help-33

[marsh citrus]

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[vivid birch]

prove absolute convergence of:
a) sigma n=1 to +inf of ((-1)^(n-1))*(n/(n^2+1))
b) sigma n=1 to +inf of 4^(1/n)

for my work, i know A converges per alt series test but i dont know how to prove the absolute convergence in particular. For B, i think I would use divergence test which would give me limit = 1, so it diverges.

[marsh citrus]

@vivid birch Has your question been resolved?

[vivid birch]

<@&286206848099549185>

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[marsh citrus]

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[jovial shadow]

Can someone help me?

[valid cape]

https://dontasktoask.com

[jovial shadow]

I need help

<@&286206848099549185>

[valid cape]

say it out loud

[brave spire]

Need help with what

[valid cape]

@jovial shadow

[marsh citrus]

@jovial shadow Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[dark sorrel]

.close

[marsh citrus]

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[finite trout]

I can see that the total function is continous, since the domain is R{0}, but I don't understand if it is continous in 0 or not? I found some sources stating, that its neither continous nor not continous if the function is not defined at a certain value, but I am unsure about that.

PS: both pictures are the same, one is just translated to english

[devout mauve]

a better question is: can you define f(0) in such a way that the function you obtain is continuous

[eager star]

What does f(0) even mean here if the set doesn't include 0, is there a way to define it?

[devout mauve]

lets call g:R\{0}->R, g(x)=1/x

is there a function f:R->R, such that f(x)=g(x) for all x in R\{0} and such that f is continuous

[crisp sigil]

Can someone check if these are right?'m sorry if I posted it in the wrong channel I'm not sure where to put it

[devout mauve]

!help

[marsh citrus]

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

[crisp sigil]

I tried doing that but It wasn't working

[marsh citrus]

@finite trout Has your question been resolved?

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[still temple]

Decide the equation for the coordinates (-1, 5) and (1,1)

[still temple]

Why can’t I do

1-5/1-1

To get k

The gradient

But I have to do

5-1/-1-1

To get the gradient

[hidden plaza]

If you do it this way the denominator should be
1-(-1)

[still temple]

What is that then

[hidden plaza]

1+1

[still temple]

Wait so I can do both ways?

It doesn’t matter much way

[hidden plaza]

Yes

[still temple]

OHHH

But why is 1-(-1) 2

Why does the negatives turn into plus

[hidden plaza]

when you have two negatives it becomes positive

[still temple]

But not when it’s addition

?

That’s what my teacher said 😭

[hidden plaza]

Wdym?

[still temple]

-2-2

Is -4

Not 4

But in multiplication it’s 4

[hidden plaza]

Well that’s different

[still temple]

Yeah I figured

[hidden plaza]

If we had -2-(-2) then it’s 0

[still temple]

-3 +2 what

[hidden plaza]

-1

[still temple]

The minuses turn into a plus no? 😭😭😭

[hidden plaza]

No not like that

If we have $-(-a))$ this is the same as saying $-1 \cdot -a$ which is $a$ for some number a

[elfin berry]

Pure

[still temple]

Wait can I solve it like an equation maybe

[hidden plaza]

Not sure what you mean

[still temple]

Wait no that doesn’t work

Bc

Like if - is before the ()

The - in the () turns into a +

😭😭😭

Right

[hidden plaza]

You have to distribute the - into the bracket yeah

And two minuses make a plus when multiplied

[still temple]

So was the answer 0

[hidden plaza]

Huh

[still temple]

The one u have

[hidden plaza]

1-(-1)?

[still temple]

This

[hidden plaza]

Yeah

-2-(-2) = -2+2

[still temple]

OHHH

so I just

Okay

Thank you

[hidden plaza]

[still temple]

I thought I had to do it in

Order of the size

Tyyy

.close

[marsh citrus]

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[marsh citrus]

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[strong pecan]

why cant we do divergence theorem
we take curl F=F
div(curl(F))
triple integral
but thats gets us 0 every time
any idea why

[marsh citrus]

@strong pecan Has your question been resolved?

[strong pecan]

<@&286206848099549185>

[marsh citrus]

@strong pecan Has your question been resolved?

[strong pecan]

<@&286206848099549185>

[strong pecan]

<@&286206848099549185>

[marsh citrus]

@strong pecan Has your question been resolved?

[strong pecan]

@patent swallow

<@&286206848099549185> s

[gleaming pecan]

$\text{If a vector field }\overrightarrow{F}\text{ is continuously twice-differentiable, then }\\div\left( rot\overrightarrow{F} \right)=0$

[elfin berry]

Joanna Angel

[gleaming pecan]

then you need to use stoke's theorem and its formula

[strong pecan]

i see

that makes sense

due to clairuts

thanks

.close

[marsh citrus]

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[lusty knot]

Can anyone help me with these 3 questions about geometry ill send one by one

[random palm]

matrix

[lusty knot]

What

??

Bruh can someone help me

This dude is trolling

unfunny

[hasty ruin]

you’re given a grid, even counting squares would work

[boreal cloak]

either that or actually using matrices

$\pm\frac{1}{2}\begin{bmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{bmatrix}$

[elfin berry]

mud ツ

[marsh citrus]

@lusty knot Has your question been resolved?

