 5, at the same time

[sharp hatch]

i don't understand

[slate violet]

say if I want a + 2 = 5 and a + 3 = 6 at the same time

that's possible with a = 3

3 + 2 = 5 and 3 + 3 = 6

[sharp hatch]

so with x^2 = 9 and x-3=5

[slate violet]

so if you start with x = 8

then 8^2 is definitely not 9

and if you start with x = -3, 3, then -3 - 3 and 3 - 3 are both not 5

[sharp hatch]

so it;s 3 and 8?

[slate violet]

nope

[slate violet]

it's this

[sharp hatch]

it's -3, 3, and 8?

[slate violet]

the set with zero elements

cause that's an impossible condition to have both at the same time

it's written $\emptyset$

[glossy valve]

south

[sharp hatch]

can you visualize it more

i really can;t understand

or is it because no values satisfy both equations so they're a null set

?

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[mortal pilot]

pls help, i tried int it using 2* 1/2 fx ^2 dx, from 2pi/3 to 0

[thick hedge]

is this a test

[mortal pilot]

is my homework

but it have unlimited attempt

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[thick hedge]

okay, so the aea of a polar curve is given by $\int_{a}^{b} f(\theta) f'(\theta) d\theta$

[glossy valve]

What a wonderful world !

[mortal pilot]

why?

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[gritty rose]

this looks wrong https://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus__Early_Transcendentals_(Stewart)/10%3A_Parametric_Equations_And_Polar_Coordinates/10.04%3A_Areas_and_Lengths_in_Polar_Coordinates

[gritty rose]

show your work

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[torn jolt]

Sort of stuck on how to begin here

[umbral dome]

it might help to rewrite the integral in terms of sin and cos

[torn jolt]

How could i do that ?

[umbral dome]

what is sec in terms of cos?

[torn jolt]

1 over cos(x)

?

[umbral dome]

yes

[torn jolt]

So the new integral would be sin(6x) over cos^5(6x)?

[void nova]

Yep

By the way, instead of over you can write / to improve readability

[torn jolt]

then u = sin(6x) ?

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[torn jolt]

can someone help me with c-e please

[gloomy kettle]

I don't understand any of that I'm never passing maths 😭😭😭😭😭😭😭😭

[torn jolt]

ur gonna be fine lil man

@honest hill can u help me?

[honest hill]

!noping

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[torn jolt]

ok sorrt

<@&286206848099549185>

try applying ln on both sides ig

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[torn jolt]

don’t give help if u don’t know what ur doing

<@&286206848099549185>

[zinc onyx]

This will help you ig

Oh wait you already solved it

[devout valley]

"But for this question don't use this formula."

[zinc onyx]

WYM bro it's jus expansion of that term

[devout valley]

Did you even read the original question, or-

[torn jolt]

nop

[zinc onyx]

Unfortunately I didn't

[onyx glen]

[VINE BOOM SFX]

[devout valley]

Also this is quite sus some of what was written there implies equality where there isn't, and some aren't done right (e.g. the e^{3x^2} one, you need )

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@torn jolt Has your question been resolved?

[calm nacelle]

a is right but b is not right

you need to replace x in the formula for e^x with 3x^2 instead

for c, you need to use a similar strategy, then multiply it by (x^2 + 4)

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[hushed tinsel]

yo guys im new to complex mathmatics, but i cant seem to understand why the argument of z here is -pi/2

[hushed tinsel]

can someone help me please

[umbral dome]

pi/2 is a right angle

and the negative means it's clockwise

there is a right clockwise angle between the positive real axis and the negative imaginary axis

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[nimble crane]

is there a systematic way to do this problem?

[nimble crane]

so far, all I've been trying is guessing and checking, but this isn't really efficient and I'm growing impatient

[calm nacelle]

https://math.stackexchange.com/questions/356272/non-linear-techniques

same problem

[nimble crane]

I see

thanks Eric 🤍

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[supple plover]

Hello I am having trouble with the first question, I answered 0 and it was wrong and I answered 1 and it was also wrong so im on my last try... I dont understand how its wrong and how to find the right answer...

[sudden condor]

the function from x=0 to x=inf keeps increasing
so the more x approaches inf f(x) will also approach what ?

[leaden ermine]

How did you conclude 0 or 1

[supple plover]

I concluded 0 because the dot was at zero and to be honest the 1 was a guess

[leaden ermine]

you are looking for what happens as x grows to infinity

not what happens at x = 0

you wanna basically see what happens as you keep walking to the right

[supple plover]

the numbers increase?...

