help-27

[woven radish]

ƒ(Why am. I here)=I don't know

[limber granite]

take logarithm both sides

[lost laurel]

would that work here?

[limber granite]

we can try

[lost laurel]

I don't think a neat integral solution exists

[limber granite]

true

[lost laurel]

@restive river are you sure it isn't 243

that would make it much easier

[limber granite]

yeah lol

then either x = 5 y = 0 or y = 5 x = 0

[lost laurel]

yup

wait

[limber granite]

yeah wait

[lost laurel]

no 3^0=1

[limber granite]

yes

hmmm

[lost laurel]

so 244 maybe?

[limber granite]

yeah lol

[stable wraith]

it has infinite solutions for x and y

[limber granite]

i suppose

[stable wraith]

what class is this?

[limber granite]

11th probably

@restive river

[lost laurel]

looks like college level stuff to me

espescially as the solutions aren't neat

[limber granite]

hmm

[stable wraith]

i dont see what college course this would be

[limber granite]

thanks for what

we didnt solve it yet

[lost laurel]

is this problem even right?

[stable wraith]

$y = \log_{3}(234-3^x)$

[limber granite]

can u recheck the question

[woven radish]

caspar

[glacial geyser]

[limber granite]

yeah I don't see any integral solutions

heyy @restive river where did u find this question

[limber granite]

x = 5, y =2

or the opposite

no wait

not opposite this time

[limber granite]

this is the solution

[lost laurel]

ok, yeah

yes

also !nosol

[limber granite]

:)

nosols?

[lost laurel]

!nosols

[devout snow]

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

[limber granite]

wht does tht mean

ohh

i am sorry

[stable wraith]

doing this problem seems like mostly trying until you get the answer no?

or did you have a trick

[limber granite]

yeah

hit and trial

[stable wraith]

boring

[limber granite]

the trick might be to take the value of x closest to 234

and then seeing wht value of y satisfies it

[stable wraith]

you need to type .close

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[lunar kiln]

,rotate

[lunar kiln]

What sub do I use here

[runic trellis]

I'm thinking $t=\pi - x $ may be good idea.

[lunar kiln]

idk i tried taht

im still stuck with the sin

[runic trellis]

You mean you get $\sin (\pi-t)$?

[woven radish]

Crystopher

[lunar kiln]

yh

i gey $-t^2\sin(\pi-t)$

[woven radish]

Big Chicken

[runic trellis]

Use that
$\sin (\pi - t) = \sin t$

[woven radish]

Crystopher

[lunar kiln]

then i still have $-t^2\sin(t)$

[woven radish]

Big Chicken

[lunar kiln]

dont know what to do there

[runic trellis]

Ye, from there I can only see using partial integration two times to solve it.

[lunar kiln]

breh

im in hs

we havent been taught that yet

ion even know how to do by parst

parts*

[runic trellis]

Only thing I can think of is to try and see if the integrand has some symmetrical properties so that you don't need to compute it.

Yes, use the substitution which gives you integrand $t^2 \sin t$. Observe the integrand and the new integration bounds when substituting.

[woven radish]

Crystopher

[lunar kiln]

huh

ok

u get pi/2 --> -pi/2

[runic trellis]

yes, you can flip the bounds by flipping the sign of the integral. So you should then get -$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} - t^2 \sin t dt =$\
$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} t^2 \sin t dt$

[woven radish]

Crystopher

[lunar kiln]

ok

so because the whole function is odd

it equals 0

[runic trellis]

exactly

[lunar kiln]

oh ok i see

thank u

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[rugged peak]

just wanna make sure this is correct

[rugged peak]

.close

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[cedar vault]

Hello I dont understand this step

[cedar vault]

Why did we do x+1 = 0 and x^2 - x+ 1 = 0

Can we do this with any multiplying variables?

what is this rule called

e.g if we had

(x+1) ( b - d - 3) = 0

could we write both seperately?

as x+1 =0
and b-d-3 = 0

because i never have studied that parts of equation are equal to result

as for example (2+2) (2+3+5) = 40

so 2+2 = 40 doesnt make sense

please anyone guide me

[safe jasper]

https://www.google.com/search?q=zero+product+property&rlz=1C1VDKB_enUS993US993&oq=zero+product+pr&gs_lcrp=EgZjaHJvbWUqBwgAEAAYgAQyBwgAEAAYgAQyBggBEEUYOTIHCAIQABiABDIHCAMQABiABDIHCAQQABiABDIHCAUQABiABDIHCAYQABiABDIHCAcQABiABDIHCAgQABiABDIHCAkQABiABNIBCDIwMDFqMGo0qAIAsAIB&sourceid=chrome&ie=UTF-8

if you have a product of expressions that equals 0, then for the product to be 0, at least one of the expressions has to be 0

so you can separately consider the cases where x+1 is 0, or x^2 - x + 1 is 0

[cedar vault]

hm that makes sense

[safe jasper]

and if you had a more complicated expression

like abcd = 0

you know that at least one of those must be 0

so you can consider the cases a = 0, b = 0, c = 0, or d = 0

[cedar vault]

so we imagine all of those

ahh thank you so much

🙂

[safe jasper]

happy to help

[cedar vault]

,close

.close

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[honest thorn]

integrate (e^√x) / (√x)

[honest thorn]

u=√x

[safe jasper]

du?