[marsh citrus]

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[past kraken]

I got y = 2(x + 3)(x - 1)

[past kraken]

is there a way to get the answer without the need to graph it?

[bitter solstice]

you can guess a bit

where does it look like the vertex of this parabola might be?

look at all the y values

alternatively

you can note that (-3,0) and (1,0) are points

those are roots / x intercepts!

which tells you (x+3)(x+1) is a part of it

so just find the factor 2 in front!

[past kraken]

ohhh

[past kraken]

yes from there I can find the axis of symmetry and vertex correct?

[bitter solstice]

you gotta find a first - like you know the equation is a(x+3)(x-1) but then yes expand it out and you can find the vertex and axis of symmetry

[past kraken]

so do I just guess the points and plug them into the equation and hope I would eventually find the right one?

[bitter solstice]

what do you mean?

you can pick any other point besides (-3, 0) or (1,0) and plug it in and you'll get the correct value for a

[past kraken]

it doesn't matter which??

[bitter solstice]

nope

they're all on the parabola

[past kraken]

ohhh

[past kraken]

tysm!!

[bitter solstice]

no worries!

[past kraken]

.close

[marsh citrus]

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[deft horizon]

need help

[marsh citrus]

@deft horizon Has your question been resolved?

[marsh citrus]

@deft horizon Has your question been resolved?

[deft horizon]

<@&286206848099549185>

[still temple]

@deft horizon yes

they travel different amounts of distance

[deft horizon]

thank you

[still temple]

but the displacement is same

[deft horizon]

.close

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[eager ibex]

I need help solving this.

I know that I need to find f''(x) which is 6x-4 and set that equal to 0

But I don't know how to move on from there.

nevermind

.close

[marsh citrus]

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[fair notch]

ignore the work for question 1 but is the correct answer 11/3?

[marsh citrus]

@fair notch Has your question been resolved?

[boreal cloak]

yeah it is 11/3

[fading lintel]

Hey guys I have a question?

Do I cancel out the 9/4 sec^2theta. Or do I simplify the radicand first?

[fair notch]

d will be -2/3 yeah because -cos(pi) is positve 1 bc -(-1) = 1

[boreal cloak]

yes

[fair notch]

and then it cancels

and then its -2/3 = D

[boreal cloak]

#❓how-to-get-help

[fair notch]

okok ty

[boreal cloak]

np!

[marsh citrus]

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[torn dawn]

Hi

[abstract knot]

hi

what do you need

[torn dawn]

Here you go

[abstract knot]

1. whats a normal to a curve
2. what does the angle of the normal tell us about the slope of the normal
3. what does the slope of the normal tell us about the slope of the tangent

[torn dawn]

1. Perpendicular to the tangent

3. -1/slope of normal = slope of tangent

[abstract knot]

right

so whats 2

[torn dawn]

[abstract knot]

lol

try to draw a right triangle

and use trig

[torn dawn]

Yes okay

[abstract knot]

please open your own help channel

this one is occupied

[torn dawn]

Man I’m not getting it

[abstract knot]

well

show me the picture you drew

[abstract knot]

why are the sides congruent

remember, theta is 3pi/4

[torn dawn]

No they are not congruent

[abstract knot]

that's what the lines through them mean

[torn dawn]

I made those strikes to mark perpendicular and base

[abstract knot]

but thats besides the point i suppose

[torn dawn]

🤣🤣

[abstract knot]

well

disregard the geometric notation for a sec

[torn dawn]

Ok ok

[abstract knot]

we know that theta is 3pi/4 right

and the slope of the hypotenuse is what trig function of theta

[torn dawn]

Yes

[abstract knot]

it was a question

[torn dawn]

Wait

[abstract knot]

"what trig function"

[torn dawn]

😄

[abstract knot]

right

and what ratio is the slope of the hypotenuse

[torn dawn]

What trigo function?

[torn dawn]

Don’t know

[abstract knot]

well

slope is rise/run

whats rise, whats run

[torn dawn]

Hearing it for the first time

[abstract knot]

slope is [change in y coordinate]/[change in x coordinate]

is that more familiar?

[torn dawn]

Yes

dy/dx

[abstract knot]

yeah

so lets think of the hypotenuse as a line (because it is)

[torn dawn]

Ok

[abstract knot]

which part of the triangle is the change in x

and which part is the change in y

[abstract knot]

yup

[torn dawn]

Okay so

[abstract knot]

and what trig function is the change in y side divided by the change in x side

[torn dawn]

dy/dx

tan theta

[abstract knot]

exactly

and whats theta

[torn dawn]

And theta = 3pie/4

[abstract knot]

pie

lol

but yeah

so if the slope of the normal is tan(3pi/4)

whats the slope of the tangent

[torn dawn]

-1

[abstract knot]

well

whats tan(3pi/4)

-1 right

[torn dawn]

Yes yes

[abstract knot]

and wahts the slope of the tangent in terms of the slope of the normal

(you did this earlier remember)

[torn dawn]

-1/mn

[abstract knot]

mhm

[torn dawn]

-1/slope of normal

[abstract knot]

right

[torn dawn]

I meant

[abstract knot]

so whats the slope of the tangent then?

[torn dawn]

1?