[leaden ermine]

yes

but they dont seem to increase arbitrarily

they seem to be kinda bounded

can you see that?

[sudden condor]

ok now that was good tbh

[supple plover]

im sorry could you explain what you mean by bounded?.. I just started learning this today haha

[leaden ermine]

a bound is basically like a border you can imagine that the function doesnt cross

it will always be below that

or above

[supple plover]

ohhh i see I believe I understand now

[leaden ermine]

can you see intuitively up until which number the functions seems to grow but not cross

[supple plover]

2?

[leaden ermine]

yes

[supple plover]

OHH okok so f(x) then equals 2 as x approaches infinity?

[leaden ermine]

basically f(x) is bounded by y = 2 for x > 0

[supple plover]

OHHHHH

[leaden ermine]

yes this is how it seems to behave based on the given function

[supple plover]

okok im finially understanding this, thank you so much the visuals helped me a lot

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[woeful anvil]

I’m just curious, how hard is a introduction to linear algebra class?

[umbral dome]

the calculations tend to be fairly straightforward (probably more arithmetic than you've done in a while). parts of it will probably be more abstract than you've encountered before

[gritty rose]

read through #linear-algebra

[umbral dome]

if you want an idea of what concepts you'll encounter (not so much what calculations you'll be doing) then you can watch through the 3blue1brown "essence of linear algebra" series on youtube

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[olive oracle]

need to find x

is it 4√2?

[robust slate]

Yes

[olive oracle]

ok sick

thanks

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[unreal cliff]

how to write a sine function for this graph

[placid oak]

play around with the equation of a sine wave

$$qy+b = sin(px+a)$$

[glossy valve]

Shuba

[unreal cliff]

uhhh

we didnt learn that

[placid oak]

a shifts it left and right, b shifts it up and down
p scales it left and right, q scales it up and down

https://www.desmos.com/calculator/1zfukwarln

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@unreal cliff Has your question been resolved?

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[opaque locust]

why do we use MVT and not rolle's??

[onyx glen]

does it really make a difference

rolle is a precursor to MVT but it is also a special case thereof

did you get points taken off for saying rolle?

[opaque locust]

o

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[scenic brook]

is x = -2 and x = 4 local maxs or global maxs?

[gritty rose]

Looks like both

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[unreal cliff]

.reopen

[sudden condor]

yea it's 33

[torn jolt]

how?

[sudden condor]

area of rectangle (9x3)
and the area of the triangle is 1/2(bh)
the base of the triangle is 6 why? because adjacent sides of a rectangle are equal
and 9-1.5-1.5=6
1/2 (6)(2)=6 for the area of the triangle
27+6=33

[torn jolt]

I guess I tried solving this from a wwrong angle but anywyas thanks!! 😄

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[sinful anchor]

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions.
options:

1. 1500
2. 2255
3. 3000
4. 2250

[sinful anchor]

In this questions ig we can't use stars and bars only because the questions are taken distinct ryt so as options are like that

now even if i do some casework i need to select atleast one question from each of the three sections first so i can do that in (5C1)^3 ways and then i need to accomodate for the rest of the two questions
case 1: if i do two questions from the same section
3C1 ways of selecting the section x 4C2 ways of selecting the two questions = 18
case 2: if i do two questions from two diff sections
3C2 ways of selecting the section pair x 4C1 x 4C1 ways of selecting the two questions from each section = 48
So total ways = (48+18) * (125) = 8250 which is nowhere near the options

Please enlighten me over my mistake my brain fr not braining

<@&286206848099549185>

[pure basin]

Hey

So I think we do casework

[pure basin]

Do u have the answer key?

[sinful anchor]

the answer is 4)

[pure basin]

ok

[pure basin]

I got 2250

I took cases

So basically just put values of A=1 and then enter all possible values of B and C then do for A=2 and A=3

[pure basin]

You don't need to select a section and it's not 4 options in a section

[sinful anchor]

ya i get it what u did so like as if u do cases in section

[pure basin]

yes

[sinful anchor]

can u explain more clearly where im going wrong in my approach

[pure basin]

You do not need to select a section

And it has 5 questions in each section not 4

[sinful anchor]

i already had selected 1 question from each section in 5c1 way so 4 questions left out of that 4 i selected

[pure basin]

uh

[sinful anchor]

i believe in my approach entries must be repeating but im unable to understand in which manner

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[torn jolt]

Determine if ${x^2+1,x-2,x+3}$ is L.D or L.I

[glossy valve]

villegas_bozo

[torn jolt]

do i x^2+1 -> (1,0,1), x-2 -> (0,1,-2), x+3 -> (0,1,3) and have to find if {(1,0,1),(0,1,-2),(0,1,3)} are L.D or L.I?

the determinant of the matrix constructed by setting each vector as a column is 5 which is nonzero so my guess is that they are L.I

[onyx glen]

if that helps you, go for it

you're essentially writing the coordinates of each vector in the basis {x^2, x, 1}

most any method to solve this would involve this basis anyway, whether directly or not

tho i would be wary of relying on determinants wholesale as a LI check!