[honest thorn]

dx= 2√x du

[safe jasper]

so integrand becomes e^u / u

dx becomes 2sqrtx du

[honest thorn]

yes

[safe jasper]

is there a way to get everything in terms of u?

like can you rewrite 2sqrtx du

[honest thorn]

i simplified it to 2e^u

[safe jasper]

yeah that's right

dx = 2u du

so integral becomes e^u / u * 2u du = 2e^u du

now you just integrate that normally, and then resubstitute

[honest thorn]

is the answer 2e^u + C

i mean

2e^(√x) + C

[safe jasper]

yes

[honest thorn]

thtanks

[safe jasper]

happy to help

[honest thorn]

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[restive river]

i got D

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[winged hearth]

.

[winged hearth]

How would i change the sin81

To sin21 cos21 etc

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[dull orbit]

in a combination 40-8-12 Choose 6 , i remove 2 different with no common members A with 8 members and B with 12. How can i express this combination NOT A u NOT B?

[limber granite]

i dont get ur question

[dull orbit]

i have two groups i want to remove, the total is 40 people, and i want to remove the group A and B

and choose 6

is 40-8-12 choose 6 -> NOT A u NOT B?

with u

[dusky drift]

Could your provide complete context?

[dull orbit]

this is the complete context

overall P(NOT A u NOT B) = (40-8-12 C 6) / (40 C 6)

[limber granite]

can u take a picture of the question from ur book or wherever u got it from and send it here so we can better understand the questions and help you better

[dull orbit]

In a group of 40 students, there are:
8 first-year students,
12 second-year students,
10 third-year students, and
10 fourth-year students.
This group has 6 invitations for a concert. To ensure no member of the group is treated unfairly, the members will hold a lottery, and the six lucky winners will each receive one invitation. Find the probability that the group does not include any first-year or second-year students.

[limber granite]

ok

so all you need to do is think that you only wna invite third and fourth year students

out of all the students

now there are 20 students combined from third and fourth year

and you gotta choose 6

so it's 20 c 6

the total number of ways you can select 6 students is 40 c 6, since there are 40 total students and you need to invite 6

so the probability comes out to be 20 c 6 / 40 c 6

[devout snow]

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[agile oyster]

hi requesting help with derivative of e^x

d /dx (f(x)) = e^x

This is my work so far:

d/dx e^x = lim _{h->0} f(x+h) - f(x) /h

lim _{h->0} e^{x+h} - e^x /h

| exponent rule a^{n+h} = a^n * a^h -> e^{x+h} = e^x * e^h

lim_{h->0} e^x * e^h - e^x / h

| we can factor out e^x

lim_{h->0} e^x(e^h - 1) /h

but how can i proceed from here?

[lost laurel]

limit of (e^h-1)/h at 0?

[agile oyster]

yea essentially if we can already proceed on taking the limit. Thought maybe we need to simplify the numerator a bit futher?

simplifyt the fraction futher**

[lost laurel]

do you know the limit as a standard result ?

[agile oyster]

No im not sure what you mean with that

[lost laurel]

do you know this?

[agile oyster]

Form my understanding we substitute h = 0 as h aproaches 0 is this what you are refering to?

I have factored out the h in previous tasks to not have to deal with the h in the denominator

[lost laurel]

no

I'm asking if you kow what e^h-1/h is near

[agile oyster]

no i dont know i don't think so

i know the derivative of e^x is e^x but im trying to see how to get there.

[lost laurel]

yeah

for that use the fact that the limit is 1

[agile oyster]

since we cant have 0 in the denominator we go for 1 in scenarios like this?

[lost laurel]

no, this limit specifically is 1

I can give an explaination that involves series if you want

so basically $e^h =1+h$ near h=0

use that

[woven radish]

ƒ(Why am. I here)=I don't know

[agile oyster]

hmmh m i feel like this should make sense

and this is diretly tied to the fact that the h is an exponent?

[lost laurel]

each infinietly differentiable function can be expressed as a polynomial about any point where its continuous and defined

so as we want the polynomial function near 0

I took the first two terms

this is the power series of $e^x$

[woven radish]

ƒ(Why am. I here)=I don't know

[agile oyster]

might take me a while to wrap my head around this.

[lost laurel]

take your time

[agile oyster]

what i see here infinitely expanding series of values for x

[lost laurel]

for $e^x$

yes

[woven radish]

ƒ(Why am. I here)=I don't know

[agile oyster]

yea

[robust dust]

don't you need to know the derivative of e^x to compute the taylor series in the first place? (so using it to find the derivative is circular logic)

[agile oyster]

hmh ok

[lost laurel]

true, but this is a way to understand the limit

e^x~1 at 0 is evident

[agile oyster]

but if i got it right as the series is expanding outwards when lim -> 0 we look at what is as close to x=0 on the series and there is 1+ {series}?

The derivative of order zero of f is defined to be f itself and (x − a)0 and 0! are both defined to be 1.