Thanks man

The answer is 1

[abstract knot]

np

[torn dawn]

.close

[marsh citrus]

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[torn dawn]

.reopen

[marsh citrus]

✅

[torn dawn]

sorry

.close

[marsh citrus]

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[marsh citrus]

@sonic dirge Has your question been resolved?

[marsh citrus]

@sonic dirge Has your question been resolved?

[marsh citrus]

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[modern gull]

for this formula
here i get -2, 3,5
but when i do it i get -2 and 7

[modern gull]

is it becuase 2y so i divide it by 2?

[raw flare]

yes

[modern gull]

okay makes sense thank u

.c

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[marsh citrus]

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[foggy wigeon]

.reopen

[modern skiff]

getting cucked trying to solve this losing my mind getting b wrong

i need a hero

other screenshots are the steps for getting b right

angle is 3.927 is radians

[marsh citrus]

@modern skiff Has your question been resolved?

[tight furnace]

Show work

[marsh citrus]

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[modern skiff]

new freezer

[modern skiff]

idk how 2 do this

[marsh citrus]

@modern skiff Has your question been resolved?

[tight furnace]

do you know the quaternion that rotates 45 degrees around the X-axis

[modern skiff]

yea 1 sec

qx​=cos(8π​)+sin(8π​)i

[marsh citrus]

@modern skiff Has your question been resolved?

[marsh citrus]

@modern skiff Has your question been resolved?

[marsh citrus]

@modern skiff Has your question been resolved?

[modern skiff]

<@&286206848099549185> id love a quaternion multiplication expert here

would make my year 😉

[marsh citrus]

@modern skiff Has your question been resolved?

[modern skiff]

<@&286206848099549185> any lads willing to check work if not willing to complete alone?

[modern skiff]

.close

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[marsh citrus]

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[rapid cosmos]

In this question I got a negative instead of a positive answer

[rapid cosmos]

This was my solution

does anyone know why it’s wrong

[desert dirge]

because your acceleration and friction force are in the same direction

but you gave them different signs

mu R acts to the left, so by how i assume you have defines pos and neg
it should be -muR when doing any force calculations

-mu mg=-2m/3 etc

[rapid cosmos]

oh ok

thank you

.close

[marsh citrus]

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[still temple]

$log(x)+log(x+4)=2$

[elfin berry]

Matt

[cobalt sentinel]

What’ve u tried

[still temple]

used the quadratic formula to get those two numbers

but how do i know which one is the correct one

[cobalt sentinel]

Plug into original question

See which of them works

Remember the domain of log

[still temple]

i think it must be > 0 right?

[cobalt sentinel]

Ye

[still temple]

ah i see

thank you

.close

[marsh citrus]

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[marsh citrus]

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[thorn wharf]

why is the base of the triangle not 6 and 5

should it not just be half of 12?

[night mica]

are there people in the planet who use inches ?

[next raft]

🦅

[thorn wharf]

😭

[raw flare]

because you also have 2 inches on top

what has 12 inches does not hav the shape of a triangle

[raw flare]

what u have is basically this

so if i substract the red part, u get a green triangle of base 5

[thorn wharf]

ahhhh

tysmmmm

[night mica]

np 🙂

[thorn wharf]

.close

[marsh citrus]

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[marsh citrus]

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[tired hornet]

Hello! I am a Christian looking to prove that God can be triune by using a basic equation. As some may know, that the Trinity is a 3 in 1 Monotheistic idea. 1x1x1=1 is a modalist idea and is a heresy, so this is ruled out. And 1+1+1=1 cannot be correct because it doesn't add up. 1+1+1=3 is false because this disapproves a monotheistic idea and more or so proves its Polytheistic. What would be the correct answer to signify a correct equation to prove that something can be triune.

[proud prism]

$1 +{2} 1 +{2} 1 = 1$

[elfin berry]

.doc

[frigid rampart]

although im not believe in any god but hope you achieve your goals and prove me wrong somehow.

[tired hornet]

Is it okay if I DM you personally about this topic? Not as like a debate or anyting, but I want your looks on this info I compiled. It is perfectly fine if you decline.

[proud prism]

idk if I’m helping, but 1+1+1 can be equal to 1, if you add modulo 2

[tired hornet]

thank you! This definitely answered my question. I am not really sure on how to close it now with the .close thingy, but I appreciate the help.

[frigid rampart]

hmmm maybe you just do 3*1

[cobalt sentinel]

Do .close

[tired hornet]

.close

[marsh citrus]

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[sterile bridge]

Hey this is more of a grammar question than a math question. I think my proof is sound it's just that idk if my 'grammar' (for lack of a better term) is acceptable or not.

[sterile bridge]

should k become j for 2kn

[still temple]

Grammar seems correct but shouldn't you use b = 2kn later on

Why did you drop the n

[sterile bridge]

right yea i dropped it because 2kn is 2*any integer but i didn't reassign k

ooops

[still temple]

And when you assume a = 2k, do mention k≠0, and n ≠0 in b = 2kn

[sterile bridge]

ok ill make sure to do that. any other suggestions?

.close

[marsh citrus]

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[keen frigate]

i got the part before the part where i have underlined

[keen frigate]

how do we get the values 1.645 and 0.13

using this table

nvm i got

.close

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[cosmic shuttle]

I have this problem. Would I set it up like this?