[torn jolt]

alr

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[torn jolt]

.reopen

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✅

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[brittle cliff]

I don't get where I got the g(x) in part c

[robust slate]

They’re integrating each term of f’(t^2) individually

[brittle cliff]

oh i get it

i was thinking where i got that

thank you 😀

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[brittle cliff]

how do I solve this?

[onyx glen]

recognize the summation as a geometric series.

you will need a calculator to evaluate trig functions at x = 1 radian

[brittle cliff]

its a calculator equation

i do 1 / 1-sin^2(1)?

[onyx glen]

missing brackets and also mind your 1st term

[brittle cliff]

like this?

[tender delta]

Yes

[brittle cliff]

ok thank you!

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[ivory stratus]

Our teacher did it with the trigonometry method by assuming a1=sin^2theta and all, but i tried using the quadratic formula and ended up with t=0,1 now every an will be 0 for 2 values of an-1, for example a1 = t = 0,1 and for both values a2 = 0, similarly for a3 and till a1998, so it is something like for 2 values a1997 it will become 0 and similar a1997 it will become 0 for a1996 till the very end which is a1 i just can write the number. I am very confused and i will be very thankful if someone helps me. Thank you! :D

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@ivory stratus Has your question been resolved?

[ivory stratus]

<@&286206848099549185>

:(

<@&286206848099549185>

[languid junco]

when you're doing the quadratic formula and everything, that's fine. this statement is absolutely true for all n

[languid junco]

but when you plug in 1 for n, the t you get is only true for that specific n

like you can imagine t could be 15, and you'd still be able to generate an a_1 from that value right

so t clearly doesn't always have to be 0 or 1

when doing sequences, you cant "jump ahead in time" and assume you already know what a_(n+1) is

by definition, a_(n+1) is generated from a_n

if you do that, you'll get some trivial answer like "0 = 0" in your case, by "solving for t" like you did, you should get t = t

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[silk nexus]

Can someone please explain why was x^2 replaced with zero in the second picture

[languid junco]

y is a function of x, so think of the Differential Equation as

y''(x) = -y'(x) -x^2 y(x)

you could replace y with f is that's easier to think about

[silk nexus]

oh that's so easy then...

shouldn't the question mention it tho?

so that is dy/dx?

So how did we find y'''

the third derivative

at 0

[kindred grove]

take the DE and differentiate both sides (with respect to x)

on the left that gets you y^(3)
on the right, -y' becomes -y''
for the derivative of x^2*y, use product rule

@silk nexus

[silk nexus]

Oh wow got it

[kindred grove]

well then you evaluate it at x=0

[silk nexus]

That's just tricky I did not notice it

Thanks 🙂

[kindred grove]

got other questions about this thing ? @silk nexus

[silk nexus]

No thank you

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[solar glade]

I understand why you use 0 as a, but where does the 8 come from?

[solar glade]

Is it cause there’s a 8 in the denominator?

[gritty flax]

<@&268886789983436800>

[grave valve]

ok why 0?

[solar glade]

Is it cause it equals 0?

[grave valve]

when do u get a vertical asymptote?

[solar glade]

When the denominator is 0

Oh

[grave valve]

correct

[solar glade]

I see

So it’s 8 cause it also equals 0

Thanks

[grave valve]

yeah

[solar glade]

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[torn jolt]

how did they get 1^e

[hot herald]

lim as n to inf of (n+1)/n is 1

[hybrid zephyr]

In n+1/n, take n common

n(1+1/n)/n

That is 1+1/n

n tends to infinity so 1/n is zero

So left is 1

So 1^e

[torn jolt]

not quite

[hot herald]

how so?

[torn jolt]

im confused what u just did

[hybrid zephyr]

The step where u have n+1/n

Take n outside from numerator

n(1+1/n)

[hot herald]

overcomplicated way of doing that,
you can just split the fraction

[hybrid zephyr]

Works

[hot herald]

regardless, the limit of that part is 1

[hybrid zephyr]

Yep

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@torn jolt Has your question been resolved?