I guess this is what we are to some amount talking about

anyway this is going to take a while to unravel.

If you can confirm if this is what you meant (Maclaurin series and Taylor series) is where the arrival to why d/dx e^x is itself i'l take a look at it with time

and i can open the thread for other people who need help and not take up the space and time ^^

[lost laurel]

you should probabaly just learn the result for now

and no, don't close this

someone will help

I can't because I don't understand how the series is derived

but many people here do

[agile oyster]

I do aprechiate the help a lot regardless

$\lim_{ h \to 0} \frac{e^{x-h}-e^x}{h}$

doesn't recognize mine

[lost laurel]

no space between the last dollar and the {h}

[woven radish]

HydroH

..,,

..,,

[agile oyster]

Sure i'l work on it a bit.

just little question before i start

[graceful charm]

why not simple take e^x comon and out of the equation and apply l hospital;s rule
im not that advanced but thats how me and friends do it at school

[agile oyster]

ok

o yea we have the definition of euler's number here essentially

both are the same

Yea i believe so.
My words would be

"eule'rs number is defined by the second thing you showed me, e = \summation 1/n!"

and to get e^x

lim n -> \inf (1+x/n)^n = e^x

seems reasonable whoever not 100% where that comes from but i can accept that

https://wikimedia.org/api/rest_v1/media/math/render/svg/2f9a1f86072b07e1f69d5e21571c207d52680d8f

Sure i think so

na i think im running in circles i think perhaps i missunderstood your question too.

$\lim_{ y \to \infty }\left( 1+\frac{1}{\frac{n}{x}} \right)^n= \lim_{ y \to \infty }\left( 1+\frac{x}{n} \right)^y$

Current loop lol

[woven radish]

HydroH

[agile oyster]

oh!

should i keep the limit as y -> inf?

I got to admit im a bit lost here ^^ i aprechiate the help regardless.
Probably a bit over my head this is my second day studying derivatives.

So far it seems i can unfortunately just replicate what you are saying :/ sorry about that.

$\lim_{ y \to \infty }\left( 1+\frac{1}{y} \right)^n\mid\mid y = \frac{n}{x}\to n = yx$
$\lim_{ y \to \infty }\left( 1+\frac{1}{y} \right)^y$

Let see if it likes takes / reads this properly

[woven radish]

HydroH

[agile oyster]

$$\begin{align}
&\lim_{ y \to \infty }\left( 1+\frac{1}{y} \right)^n\mid\mid y = \frac{n}{x}\to n = yx \
&\lim_{ y \to \infty }\left( 1+\frac{1}{y} \right)^y
\end{align}$$

[woven radish]

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

[agile oyster]

y = n/x
its in there?

Anyway i'l work on this but i have to take a break eat and do irl things.

I'l get there, maybe tomorrow ^^

[woven radish]

..,,

[agile oyster]

and thus we get e^x

Okay wow thats pretty nice i'l go over it in more detail later tonight for sure but it seems to make sense

yea and since we had e^x factored out e^x 1 = e^x

damn thats pretty good

Well done i think i followed your explanation surprisingly well

I shall with the hopes that you have a fantastic day and ty so much

.close

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[uneven ginkgo]

how do i do this

[sand dove]

you can do a sum/integral comparison

[uneven ginkgo]

yea setting up an integral from 1-inf for 2/x^5 but what is the accurate part about

[sand dove]

nono, you sum up to a certain n

and so the accuracy is how much you're off from the total sum

it's the difference

$\sum_{k=n+1}^\infty\frac{2}{k^5}$

[woven radish]

rafilou2003

[uneven ginkgo]

so it needs to be accurate to the 10^-7th decimal?

[sand dove]

not exactly but close

[sand dove]

this just has to be smaller than 10^-7

[uneven ginkgo]

so just plug and check?

[sand dove]

well no

plugging in would be too tiresome

you have to do it the smart way

aka compare it with the integral

$\int_{n+1}^{\infty}\frac{2}{x^5}dx$ and $\int_{n}^{\infty}\frac{2}{x^5}dx$

[woven radish]

rafilou2003

[uneven ginkgo]

aight got u

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[restive river]

Why is this true?

[final scarab]

6.28 is approximately equal to 2pi

[restive river]

Oh so is it asking for the other zero?

Because I thought it would just be 0

[final scarab]

no

do you know how to calculate minima

find values of x such that f'(x) = 0

[restive river]

Then if it's negative before it's minial

?

[final scarab]

then put that x in f''(x). if f''(x) is negative then that x will give a maxima point and vice versa

[restive river]

I see

Let me go do that

[final scarab]

👍

[restive river]

Did I get the derivative correctly? @final scarab

[final scarab]

,w differentiate sqrt (x) * sin x

[woven radish]

Results provided by WolframAlpha

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

Requested by sirgareth1

[final scarab]

uh no

show work

actually theyre equivalent mb @restive river

[devout snow]

@restive river Has your question been resolved?

[restive river]

Wait so can you further explain why the answer is 6.28

Mb I went to go do something

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@restive river Has your question been resolved?

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@restive river Has your question been resolved?