[languid marten]

seems about right

if you're integrating it. then.

[cosmic shuttle]

Yea what I need to do next is expand everything

So I think it would look like 54x^3+127x^2+80x+16 = A(2x) + B(2x^2) + C(3x+2) + D(3x+2)^2

[languid marten]

yeah, you did it right

[still temple]

$54x^3+127x^2+80x+16 = A(2x) + B(2x^2) + C(3x+2) + D(3x+2)^2$

[elfin berry]

Mr. Macro

[cosmic shuttle]

Alright I think I’ve got it. Just making sure I’m doing it correctly

.close

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[marsh citrus]

@toxic adder Has your question been resolved?

[marsh citrus]

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✅

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[marsh citrus]

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[marsh citrus]

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[prime egret]

.close

[marsh citrus]

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[still temple]

Find parameter p such that the points A(1,-1,0), B(2,0,1), C(1,p,3) and D(2,2p,5) lie in the same plane

[still temple]

what I did was create a plane equation. so AB = (1, 1, 1) and CD = (1,p, 2)

so (x,y,z) = (1,-1,0) + s(1,1,1) + t(1,p,2)

what do i do next

i was thinking using a point on the plane like 2,0,1, plugging that for x,y,z and setting up a 3 equation 3 variable system but that did not work

maybe doing cross product with AB and CD to get the normal in terms of p can work. The cross product is (2-p, -1, p-1)

doing this, and converting to general equation of line, I get D = 3p - 3

so i get the equation of plane:

(2-p)(x) - y + (p-1)z + 3p - 3 = 0

the problem is that whenever i try to find p, I always get p = 0

why is this the case?

<@&286206848099549185>

[jagged relic]

That's not how it works

The equation of the plane is (2-p)x - y + (p-1)z + k = 3p - 3

The problem is that you don't have enough information if you do the cross product between AB and CD

For an arbitrary p, you won't get the normal of the plane that goes through all points, because there is no such plane

Instead, take the cross product between AB and AC for example

There is always a plane that goes through 3 points

[marsh citrus]

@still temple Has your question been resolved?

[whole vessel]

i need help

[still temple]

ah i see

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

ok i did that

and got normal (2-p, -3, p+1)

so then in general form: (2-p)x -3y + (p+1)z + D = 0

if i plug in one of the points (for example, point A), I get D = p-5

so, now I have equation (2-p)x -3y + (p+1)z + p - 5 = 0

if I plug in point D(2,2p,5), I get p = 2

which is the right answer

[jagged relic]

[still temple]

so it worked

but let me ask this

can i do it like this:

so i find my normal, then I set up my equation. Can a plug in any point to find D?

or does it have to be A, B or C

let's say I plug in point D(2,2p,5) to find D

can i plug it in again to find p?

[jagged relic]

You can plug in D, but then to get p you use another point

[still temple]

ah i see. Can i plug in B then C, or A then C or B then C, etc

or is that not good since I am excluding D

[jagged relic]

You can plug in any of {A,B,C} and also D, in any order

Let me rephrase

[still temple]

ok so i need to have point D in there somehwere

[jagged relic]

You can plug in A,B, or C, and then plug in D

Or you can plug in D and then one other

[still temple]

i see

so I must include D

can't exclude it

[jagged relic]

Because you got the normal from A,B, and C

[still temple]

yes

p will equal to 0 if I don't plug in D

and I do not want that

[jagged relic]

Well not really, p can have any value, but the plane won't go through D

[still temple]

yeah true

i see

thank you very much!

.close

[marsh citrus]

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[next folio]

how would i do l’hopitals on this

[gusty bay]

Is it sin(16/x)

[high ledge]

$x\sin(\frac{16}{x}) = \frac{\sin(\frac{16}{x})}{\frac{1}{x}}$

[elfin berry]

Rub05

[high ledge]

@next folio

[gusty bay]

What after?

[next folio]

ic

what now

,rotate

[high ledge]

Wrong

[next folio]

?

cos

right

but what now

@high ledge put the denominator back in the numerator then cancel?

,rotate

[high ledge]

Yes

[next folio]

thank you

.close

[marsh citrus]

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[slate blaze]

what did I do wrong

[gusty bay]

Which one

[slate blaze]

c

what did I do wrong

[gusty bay]

You can take 6 common

Nothing wrong in taking 2 also

You can also take b² common

[slate blaze]

that's what i was doing before

but the exponents confused me

[gusty bay]

Take b² common

[slate blaze]

wym

[still temple]

you can also factor out a b^2

is what he means

[slate blaze]

oh

[gusty bay]

My bad

[slate blaze]

how would i do that

[gusty bay]

Say I factor out 6b² from 12b⁴+18b²

You can just rewrite it as 6b²(12b⁴+18b²)/6b²

Now just divide them

[still temple]

factor out a 6b^2 from the expression

What would you get

[slate blaze]

i got 6(2b^2 + 3b)

[still temple]

nope

When you multiply the 6 back in you dont get the original expression

[slate blaze]

this is confusing

like whats happened with the exponents

[still temple]

Do you know your exponent division and multiplication rules

[gusty bay]

What is b⁴

[gusty bay]

b×b×b×b

b²=b×b

[slate blaze]

what is that doing

as ik that

like am i supposed to mention b×b×b×b in the equation?