[torn jolt]

n/n + 1/n?

[hot herald]

yes

[torn jolt]

1+0

oh

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@torn jolt Has your question been resolved?

[torn jolt]

you can cross multiply like that? @hot herald

[hot herald]

yes, the square root is positive so there is no issue

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[real wasp]

i dont understand.. i solved and got 57.1, but my teacher said this answer is being marked as wrong. 4(8)=32. (pi4^2)/2 is 25.1327412287. add 32 and that number to get 57.1???

[real wasp]

have i done something wrong

[gentle lantern]

radius is not 4, but 2

[real wasp]

could you explain why?

oh my goodness

is it because im focusing on the diameter

[gentle lantern]

exactly

[real wasp]

oh thank you so very much i see now.. this right?

ok that confusion is cleared up TYSM i was wondering like omg this is so simple how is this wrong

gonna go fix

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[glass gorge]

I feel like an idiot can someone walk me through how you actually find the equation given the graph

[glass gorge]

because I feel like I'm very close

it's the stretch factor that's getting me

[sudden condor]

you could've checked the function by testing at x=0
but yea you were close to it

[glass gorge]

how do you mean?

oh wait

it's just plugging the horizontal and vertical asymptotes into the equation no?

[sudden condor]

something like that

$y=\frac{a}{x-h}+k$

[glossy valve]

yoboiqimmah

[glass gorge]

gotcha

[sudden condor]

asymptotes are x=h and y=k

[gentle lantern]

just see where the asymptotes in the x axis are, that is where the denominator will be 0

[glass gorge]

I understand hold on

and the vertical goes into the denominator the horizontal is added

[sudden condor]

yep

[glass gorge]

so given the equation your asked to procure the graph but how would you do that?

[sudden condor]

I would start by drawing traces of the asymptotes
then check x-intercepts and y-intercepts
and then i'll draw it out

[glass gorge]

gotcha one moment

so the horizontal asymptote in this case is the numerator and the vertical is the denominator?

[glass gorge]

or what did I miss?

[sudden condor]

nope the horizontal asym. is the eqaution y=k here

[glass gorge]

so how do I translate this into the formula?

[sudden condor]

function doesn't look clear

[glass gorge]

x-8/x+2

[sudden condor]

for this type the horizontal asym. is not obvious at first but it's the ratio of the coefficients of the highest degree terms

[glass gorge]

how do you mean?

[sudden condor]

$y=\frac{ax+b}{cx+d}$

[glossy valve]

yoboiqimmah

[sudden condor]

the vertical asym. here is x=-d/c
and the horizontal asym. here is y=a/c

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[glass gorge]

@sudden condor I'm confused how would I apply that

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[drifting summit]

Prove the function f: R -> R, f(x) = floor(x) is itnegrable over [0, n] and find it's integral

[drifting summit]

My idea was to use the ART,

Let $$(P_n)$$ be a sequence of Regular partitions divided into n intervals. We must show $$\lim\limits_{n \rightarrow \infty} \displaystyle\sum_{i=1}^{n}U(f, P_n) - L(f, P_n) = 0$$

[glossy valve]

toast

[drifting summit]

$$\lim\limits_{n \rightarrow \infty} \displaystyle\sum_{i=1}^{n}(M_{i} - m_{i})(x_i - x_{i-1}) = \sum_{i=1}^n (i-(i-1)) \cdot 1 = \sum_{i=1}^n 1 \neq 0$$

[glossy valve]

toast

[drifting summit]

hm i think i mgihtve done somethign wrong...

$$\lim\limits_{m \rightarrow \infty} \displaystyle \sum_{i=1}^{n}(M_{i}-m_{i})(x_{i} - x_{i=1}) = \lim\limits_{m \rightarrow \infty} \sum_{i=1}^n \bigg(\dfrac{in}{m} - \dfrac{(i-1)n}{m}\bigg)\bigg(\dfrac{n}{m}\bigg) = 0$$

[glossy valve]

toast

[drifting summit]

maybe its suppsoed to be like this

ignore typos

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@drifting summit Has your question been resolved?

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@drifting summit Has your question been resolved?

[devout inlet]

I think this could be useful to you (see the part at the end about mathematical induction to relate to your problem)

I think your approach works too though.

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@drifting summit Has your question been resolved?