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[placid rover]

-x =< y =< 0 OR 0 =< y =< -x
-x/2 =< y + x/2 =< x/2 OR x/2 =< y + x/2 =< -x/2
|y + x/2| =< x/2 OR |y + x/2| =< -x/2
|y + x/2| =< |x/2|
|2y + x| =< |x|

[placid rover]

would someone mind verifying this is correct

.close

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[placid rover]

verified zz

[heavy current]

[nova glen]

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[wary ruin]

Can someone help me the solution foor the left imag?

[solid oriole]

So are you trying to find the volume, or...?

[wary ruin]

"Deescribe the region in cylindrical coordinats" @solid oriole

[restive river]

lost on whats being asked

[wary ruin]

Deescribe the region in cylindrical coordinats, spusho

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[topaz beacon]

youre maximizing the area

reread the problem.carefully

[foggy spoke]

How to set it up as a maximizing problem

Hm

Oh I solved got area

For

Not perimeter

[topaz beacon]

<@&268886789983436800>

[foggy spoke]

Thanks guys

.close

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[sonic geyser]

is this correct <@&286206848099549185>

[outer yarrow]

Your handwriting is ass I can’t tell

[sonic geyser]

i send again

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[solid oriole]

So is the problem "Evaluate $\int_0^{\infty}(x+1)dx$"

[woven radish]

خرشوف

[lethal jacinth]

the integration becomes x^2/2 + x

[devout snow]

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[devout snow]

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[abstract ginkgo]

the air of a rectangle is 15m
If the width is 5 meters bigger than the length the what are the dimensions?

[abstract ginkgo]

I know I need to do substitution with two formulas

But I currently only have one

Idk how to make the second one

[shut pagoda]

what is your first one

[abstract ginkgo]

15 = x * x+5

[shut pagoda]

you already did the substitution

you can just solve it now

[abstract ginkgo]

wait

I’m actually slow

X = sqrt 10?

[shut pagoda]

make sure you remember the parenthesis

[young zodiac]

what does air of a rectangle mean

[shut pagoda]

its (x)(x+5)=15

[abstract ginkgo]

I need to develop

[abstract ginkgo]

Surface

[shut pagoda]

area?

[abstract ginkgo]

Yes

Sqrt 3 / 2 = x?

[young zodiac]

so x^2+5x-15=0

[abstract ginkgo]

15/5 = 3

Factor out the square root

Sqrt3 = x+x which is also 2x

[young zodiac]

so this is the answer

[abstract ginkgo]

How

[shut pagoda]

do you know the quadratic formula

[abstract ginkgo]

Yes

Wait I can quadratic it

[shut pagoda]

just use that on x^2+5x-15=0

yeah

[abstract ginkgo]

X^2 + 5x - 15

[shut pagoda]

no

how did you get that

[abstract ginkgo]

And then I’ll have admissible and on inadmissible formula

Or answer

Not formula

[shut pagoda]

yeah

[abstract ginkgo]

2 and -7

Ty guys

[young zodiac]

what

how did you get 2 and -7

[abstract ginkgo]

Quadratic

If I have a expoentioa function and a linear function and I need to see if they intercept

Do I put them on opposing sides of the equation

Develop and then use the discriminate?

[devout snow]

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[devout snow]

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[cursive vapor]

#6

[surreal night]

,rotate

[surreal night]

!status

[devout snow]

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

[cursive vapor]

1

this is new to me

[surreal night]

what are the requirements to be a function

[cursive vapor]

i know that a function means every x value must only have 1 y value

[surreal night]

exactly

[cursive vapor]

its the standard form im struggling with

[surreal night]

can you take the inverse of the given function?

[cursive vapor]

i haven't seen that form of an equation in like 2 years

[surreal night]

with all the variables still in it

[cursive vapor]

inderd

indeed

[surreal night]

so what does that give

[cursive vapor]

√((x-d)/a) + c = y

if i did it rigjt

my brain is sort of fried rn

[surreal night]

that looks right

what is the range of the original function

*sorry, range

[cursive vapor]

its quadratic right so [0, ∞)?

[surreal night]

almost, its from d

[d,inf)

[cursive vapor]

oh right cuz d is a translation up

[surreal night]

so, you have $f(x): \mathbb{R} -> [d,\infty)$

[woven radish]

Flappie

[proud perch]

if you don't mind there's a much easier way to think about this

don't mean to interfere though

[surreal night]

thus, $f^{-1}(x): [d,\infty)\rightarrow \mathbb{R}$

[woven radish]

Flappie

[surreal night]

go ahead

[proud perch]

step 1: get the equation in the form:
something = (x-c)^2

[surreal night]

i dont actually have the solution in my head, so im just sort of guessing

[proud perch]

then realize that if you want only one solution to the square root, then x-c must be non negative

that's it

[surreal night]

but you still need to know what values of x are allowed

for that you need the range of the function

[cursive vapor]

im afraid I don't follow

[proud perch]

no not really

from the condition x - c >= 0 you easily arrive at the answer

[surreal night]

ah, i see what the question is now

😅

i was thinking too far ahead

[cursive vapor]

ohhhh wait

I think

wait

[surreal night]

look at this

for what values of x is this real

[cursive vapor]

because the solution to a sqr root is + or -?