[gusty bay]

Not necessarily

I thought it would help

[slate blaze]

oh wait so you subtract the exponents?

b^4 - b^2 = b^2

[gusty bay]

Yep

Noooooooo

[slate blaze]

😭

math is confusing

[gusty bay]

a^x/a^y=a^(x-y)

Get it?

[slate blaze]

still a bit confusing

[gusty bay]

For example 2⁴⁰/2³⁰=2¹⁰

[slate blaze]

yes

rhe exponent 40-30

[gusty bay]

Yes yes

We have 6b²(12b⁴+18b²)/6b² right?

[slate blaze]

yes

[gusty bay]

Now divide 12b⁴+18b² with 6b²

[slate blaze]

the exponents as well?

[gusty bay]

Why else my dear

[slate blaze]

so by doing that

talking abt the exponents 4÷2

2÷2

and sorry if I'm asking to many questions

.close

[marsh citrus]

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[still temple]

why is $n = a_1 \times a_2$

[elfin berry]

Derivative

[still temple]

how do i do this by right hand rule

[main idol]

https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/normal-vector-from-plane-equation

If n is the normal vector

[still temple]

ok thanks

.close

[marsh citrus]

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[solar crystal]

?help

[solar crystal]

a box contains 80 good and 10 defective screws. If ten screws are used, what is the probability that none are defective

what is the a value for hypergeometric distrubution

what is the number of succesfull outcomes for this question

[marsh citrus]

@solar crystal Has your question been resolved?

[trail timber]

80 could be an answer

You can use a calculator or statistical software to compute the probabilities based on the hypergeometric distribution formula.

[marsh citrus]

@solar crystal Has your question been resolved?

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[violet bane]

hmm awful question, but why would the chain rule for paths not equal 0?

[violet bane]

isn't the gradient always perpendicular to the tangent line

confused ab that

[marsh citrus]

@violet bane Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[violet bane]

don't rlly understand this

[violet bane]

isn't the gradient vector always perpendicular to the tangent line?

confused why this wouldn't equal 0

[fervent rampart]

that appears to be the gradient of the directional derivative

[marsh citrus]

@violet bane Has your question been resolved?

[brave marsh]

The gradient is perpendicular to level curves f(X) = 0. r(t) may not necessarily be such a curvwe.

[marsh citrus]

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[lone ruin]

Hey Everyone, got a geometry question.

So I've got an inner and outer cylinder representing a rotating space habitat's roof and floor. I'd like an equation or the steps to solve for the amount of land visible from a single point. There is the straight line distance and the distance around the outer cylinder (idk arc something). I'm looking for the second one. Heres a picture:

[sacred kestrel]

this won't solve your whole problem but getting the double root of the point where the observer is and the circle would give you the two points where the vision will be occluded by the circle.

[lone ruin]

Would it be possible to take the tangent line of the inner circle and find where it intersects the outer circle and figure out the arc of the outer circle using those points?

Taking that arc /2 should be the max distance you can see from where you are standing

[sacred kestrel]

you can take the angle between those two points at the origin of the inner circle to find the arc length of the larger one i suppose.

[lone ruin]

Oh, indeed. Thats another option.

I think this is good enough for now. Thanks @sacred kestrel

[lone ruin]

.close

[marsh citrus]

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[next folio]

only need help on part b

idk what to do

[copper ice]

so after you take derivative of the expression you get something like this. Now replace x with inf and see 2/inf is 0

and 0 times everything is 0

[next folio]

ye but idk how to go about getting the derivative of that

Lol

[sacred kestrel]

d/dx [a^x] = (ln a)(a^x)
d/dx [ln x] = 1/x

[copper ice]

oh yeah i messed up

[sacred kestrel]

this is a tough derivative

[next folio]

ye idk what to do for this

Lol

[sacred kestrel]

very carefully applying the rules you know.

[copper ice]

but this only change (lnx+1), right?

to this

no?

[next folio]

but this doesn't ahve to do with l'hopital's though

unless there's a denominator

[sacred kestrel]

i assume they are counting the denom in the exponent?

[next folio]

well you can't apply l'hopital's unless there's a denominator right

idk

,rotate

[next folio]

this is what i got

so far

unsure if its right

[sacred kestrel]

infinity^0 is a form of indeterminance, so i guess l'hopitals is valid here

[next folio]

is my work right

[sacred kestrel]

yes

no

[next folio]

?

[sacred kestrel]

you should get a final expression of 2/xlnx

[next folio]

why's that

and where did the other ln go

[sacred kestrel]

for the numerator we have 2ln(lnx)

2 gets pulled out

we are left with ln(lnx)

[next folio]

ln(lnx) 1/lnx 1/x

ohh shit

ok ok idk hwat i was doing

[sacred kestrel]

what is the limit now for 2/xlnx?

[next folio]

infinity

0

[sacred kestrel]

you mean 2/infinity

right

so the limit of the natural log of our expression is 0, now we have to undo our natural log

[next folio]

e^0 = 1

[sacred kestrel]

exactly

[next folio]

holyyy

[next folio]

you're a life saver

i've deadass been doing the smae homework for 5 hours today

that was the last problem

thank you sm

[sacred kestrel]

no problem, enjoy some rest

[next folio]

.close

[marsh citrus]

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[wispy gyro]

Can someone help me convert the parametric system x = sint, y=sin3t to an implicit equation?