[drifting summit]

Yeah

Used Archimedean Riemann theorem

[drifting summit]

Have to really look into this

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[ember socket]

we can see that the horizontal assymptote occurs at y=4 and the veritcal assymptote occurs in x=-1, let x=-1 and y=4 be the asymptotic origin there fore we can see that there are no reflections to the graph. lets take the point (-2,3) and that is the dilation point. with our 2 assymptotes, let y=(a/(x+1))+4 then sub in point (-2,3). we get 3=(a/(-2+1))+4 then -1=a/-1 then a=1. therefore there is no dilation and we can confirm that the equation to this rectagular hyperbola is: y=(1/(x+1))+4. i think you may have mistook the -2 as the assymptote.

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[dim gyro]

what are the rules concerning taking a dervative x^Ax

i thought it would be 2x(A+A^t)

but im wrong so im just confused

[twin wolf]

how did u get 2x(A+A^t)

[dim gyro]

i mean i was just using the product rule where you take the dervative of x and you hve ax+ a^t x

[unique wagon]

where did the variable t come from

[dim gyro]

its the transpose.

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[young hearth]

currently trying to find the x and y intercepts right now for this polynomial but I’m currently stuck if these are my zeros or not

[young hearth]

It feels like i’ve made a mistake somewhere

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[stable bane]

Solve for 0 ≤ theta ≤ 2pi

[trail pike]

assign x to cos theta then solve the inequality for x, then substitute x for cos theta then solve for theta

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[hollow vessel]

Prove that the greatest common divisor of a and b, as defined in the text, can be obtained
by factoring a and b into primes and collecting the common factors.

I have an idea to use something with the cyclical groups of the integers on a and b but i cant seem to figure out how to fit the pieces

[covert heath]

'cyclical group of integers'-

analysis?

[hollow vessel]

abstract algebra

[covert heath]

oh no

[hollow vessel]

T_T

Its seem to me that aZ ∪ bZ = gcd(a,b)Z by definition

[devout nova]

cuz primes cannot be decomposed any further

[hollow vessel]

Yea but how would I prove that formally

Using group theory cause it is an abstract algebra class

[covert heath]

maybe try the channel for AA?

[hollow vessel]

Oh sorry is this not the right channel?

[covert heath]

I mean, more advanced topic

[hollow vessel]

Ah gotchu thx

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[desert breach]

testing for converge/diverge

would seperating the series into two series work

[onyx glen]

no

[desert breach]

why not

[onyx glen]

you would get a difference of two series which both diverge

you cannot say anything about that

[desert breach]

so how do i solve this

[onyx glen]

writing as $2^{1/n} - 1$ might lead you to some ideas

[glossy valve]

Ann

[onyx glen]

and remembering a particular famously divergent series also

[desert breach]

i mean yeah harmonic

if not TFD likely use a comparison test

not sure how id compare to 1/n

[desert breach]

how does that help though

i went through that process already and it just leads me to a more complicated series

[gritty rose]

show

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[celest tapir]

If I have:
$$f(z) = \begin{cases} \frac{\bar{z}\abs{z}^2}{z^3} & z \neq 0 \ 0 & z = 0 \end{cases}$$
How do I check continuity using the $\varepsilon-\delta$ definition?

[glossy valve]

dyxn

[celest tapir]

If you plug and chug you get 1 < ep

[onyx glen]

you get |f(z)| = 1 everywhere in fact

[celest tapir]

yeah

[onyx glen]

yeah so

ain't no way shit could ever be continuous

simple as

take ε = 0.42069 or sth

[covert heath]

😭

[onyx glen]

f(z) never gets within that much of 0

[celest tapir]

$0 < \abs{z - z_0} < \delta \implies \abs{f(z) - f(z_0)} < \varepsilon$

[onyx glen]

yeah i used the funny number, deal w/ it :PPPP

[glossy valve]

dyxn

[celest tapir]

This is the implication right?

[onyx glen]

sure

but its consequent is false no matter the z if we take ε = 0.42069

[celest tapir]

"For every epsilon, there exists delta..."

Ah so for epsilon = 0.42069 there is no delta

Is that right @onyx glen ?

thanks

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[rigid glen]

i have been stuck on this geometry problem for a while how do i draw the object described in this and how do i find out if the points are equidistant
Given a line segment AB, prove that the points A,B are equidistant from any line(e) that passes through the midpoint M of the segment AB.

[rigid glen]

I have done this but I am not sure if it's correct

[steel solar]

Yep. That works.

Just show that in general, the 2 triangles will be congruent.