[proud perch]

yes

[cursive vapor]

right okay and you want it to only be +

[proud perch]

• or 0

non negative

[cursive vapor]

Right

Thanks

[proud perch]

so x-c >= 0

[cursive vapor]

.close

[devout snow]

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[devout snow]

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[terse plover]

hello, could anybody help me out with this question?: A store offers a one-day 10% discount on all cell phones. They also offer a warranty that costs either 5% of the discounted price or $35. Write an equation based on the original price that models each possibility for the warranty.

[terse plover]

(how far ive gotten so far for reference)

sorry if it being in french is an issue

please let me know if any translations are required

[torn vessel]

is there a condition on which warranty cost they go with? like 5% or $35, whichever is larger? smaller? or is it just two different functions for warranty

[devout snow]

@terse plover Has your question been resolved?

[terse plover]

no there arent any conditions

I figured it out, no worries 👍

[devout snow]

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[cursive vapor]

ok

[cursive vapor]

Not gonna close this time BC I know fs Ill probably have more questions

,rotate

[cursive vapor]

,rotate

[cursive vapor]

8 and numerical 3

[hexed moon]

i cant help you with 3 but I can w 8

you can use the properties of logs to simplify the log with m

[cursive vapor]

i know m = 27

[hexed moon]

to take the 2 part of m^2 to the outside of the log

wait hold up nvm i cant help u

i have no clue what those x's and y's came from

[cursive vapor]

meaning i know log(100m⁴)/log(3) is 16.19180655....

obv i need an exact value

idk how to pull it out of x and y terms

[molten scroll]

We are looking for when we reach the double of 4500, 9000. I.e.: we are looking for an expression in the form of 4500 x (1 + r)^12 = 9000, where r is the rate. Solve the equation.

[cursive vapor]

what's the formula again

I just need a refresher on what each term in the formula means

[molten scroll]

I think intuition works better in this scenario

[cursive vapor]

i mean it's like p(1 + r)^n

wait so

N = number of years

r = interest rate

p = initial

and it all equals final?

[molten scroll]

Imagine you have like 10 euro in your wallet now.
Imagine you give the money to the bank and they promise to you that they can increase the money by 10% every year (wow).

The formula that we will use is as follows: 10 x (1.1)

You leave the money for n years in the bank, it will grow annually exponentially, because more and more money is made from that, the new formula is: 10 x (1.1)^n

[cursive vapor]

ohhhh

ok

Thanks

[cursive vapor]

this one pisses me off because it feels easy

[molten scroll]

If the bank actually descreased the value by 10%, you would multiply by 0.9 instead (1-10%) = (1-0.1)

[devout snow]

@cursive vapor Has your question been resolved?

[cursive vapor]

boost

<@&286206848099549185>

[molten scroll]

I solved it but try yourself

I'll help you if you get stuck

This exercise is just applying all the logarithms rules that you know

Hint: the exercise uses the first rule a lot

[cursive vapor]

I.FIGURED IT OUT

Thank you all for participating

.close

[devout snow]

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[echo sandal]

[echo sandal]

Easiest way to do this?

[lunar harbor]

Hint: Consider the number of intersection points between the two graphs

[echo sandal]

One point

[echo sandal]

Tangent should be 1 point

I equated them

[lunar harbor]

Well given this

How many solutions does your equation have

[echo sandal]

One

[lunar harbor]

Yup

See if you can fill in the rest

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[open fox]

I am not understanding the math theory here in order to answer the question

[tawdry torrent]

It is basically asking when the function Isn't differentiable,
at the points of discontinuity functions can't be differentiable

[open fox]

Idk what différentiable is

[open fox]

Where do u identify points of discontinuity

[lost laurel]

do you know how to differentiate a function ?

[open fox]

Probably but I am not familiar with this term

[lost laurel]

what's your native language, I'll google the terms that I'm using

[open fox]

It’s English lol I’m just dumb

[lost laurel]

heard of the derivative of a function

[open fox]

Yea

[lost laurel]

this is the same thing

[open fox]

Ok so how do I apply this to this question

[safe jasper]

which x values can you not take a derivative for?

one thing that's useful is that for the derivative to exist at a point, the function must be continuous at that point

[open fox]

How am I supposed to know that using the graph

[safe jasper]

any x values where the function isn't continuous, the derivative doesn't exist

are there any gaps in the graph

or holes

or asymptotes

[open fox]

Hold on let me try to find my notes

I can’t find them

Does anyone have notes on the rules to determine if a function is différentiable or not based of a graph

<@&286206848099549185>

[spare dove]

sharp points right?

if the graph has any breaks or sharp ends its not differentiable

[devout snow]

@open fox Has your question been resolved?