[wispy gyro]

.close

[marsh citrus]

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[naive apex]

huh

[wispy gyro]

I figured it out

[marsh citrus]

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[slate blaze]

what did I do wrong?

[odd crest]

the second part

does it have x^2 in it?

[lean flame]

Apart from that, the first line you wrote is invalid, cannot factor out stuff and keep things the same inside

Second line is good

[slate blaze]

so i just remove first line?

[slate blaze]

where

[odd crest]

16xy^3

[slate blaze]

isnt that correct tho

in the question it says 16xy^3

[odd crest]

right but when you divide that by 2x^2y

what is the result

[slate blaze]

8x^y2

as for exponents u gotta subtract?

x^2 - x^1 = x and for the y^3 - y^1 = y^2

.close

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[forest stream]

am i able to evaluate these using l'Hopital's rule?

[forest stream]

thats only for differences right

if so i wouldnt know how to evaluate these

[glass silo]

e.g. for the first one, you can rewrite it slightly as $\frac{\arctan(x)}{ \pqty{ \frac1{\ln(x)}} }$, second and third one make use of similar and that $a^b = e^{b\ln(a)}$

[elfin berry]

@glass silo

[glass silo]

(something something, just because you can...)

[forest stream]

wait sorry how can you rewrite ln(x)arctan(x) as that?

as arctan(x)/(1/ln(x))

@glass silo sorry for ping

[glass silo]

Because a = 1/(1/a) for any a

alright well at least in theory, you can get something that's l'opitalable, whether it works out to something useful

[marsh citrus]

@forest stream Has your question been resolved?

[marsh citrus]

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[zinc scroll]

just started trig 2 and missed the first lesson.

How do I show that sin2A = 2sinAcosA by using the Sin(A+B) identity?

[worthy notch]

Do you know the sin(A+B) identity? Use that and plug in A for both A and B, since 2A = A + A

[zinc scroll]

sry i don't understand

[elfin berry]

Pure

[zinc scroll]

thanks!

[hidden plaza]

[marsh citrus]

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[marsh citrus]

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[onyx sentinel]

How do they get change in x_1 = 1/2 and change in x_2 = 1/2

[still temple]

Please close those tabs 🙏

I ain't solving no question from a person with that many tabs open bro

[main idol]

Did you calculate x1, x2, x3

[still temple]

You're ancient 😨

[main idol]

Stop talking then

[still temple]

[onyx sentinel]

like the values they give me? the 5/4, 7/4, and 5/2?

[main idol]

Yea do you know how those were obtained

[onyx sentinel]

i dont know i thought they just give those values to you at the start of the question

[main idol]

Look at the figure

5.2.7

[onyx sentinel]

oh its the values in between the values in P

[main idol]

Show the figure

[main idol]

Yes

Use the definition of delta x_i

[onyx sentinel]

3/2 - 1?

why is it not 5/4 -1?

another question so for some other questions when im calculating the lower and upper sum ill calculate the maximum and min values of f on the subintervals do i still need to do that or do i just use x*

[main idol]

Because that's not the definition of delta x_1

[main idol]

No

Don't guess. Look up the definition of delta x

[onyx sentinel]

it says the change in movement or the difference between 2 values of variable x. i thought 3/2 - 1 would make sense because it would give the difference of 1/2

and then the next would be 2 - 3/2 which gives 1/2 and then 3 - 2 which would give 1 which would match up with what the example says

[marsh citrus]

@onyx sentinel Has your question been resolved?

[main idol]

The first sentence is right

[main idol]

Oh my bad. You meant this for delta x_1

Yes that's right

[main idol]

I was asking for general delta x here

[main idol]

The rest is correct yes

[marsh citrus]

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[mossy creek]

Hi everyone, relatively simple question. But I'm having a discussion about probability and wanted to check my work.

A group I play cards with is having a discussion on the fairness of the random shuffling and dealing on the online platform.
Specifically, on the probability of any of the players having both of the highest cards in any suit (Ace and the 10).

It's a deck of 32 cards, all are dealt, so each of the 4 players gets 32 cards.

My work:

Starting with just one suit, hearts. The ace is dealt for certain, so that probability is irrelevant.
Whoever has/gets the ace, has only 7 more cards to getout of the remaining 31. That means 1/31 * 7 = a chance of 0.2258 , 22.58% that whoever gets the ace of hearts also gets the 10 of hearts.

(I'm quite confident about this at least).

Continuing that: that means a 77.42% chance of the Ace and 10 of hearts being seperated.
Using the same calculation for the remaining 4 suits : that's 1 * 0.7442 ^ 4 = 0.3067

So a total of 30.67 % chance of it not happening for any of the suits. Or, it should happen for at least one suit in roughly 70% of hands.

[marsh citrus]

@mossy creek Has your question been resolved?

[young owl]

1/317 = 22.58% ??

It's a deck of 32 cards, all are dealt, so each of the 4 players gets 32 cards.
??

[sleek slate]

I have only seen a deck of 52 cards, what's a deck of 32 cards?