[rigid glen]

english is not my main language what is congruent

[subtle hatch]

Same shape and sizs

E

[rigid glen]

oh

thanks

[rigid glen]

yeah but even if they triangles are congruent can you explain to me how that makes the points A and B have an equal distance from the line e

i know they will be but why

[steel solar]

Well, then AE1 and AE2 would be the same length, right?

And isn’t that what you desire?

Becuase congruent triangles have the same angles and same side lengths.

[rigid glen]

ohh yeah

[steel solar]

(E1 is a point, right?)

Or, if you get what I mean.

[rigid glen]

not given by the exercise but yeah

it is

anyways thanks!

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[lapis marsh]

determine if this is an arithmetic sequence or a geometric sequence

determine v, U20,S20
q, u20, s20

I already know the arithmetic sequences but I don't know the geometric sequences yet I was unfortunately not present at that lesson

I did get the formula

Recursive: Un-1 . Q
Explicit Un = U1. Q ^n-1

For the sum of the first n terms

Sn = U1. (1-q^n)/ (1-q) if q is not equal to 1
Sn = n.u1 if q = 1

[lapis marsh]

Full exercise I already know a,b c are not arithmetic sequences and geometric sequences

@half rover

[covert heath]

<@&268886789983436800> here to

too

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[meager bison]

Hey

[meager bison]

I need helping

[solid ruin]

[honest hill]

!da2a

[full forum]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[honest hill]

use log rules

[meager bison]

How

What’s the log rules

[onyx glen]

properties of logarithms

such as $\log_a(x) + \log_a(y) = \log_a(xy)$

[cursive tusk]

logx-logb=log(x/b)

[glossy valve]

Ann

[onyx glen]

do you know these?

[meager bison]

No

[honest hill]

,tex .log rules

[glossy valve]

Bonk

[honest hill]

have you ever seen these?

[onyx glen]

is this an "i was sick for N weeks and now i have this homework and i am completely lost and have never done anything like this before" type situation

[meager bison]

Yeah but don’t know how to use it

Yeah it’s hard lol

Can you solve it step by step

[honest hill]

use the product rule

[honest hill]

!noans

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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.

[meager bison]

I don’t even know what I’m doing

[void nova]

Well, can you at least give an attempt and show it to us?

[void nova]

It is not that hard to recognize how to use this in your exercise

(I'm not saying that you only need that to solve the whole exercise, by the way)

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@meager bison Has your question been resolved?

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[plucky grove]

i dont understand how they got to

[honest hill]

!original

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

[plucky grove]

its above what i just send

unless you want the untranslated version

[honest hill]

ik vind het leuker om het in het nederlands the lezen 🙂

[honest hill]

je hebt g(x)=f'(x)

[plucky grove]

yup

[honest hill]

dus $\int g(x)\dd x=\int f'(x)\dd x=f(x)$

[glossy valve]

Bonk

[honest hill]

want integraal is het omgekeerde van de afgeleide

[plucky grove]

oh ja

ik snap het

dank je wel

[honest hill]

en met de grenzen erbij $\int_p^{2p} g(x)\dd x=\int_p^{2p} f'(x)\dd x=f(2p)-f(p)$

[glossy valve]

Bonk

[honest hill]

heb je weleens $\int_a^b f(x)\dd x=F(b)-F(a)$ met $F'(x)=f(x)$ gezien?

[glossy valve]

Bonk

[plucky grove]

nee

of wacht eens ff

ja als F gewoon primitieve betekent dan wel

[honest hill]

ja, F is primitieve

de afgeleide van de primitieve is gewoon weer de functie

dat is dus wat deze vraag is

[plucky grove]

ja ik heb het door dank je

[honest hill]

🙂

!done

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[plucky grove]

.close

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[tough dirge]

im looking at just the first derivative right now

[tough dirge]

wouldnt it be equal to y' = -1/2(e^x-e^-x)

since the derivative of e^x is just e^x but with e^-x the derivative of that you would use the chain rule (?)

[rapid rain]

e^(-x) derivative can be computed with chain rule

[rapid rain]

but this is false

[tough dirge]

how then?

oh

i think im dumb

the negative one multiplies with e^-x and goes inside the parentheses

got it now

.close

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[woven ice]

This is really testing me rn

The Side lengths giving are
xy+z
5x2-xy-z
3z+2
x2-3y
?

I’m tryna find the missing side length

[rapid rain]

yeah

[woven ice]

The perimeter is on there

[rapid rain]

so do you know how to proceed?