[open fox]

What do u mean by that like can u show an example I’m sorry I’m asking a lot this is more then u have to do u don’t have to show me

[spare dove]

yea i can 1 sec

either the graph goes like this

[open fox]

Oh I see

[spare dove]

or a sharp corner like this

|x| is continuous but not differentiable cuz of that reason

[open fox]

Oh okay

[spare dove]

basically the reason for this is the left hand limit and the right hand limit go bananas and arnt equal

[open fox]

The visual helps a lot

[spare dove]

so even if it is continuous it cannot be differentiated

[ancient rose]

Go bananas is certainly a first

[open fox]

Thanks

[ancient rose]

Whenever a function is sussy, do the limits

[open fox]

.close

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[open grail]

hello

[open grail]

(vector functions)

can someone explain the range and domain of this question

im not 100% sure

[devout snow]

@open grail Has your question been resolved?

[open grail]

<@&286206848099549185>

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[tired scarab]

i did the first three problems

cant figure out the last two

im thinking
dS/dt = dS/dr*dr/dt

for the forth problem

so dS/dt should equal to 8pir(dS/dr) * 2/4pir^2(dr/dt)

i found the dr/dt in the previous problem

<@&286206848099549185>

.close

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[tired scarab]

.reopen

[devout snow]

✅

@tired scarab Has your question been resolved?

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[spring oak]

Hints please

[devout snow]

@spring oak Has your question been resolved?

[uncut crow]

the first thing i’d try is factoring

if you can break down x^3 - 8x^2 + 20x - 13 into factors other than 1, that shows it is not prime

presumably you can do that for large enough x

[verbal loom]

since (x-1) is a root, you can divide it and get a quadratic equation, with that you can use the quadratic formula

[winter patrol]

no point in using QF

you don't really care about when that quadratic factor is 0

[devout snow]

@spring oak Has your question been resolved?

[safe jasper]

it's simpler than that

factoring is the right approach

as mentioned, x-1 is a root, so this thing factors into (x-1)(x^2 - 7x + 13)

now the only way this is prime is if its only factors are 1 and itself

so you have two cases:

case 1:
(x-1) = 1, (x^2 - 7x + 13) = x^3 - 8x^2 + 20x - 13

case 2:
(x-1) = x^3 - 8x^2 + 20x - 13, (x^2 - 7x + 13) = 1

each case is a system of two equations that you can solve

@spring oak

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[smoky sentinel]

Pls help me i dont know what i did wrong

[smoky sentinel]

.close

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[real cove]

I have to show that the fraction is the generating function of the sequence

I'm thinking second derivative but I can't make the calculations work

[verbal loom]

!status

[devout snow]

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

[real cove]

2

I've tried starting with the series and getting it to where it is a second derivative of the uniform series

[elfin hill]

That's not exactly it but you have the idea

If you differentiate the uniform series you get a series of the form n^2

In

n sorry

If you differentiate it again you get n(n-1)

So you need to multiply by x in between

[real cove]

Sorry I didn't see your answer

[real cove]

I got here but then I can't figure out what to do with the -1

I separated it into 2 series and worked them out separately but in it isn't working out for me in the end

[devout snow]

@real cove Has your question been resolved?

[devout snow]

@real cove Has your question been resolved?

[devout snow]

@real cove Has your question been resolved?

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[prime narwhal]

what would i do

[devout snow]

@prime narwhal Has your question been resolved?

[late pivot]

It is enough that the slope of EH and FG are the same for it to be a parallelogram.

[prime narwhal]

So just two sides across from each other need the same slope?

That's enough?

You don't need to calc both sets of sides?

[late pivot]

Oh. My mistake. Yep you should compute the slopes of EF and HG also.

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[honest thorn]

definite integral 2 minus -2 , (2x+1)(x^2+x+3)^3

[honest thorn]

so i integrated it

and got (x^2+x+3)^4

then i just subbed the values in and subtracted

but i got wrong answer

.close

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[worldly crystal]

would like help understanding modulo tables and how to answer them

[worldly crystal]

the fourth question is as follows:is the above system a group?if yes,give any two conditions met by the above system.

[devout snow]

@worldly crystal Has your question been resolved?

[devout snow]

@worldly crystal Has your question been resolved?

[late pivot]

The inverse of 3 is x such that 3 + x = 0.

As for whether it's a group. Yes. Based only on the table, associativity can be tedious (although an algorithm exists for that, I'll google it first). So we'll skip that (it is associative). Identity and Inverse property should be easy. Do you know those?

Here's a procedure/algorithm for the associativity test: https://en.wikipedia.org/wiki/Light's_associativity_test#Example
A trivia I guess...

[worldly crystal]

nope,please explain a lil bit,then ill be fine thankyou

[late pivot]

I'll not explain the algorithm because I am quite sure this will not be taught.

[worldly crystal]

ok

[late pivot]

The * here is not multiplication, but the binary operation under consideration.
Associativity: (a * b) * c = a * (b * c). This means that you do not need parenthesis anymore in a1 * a2 * a3 * a4 for example. As you know, this is satisfied by the (typical) additon.
Identity: there is a identity element, or "id" such for all element x in set, x * id = id * x = x. This is 0 in the typical addition.
Inverse: every element x in set has a unique partner element x^-1 such that x * x^-1 = id. This is the "negative" of a number in the typical addition.

[worldly crystal]

tysm,this is the clarification i needed,do you mind giving me some random exercise i can attempt later?

[late pivot]

Hmm... Set = {1,2,3,4} and operation is multiplication modulo 5. Is this a group? What about Set = {1,2,3,4,5}, multiplication modulo 6?