[young owl]

from 7 to ace in each suit usually

7, 8, 9, 10, J, Q, K, A * 4

[mossy creek]

apologies, I made a typing error there, meant to be 1/31*7

[young owl]

it's still very much not 22.58%

oh you meant 7/31

ok

[mossy creek]

yeah so its a 1/31 chance for each of your 7 cards to be the 10

[young owl]

not really since each time you take a card there are less cards left

[mossy creek]

right but does that matter? You take 7 out of the 31 cards. If you were to draw all 31 cards the chance would be 100% (31/31 =1)

[young owl]

it does matter

once you take a card among the 31 left, there are only 30 left, the chance to get 10 next is now 1/30

not 1/31

in the end the difference is quite big since you'll have 8 cards

[mossy creek]

What would be the correct calculation then?

[young owl]

there are 4 players, each card has the same proba of being in the hand of any player, so the 10 of heart has a 1/4 to end in the end of the player that has the ace of heart and same for each suit

[mossy creek]

because, using the same for the other 3 players: each draw 24 of the 31 cards. 31/24 = 0.7742 77.42% . added up with the 22.58 makes 100%

Right but the person getting the ace has the ace, so only 7 cards left to get dealt, can't quite be 1/4

[young owl]

I consider the hand not individual cards

when the game ends, each player got 8 cards

the 10 of heart has 1/4 of chance for each player's hand

[mossy creek]

yeah of course. But does that mean it's the same chance for them both to be in the same hand

[mossy creek]

considering this

[mossy creek]

and this

[young owl]

when the game is already ended you don't care about order of cards, we're only saying that each player had the same probability of getting a given card at each game if it's distributed fairly

so you had a proba of 1/4 of getting 10H, your friend too, your other friend too... etc

so the proba it ends in the end of the player who has AH is 1/4

[mossy creek]

Indeed he order doesn't matter, so giving 1 player the ace first, then dealing the rest, should result in the same probabilities, right?

[young owl]

no because a choice of player has been made once you give the ace

[sleek lake]

it's proly a derangement on 4 tens

[young owl]

I tried thinking about derangement but the method was a bit of a pain so I'm trying to do it with expected values

[sleek lake]

you deal AAAATTTT
9 permutations of T positions gives no one the pair

so 62.5%

[mossy creek]

choice of player shouldn't matter though, as the question is if ANY of the players get it. Not if any single player does

[young owl]

that's why I say you can't make a choice of player without multiplying after

[sleek lake]

okay it's not that my bad

[mossy creek]

Doesn't matter who gets the ace, and we know the ace is dealt for certain

[sleek lake]

you can get 2 aces and 3 tens it's not like one of each is guaranteed

[young owl]

I'm taking a short break, I'll either post my a sol or run a simulation if I haven't find yet after

[mossy creek]

The ace being the first card or any other card is not important. So dealing ace first, then all other cards should not have different probabilities than just dealing normally and the ace landing in any hand naturally

The choice of player makes no difference, as one player is always chosen for certain

[sleek lake]

i agree that it makes sense, but only once

[mossy creek]

yeah that's why I'm fairly confident on the 22% part. It's the next calculation that I'm unsure is valid

[sleek lake]

ace of hearts is separated 77.42% no reason to doubt it, but you can't extend it for all

[mossy creek]

Thought that might be wrong, yeah. how would you calculate that correctly?

Now I just took the same 77% for all other aces. But I can't wrap my head around how the seperation or non-seperation of the "previous" aces might effect the probabilities

[sleek lake]

well it's too hard

[mossy creek]

ah :p

[sleek lake]

inside 77%, you have 2 players with 1 card and 2 players with 0
(14/30)(23/29) that the second ace is separated, in a way that it ends up with the player who had an ace or ten already
and (16/30)(22/29) that it's separated otherwise
and it keeps blowing up

[mossy creek]

yeah fair enough. Would that be a significant difference at the end you think?

Or is it correct to say the end result of roughly 70% is a decent approximation?

[sleek lake]

i don't know if it's good enough in principle

simulation shows 64%

[mossy creek]

alright, thanks for the effort!

[sleek lake]

i mean per game

you said per hand, so specific player?

21%

[mossy creek]

nah not for any specific player.

Just the chance that any of the 4 A10 combination is paired in any of the 4 hands after each deal

[sleek lake]

ok

[mossy creek]

thanks for the help and effort

You as well @young owl

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[marsh citrus]

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[amber tulip]

can someone help me with this qustion pls?

[marsh citrus]

@amber tulip Has your question been resolved?

[amber tulip]

<@&286206848099549185>

[marsh citrus]

@amber tulip Has your question been resolved?

[still temple]

Didn't you already ask this question somewhere else before?

You can determine angle CBA in terms of x

Then you can get angle BCP because BCP is isosceles. Then you get angle QCP because it's ACB-BCP. Then you can get angle CQP because CQP is isosceles

[marsh citrus]

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[amber tulip]

.reopen

[marsh citrus]

✅

[amber tulip]

ill try

[marsh citrus]

@amber tulip Has your question been resolved?

[marsh citrus]

@amber tulip Has your question been resolved?

[marsh citrus]

@amber tulip Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[wet tendon]

we’re supposed to use product rule; how did they get from the 2nd line to the 3rd? (problem 3) I’m confused specifically on the 2nd term on the 3rd line (1/2t^1/2)

[lone heart]

Can you send a better quality picture?