[woven ice]

No, I don’t remembers

I’m reviewing

[rapid rain]

what's the perimeter?

[woven ice]

Let me get it

[rapid rain]

not the value

what's the link between the perimeter and the side lengths?

[woven ice]

14x*2+-7z+1

[rapid rain]

missing +3xy

but that's the value of the perimeter

[woven ice]

Yes

[rapid rain]

I want to know more generally

what's the link

between the perimeter

and all the side lengths

[woven ice]

It just gave me the perimeter and 4 side lengths, it wants me to find the 5th

It’s the missing one

[rapid rain]

uh huh

but follow me for a moment

if you didn't have the value of the perimeter

[woven ice]

It’s grade 9

[rapid rain]

but you had the value of the 5th length

say it was T

how would you get the perimeter?

[woven ice]

Add them all up?

[rapid rain]

well yeah

[woven ice]

By the common values

[rapid rain]

so

you're looking for the missing side length, call it T

you know that the perimeter is just the sum of all the side lengths

[woven ice]

Mhm

[rapid rain]

so what's the perimeter in terms of T?

[woven ice]

I’m blanking

Maybe add them all up and then minus?

[rapid rain]

you might be skipping steps

Right now I don't want you to find T

(even though that's our end goal)

[woven ice]

Ok

[rapid rain]

I know 4 of the 5 side lengths

and I decided to call T the missing one

what would the perimeter be then?

[woven ice]

Are you asking me or is this like a problem for me to solve

Bc ik the perimeter

[rapid rain]

this is something to just deduce

[rapid rain]

forget about the fact that this knowledge exists

erase this value from your mind for a moment

[woven ice]

I would add them up using the common factors

Each side length

[rapid rain]

what would this get you?

Yeah, add up each side length

[woven ice]

The total for the 4, but missing the 5th

[rapid rain]

ok, but technically if we call the missing 5th length "T"

we have them all

so what's the perimeter in that case

[woven ice]

I’m following

[woven ice]

The total for 4 plus T

[rapid rain]

yes

so can you calculate that?

[woven ice]

I can try

This might take me a while lol

I’ll tell you when I’m finished

I got 6x*2+3z+2-3y

For the total

@rapid rain

[rapid rain]

lemme check

[rapid rain]

+T

[woven ice]

Yea

Did I get them right?

Adding them up

[rapid rain]

$6x^2 + 3z - 3y+2$

[glossy valve]

rafilou is not not born in 2003

[rapid rain]

looks correct

ok

so

$Perimeter = 6x^2 + 3z - 3y+2+T$

[glossy valve]

rafilou is not not born in 2003

[rapid rain]

but now, we can remember that we actually know the value of the perimeter too!

[woven ice]

Yea

[rapid rain]

$Perimeter = 14x^2 + 3xy - 7z + 1$

[glossy valve]

rafilou is not not born in 2003

[rapid rain]

so now

how do we find the missing length T?

[woven ice]

So we find the difference?

[rapid rain]

the difference between what and what?

[woven ice]

The 4 lengths and the perimeter

And the difference will be T

[rapid rain]

so 4 lengths - perimeter?

or perimeter - 4 lengths?

[woven ice]

Perimeter- 4 lengths

[rapid rain]

yes

[rapid rain]

the sum of 4 lengths is this

[woven ice]

I can even tell some of them right away

[rapid rain]

the perimeter is this

[woven ice]

Let me start with the x^2

It’s going to be 6x^2

[rapid rain]

?

[woven ice]

12x^2 - 6x^2

[rapid rain]

12?

[woven ice]

Ooh

It’s 14

So 8x^2 then

-10z will be another one

Wai

When me minusing do we flip the signs

Because I have +1 - +2

So -1

And we can’t minus the others

So in total

$8x^2+3xy+3y-10z-1$

[glossy valve]

AJ

[woven ice]

Is that correct for the missing lengthy

[rapid rain]

let me rewrite it

$T = ( 14x^2 + 3xy - 7z + 1) - (6x^2 + 3z - 3y+2)$

[glossy valve]

rafilou is not not born in 2003

[rapid rain]

$T = 8x^2 + 3xy -10z + 3y - 1$

[glossy valve]

rafilou is not not born in 2003

[rapid rain]

yes you're correct

[woven ice]

Oh so that’s the answer?

Yay!!!

Thank you so much, I have another problem of you don’t mind

*if

Lemme write it out

My handwriting sucks

Number 11

[rapid rain]

so again

if you knew that missing side length

how would you get the volume of the shape?