Both operations are associative, so you may skip that.
I removed 0 because of zero property of multiplication. Why does this property automatically make the table not form a group?

[worldly crystal]

i got no idea dude,i cant visualize this unless its in a table,thx thought ill take a look at it later via screenshot

other than tht im set now

thx for the help

you can close this now

[devout snow]

@worldly crystal Has your question been resolved?

[late pivot]

.close

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[brisk panther]

More of a soft question but how would you define tetration with decimals in the idk what you call it

[brisk panther]

with decimals in the "exponent" ?

like for example

what is 2 ↑↑ 1.5

[fierce heath]

so were all on the same foot

what is 2 ↑↑ 3 is

2^(2^2)

?

well if 2^0.5 is sqrt(2)

[brisk panther]

yes

im uising arrows because

i cant write it the other way

[fierce heath]

and 2^1.5 is sqrt(2^3)

[brisk panther]

2↑↑4 = 2^2^2^2

how would you define this for lets say

2↑↑1.5

[fierce heath]

well

[brisk panther]

if it helps

[fierce heath]

2 ↑↑ 0.5 would probably be something like

[brisk panther]

2↑↑0 = 1

[fierce heath]

define some new function lets say like super sqrt

[brisk panther]

and 2↑↑n = 2^ ( 2↑↑n-1)

[fierce heath]

actually no

this is purely hypothetical right

[brisk panther]

ehh

im trying to find a nice way to define it

which makes sense

like how the gamma function helps define factorials for numbers wihch arent whole numbers

[fierce heath]

youve probably seen super roots and super logarithms

right

[brisk panther]

no

oh i see

[fierce heath]

if you believe super roots are a real thing which do exist

[brisk panther]

ya i get it kinda

[fierce heath]

me personally i would define

N ↑↑ (A/B)

to be

Bth-super-root(n ↑↑ A)

but thats just me

so for 2 ↑↑ 1.5

it would be

super-sqrt(2 ↑↑ 3)

or super-sqrt(16)

[brisk panther]

,w ln(16)/W(ln(16))

[woven radish]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by diddletoucher

[brisk panther]

,w what is ln(16)/W(ln(16))

[woven radish]

Results provided by WolframAlpha

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

Requested by diddletoucher

[brisk panther]

stupid wolfram

[brisk panther]

so 3 ↑↑ (4/2)

3 ↑↑ 2

3^3 = 27

superroot of 3 ↑↑ 4

3^3^27

but this isnt 27^27

is it

[fierce heath]

give me a moment

ssqrt(2 ↑↑ 4)
ssqrt(2^2^2^2)
ssqrt(256)
ssqrt(2*2*2*2*2*2*2)
ssqrt(4*4*4*4)
ssqrt(4^4)
ssqrt(4 ↑↑ 2)
4```

damn

it works for 2 so maybe it will work for 3

[brisk panther]

i think it only works for 2

because 2*2 = 2^2 = 2 ↑↑ 2

2^2^2^2 = 65536

[fierce heath]

damn

back to the drawing board

i have no other ideas

[brisk panther]

i think its an open problem now that i look at it

[devout snow]

@brisk panther Has your question been resolved?

[brisk panther]

.close

[devout snow]

Channel closed

Closed by @brisk panther

Use .reopen if this was a mistake.

[devout snow]

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[hollow current]

If I put in x = 0

[opal cloak]

what is the question?

[hollow current]

What is the solution

For x = 0

[opal cloak]

undefined

[hollow current]

what?

[opal cloak]

are u taking a limit?

[hollow current]

Yeah

limit

[arctic field]

!xy

[devout snow]

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

[opal cloak]

oh well then that changes things

[hollow current]

I dont understand this

way

[arctic field]

you can't just take the fraction out of context

[arctic field]

it's just calculating the derivative

derivative of e^x is e^x

[hollow current]

What is a derivative

[arctic field]

that limit

[hollow current]

So at the part

Do I put for x -> 0?

[arctic field]

what?

[hollow current]

I don't understand how it is -2 + e^0

[arctic field]

the derivative of e^x is e^x

so the derivative of e^x at 0 is e^0

[hollow current]

What about the e^x / x

Isnt it e^0 / 0?

[arctic field]

what?

[opal cloak]

l hopital i believe

[surreal night]

you cant divide by 0

[arctic field]

no

that's not even defined

[opal cloak]

1-1/0

[arctic field]

yet another blind lhopital applier

[hollow current]

Yeah thats what im asking rn

Ah lhospital here?

[surreal night]

!occupied

[devout snow]

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

[arctic field]

no!

[fair sierra]

can anyone help with how to draw the network diagram ?

[arctic field]

no lhopital

[surreal night]

!occupied

[devout snow]

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

[tall stirrup]

you can't tho you can take a limit of indeterminate

[hollow current]

XD

[arctic field]

there's literally nowhere here that you apply lhopital

[hollow current]

Wdym by that

[arctic field]

i wasn't talking about you

[surreal night]

l'hopital is like something you use when you have no other options

[arctic field]

if you apply lhopital here then you don't understand limits

[hollow current]

I dont understand this progress

from there to there

[surreal night]

stop taking it out of context

[arctic field]

again, you need to include the limit

[surreal night]

!original

[devout snow]

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

[surreal night]

show everything, and then show what part you are confused about

[hollow current]

I did

[hollow current]

here

[surreal night]

is htis the full context?

[arctic field]

$\ds \lim_{x \to 0} \f {e^x - e^0} {x - 0}$ is the \textbf{definition} of the derivative of $e^x$ at $0$

[arctic field]

the definition

if you don't know what a derivative is

you need to go and review it

[surreal night]

aha

so there is more context

[hollow current]

What is a derivative in german?

Ableitung?

Is it like 1x = 1

Is this derivative?

[tall stirrup]

yeah

[hollow current]

ahhh

e^x = e^x yeah

[surreal night]

$\frac{d}{dx}$ this is a derivative

[woven radish]

Flappie

[hollow current]

Ahh

[tall stirrup]

more appropriately d(x)/dx =1

[hollow current]

And why is the 0 up on the x?

[surreal night]

and $\frac{d}{dx}e^x=e^x$

[woven radish]

Flappie

[hollow current]

And why do I even use derivative here?

[arctic field]

$\ds \lim_{x \to 0} \f {e^x - e^0} {x - 0}$ is the \textbf{definition} of the derivative of $e^x$ at $0$

[hollow current]

I dont?

[smoky gyro]

superblunder 😭

[arctic field]

precisely

it is a superblunder

[hollow current]

😭

[arctic field]

i'm gonna post this for the third time

$\ds \lim_{x \to 0} \f {e^x - e^0} {x - 0}$ is the \textbf{definition} of the derivative of $e^x$ at $0$

[hollow current]

Okay

I kinda get it and kinda not lol

[arctic field]

the derivative of e^x is e^x

[hollow current]

Yeah

[arctic field]

evaluated at 0 is e^0

that's it

[hollow current]

Is it like

derivative of 3x^2 = 6x
evulated at 1 is 6

?

[arctic field]

yes

[hollow current]

xD

[surreal night]

do you know the definition of a limit?

[hollow current]

But I still dont get it

Why there is a derivative

[arctic field]

why are you calculating the limit

the limit is the derivative

by definition

[hollow current]

It is like infinity approaching to a certain point?

[surreal night]

no

by definition $f'(x) = \lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$

[woven radish]

Flappie

[surreal night]

sorry, i meant derivative

[hollow current]

Yeah I know this one

[arctic field]

more appropriate here is [ f'(a) = \lim_{x \to a} \f {f(x) - f(a)} {x - a} ]

[ancient rose]

google "limit definition of the derivative"

[hollow current]

Yes

It is a formular

That is used here in this task

[ancient rose]

yes

good job

you notice that, when you take out that pesky -2

you get the exact formula

[arctic field]

[ \lim_{x \to 0} \f {e^x - e^0} {x - 0} = e^0 ]

[ancient rose]

exactly

f(x) - f(h) / x - h

[arctic field]

there's nothing else to say

[hollow current]

Yes I do

[ancient rose]

you can make that entire thing just go away as f'(h)

[hollow current]

But how do I calcute e^x - e^0 / x

[ancient rose]

ta da

you dont

bro it can't be this complicated istg

[arctic field]

the limit definition of the derivative tells you

[ancient rose]

what are you not grasping

x - 0 = x right?

[hollow current]

Yeah

[ancient rose]

then just keep it as x - 0

then when you see the limit

you just substitute

its like an identity

you know how tan x = sin x / cos x

[arctic field]

[ e^0 = \lim_{x \to 0} \f {e^x - e^0} {x - 0} ]
[ f'(a) = \lim_{x \to a} \f {f(x) - f(a)} {x - a} ]

[arctic field]

i put it closer together for you to see

[hollow current]

ah

[ancient rose]

doing god's work snoseph

[hollow current]

ok

I see it

[ancient rose]

you see it but do you get it

[arctic field]

in case you couldn't keep it in your mind for some reason

[hollow current]

Yes

I get it

It is just it

Like u said

x - 0 = x

Thank you

I get it

[hollow current]

istg he is...

im so sorry

[plush sphinx]

3 * 2^x + 2^x = 8 help

[surreal night]

!occupied

[devout snow]

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

[tall stirrup]

3* 2^x + 2^x =8
4*2^x = 8

[plush sphinx]

Where did 4 come from?

[tall stirrup]

3+1 = 4

[plush sphinx]

???

[tall stirrup]

2^x(3+1) =8

can you get this?

[arctic field]

!occupied

[devout snow]

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

[arctic field]

!help

[devout snow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[plush sphinx]

thanks

2^x+1 + 2^x = 12

[smoky gyro]

blud has not read the messages

[devout snow]

@hollow current Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[tall stirrup]

hmm

what was that btw

why did we use the definition hmm

[devout snow]

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[reef basalt]

Is this step correct?

[safe jasper]

yes

so far that is correct

[reef basalt]

So how should I proceed now

[safe jasper]

is there a way to simplify (0.2)^x / (0.1)^x?

recall the properties of exponents