[woven ice]

Volume is length times width times height right

We have length and height

3 and 6x

Making it 6x times three

Which idk bc I’ve never times a variable by a number

Because in my unit they are different

[rapid rain]

the constants multiply with each other

the same variables are multiplied with each other

so

5z * 2zy = (5 * 2)(z * z)y = 10z^2 y

[woven ice]

So how would I time’s 6x times 3

[rapid rain]

6x * 3 = (6 * 3)x

constants times constants

x times x

y times y

z times z

etc...

[woven ice]

Ok so we have 18x

And our volume is 18x^2+54x

So I’m guessing

We divided

Divide?

[rapid rain]

yeah

again

if "T" is the missing side length

then 18x * T is the volume

but the volume is also 18x^2 + 54x

so T is the division

[woven ice]

How would I do that

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@woven ice Has your question been resolved?

[woven ice]

Not yet

Um guys he went offline

Annnyone open…?

?new person needed

?close

!close

!solved

<@&286206848099549185>

My helper left

Idk what to do

.close

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[sturdy obsidian]

$\int_i^{\pi} x^{dx}$

[glossy valve]

Kaikhosru Shapurji Sorabji

[onyx glen]

nope

this is definitely a troll question

[sturdy obsidian]

is this actually not possible

https://www.youtube.com/watch?v=VVF2nZ0WOY4

because this exists

[sturdy obsidian]

it's got a minus 1 though, it cancels out when you do the taylor expansion of e^ln(x)dx

[onyx glen]

so he managed to assign it some kind of meaning by some formal manipulation

you are taking it more seriously than you should be

what is your goal here?

to play around with formalism and unhinged notation?

[sturdy obsidian]

Yes

[onyx glen]

ok then ill leave you to it

[sturdy obsidian]

No worries

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[manic cape]

if i have an isoceles triangle

[manic cape]

pqr

pq=qr

then which angles will be equal?

[knotty grail]

p and r

[manic cape]

the angle which is in front of that side

right?

[sick vortex]

yeah "front" or "opposite" however u look at it

what blurple said tho

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[manic cape]

how I solve it?

.close

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[torn jolt]

I don't understand how to solve it, I know the following:
Y1 ~ N(2mu, 2sigma²)
Y2 ~ N(0, 2sigma²)

I thought maybe I could use Covariance here to prove it, but I'm not sure since my lecturer taught me the following: If variables X and Y are independent, Cov(X,Y) = 0. But he said, that if Cov(X,Y) = 0, it doesn't always mean they're indepedent

[rustic frigate]

If I remember correctly it’s an iff when the distribution is normal

So look that up in ur book/notes and that would in this case be valid

[torn jolt]

Yeah I mean it also seems like the only possible way I can prove it, thank you I'll try to find something

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[minor cliff]

So like I understand how the first condition is proven correctly, cause the series is clearly approaching zero.

But what I don't understand is their argument for S2N equaling The Nth partial sum for which I presume to be SN equalling zero..?

Like how tf do they know that and we aren't even given an equation, nor do they seem to really use one here it's almost as if they applied common sense but I can't quite think of it, could anyone help me?

[minor cliff]

(yes you could make it out an equation by looking at those set of numbers, but clearly thats not needed I suppose seen by how easily they just argued that the 2nd condition is not met)

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@minor cliff Has your question been resolved?

[gritty rose]

are we supposed to know what "second condition" is

[minor cliff]

Well it's for alternating series that converge here I'll tell you the two conditions

1.) Lim (an) as n -> infinity, is equal to Zero.

and 2.) a(n+1) is less than or equal to a(n). In other words, it's a fancy way of saying that the sequence is decreasing.

[minor cliff]

Sorry if I didn't state it, but its basically the two conditions an alternating series must meet, in order to converge.

Part of the infinite series chapter of BC Calculus

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@minor cliff Has your question been resolved?

[gritty rose]

Put parentheses around consecutive terms to see why S_(2N) = S_N

2/1 - 1/1 = 1
2/2 - 1/2 = 1/2
2/3 - 1/3 = 1/3

[minor cliff]

holy shit

lmaoooo

I didnt even realize wtff

[minor cliff]

Wait so its equal though, because multiplying it by two doesn't change the fact that it still approaches zero correct?

Unless, you weren't multiplying by two, and instead 2N is basically saying 2 terms..?

[gritty rose]

what is "it"

[minor cliff]

The terms you put paranetheses around

[gritty rose]

S_N is the Nth partial sum

the line above that is wrong

but the quotes are correct