[hasty ruin]

also that moire pattern is burning my eyes

[wet tendon]

this is the best I can do sorry 😭

why not distributing 1/2 t ^(-1/2)?

why just the t^(-1/2)

[hasty ruin]

it’s also distributing that yes

[wet tendon]

would you be able to show me step by step how they got that second term 🙏

1/2t^1/2

[hasty ruin]

t^(-1/2)=1/t^(1/2) by exponent rule

$a^{-b}=\frac{1}{a^b}$

[elfin berry]

IV

[wet tendon]

oh and then they just multiplied the 1/2?

to get 1/2t^1/2

[hasty ruin]

ye

[wet tendon]

OK THANNKS

.close

[marsh citrus]

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[warm iron]

i can understand that if the lim of f exists then it has to be 0
but does the limit necessarily existss for such a function ?

[stark trail]

What

They’re defining C to be the set of functions where that is true

It isn’t necessarily true for all differentiable functions

[warm iron]

no no i mean limf(x)

can i say limf(x) exist for any such function

[stark trail]

No?

[warm iron]

examples ?

[stark trail]

f(x)=x^2

[warm iron]

to be precise my question is if
$$f\in C$$ then dooes lim f(x) exists

[elfin berry]

sudeepta1234

[stark trail]

No

[warm iron]

your function is not in C

[stark trail]

just because lim f+g=0 this does not mean lim f = -lim g

In general

take x and -x as example

Lim of their sum is 0

[warm iron]

i can understand
but can you help me with a proper counter '

[stark trail]

lim of each individually is infinity/negative infinity

[warm iron]

here the have more restrictions , not a good idea to consider them similar to the generic case

[stark trail]

Construct any example where 2f(x) = -f’(x)
And either of the two sides is unbounded as x-> infinity

All functions that solve that diffeq are of the form f(x)=Ce^(-2x)

[warm iron]

yeah but for such functions $lim_{x\rightarrow\infty}f(x)$ exists

[stark trail]

Then we’ve proven there are no counter examples

[elfin berry]

sudeepta1234

[stark trail]

If you must satisfy that diffeq

[warm iron]

but that doesn't sound too rigorous.

[stark trail]

In general though there are counter examples

[stark trail]

If you’re in C, you satisfy that diffeq

If you satisfy that diffeq then both f and f’ limit to infinity exists and is 0

True?

[vestal forge]

it doesn't seem like it has to satisfy that, since C didn't mention anything about them being equal everywhere

[stark trail]

Oh right

[warm iron]

yes exactluy

[stark trail]

I forgot how I made that

[vestal forge]

but it does seem like limit of f has to exist here

because if we think about the way that we try to make 2f + f' be indeterminate where lim of f must not exists

the only case that we have is infty - infty or -infty + infty

[hasty ruin]

the interesting part is does lim give you enough wiggle room to form a counterexample

[vestal forge]

but if you think about the behaviour of f(x) and f'(x) near infty as being so, it seems impossible.
If f(x) is getting larger and larger for x near infty, that means f(x) is growing, so how can f'(x) be -infty there?

similarly for the other case

[warm iron]

yes intuitively its certaiinly seems like lim must exist for such a functionn
the problem is they want me to provide a proof

[blazing pulsar]

I expect OPs statement to be correct that the limit of f exists. But I'm going to bed and don't really have time to work out the details

It's quite similar to a famous calculus trick

Yeah okay, an immediate google search yields this, which is exactly this when a(x) = 2 and b(x) = 1. The special case where a(x) = 1 and b(x) = 1 has a well-known 1 line proof, but this would involve a bit more work: https://math.stackexchange.com/questions/975392/if-fx-fracfxx-to0-then-fx-to0?noredirect=1

This is a much stronger result than what you asked for

[warm iron]

thanks

[blazing pulsar]

I actually came up with the proof while brushing my teeth and I am kind of embarassed I didn't realize it earlier

$\lim_{x\to\infty} f(x) = \lim_{x\to\infty} \frac{e^{2x}f(x)}{e^{2x}} = \lim_{x\to\infty} \frac{e^{2x}(2f(x)+f'(x))}{2e^{2x}} = 0$

[elfin berry]

JessicaK

[blazing pulsar]

You do need to be a little careful to justify that everything applies here but that's the core idea.

[marsh citrus]

@warm iron Has your question been resolved?

[marsh citrus]

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[sour lantern]

First day of the unit and I am so lost

[grizzled bobcat]

use pythagorean identity

[sour lantern]

i got 1 + sin2x / cos2x = 1/cos2x

i dont know where to go from here

[cobalt sentinel]

Don’t do that

Leave it as 1 + tan^2 (x)

It’s a Pythagorean trig identity

[sour lantern]

ye

[velvet locust]

take the lcm of

1 + (sin^2(x))/(cos^2(x))

[grizzled bobcat]

if you want LHS to equal RHS
LHS = 1 + tan^2(x)
LHS = 1 + sin^2(x)/cos^2(x)
LHS = cos^2(x)/cos^2(x) + sin^2(x)/cos^2(x)

[cobalt sentinel]

What is tan^2 (x) + 1 equal to @sour lantern

[grizzled bobcat]

should be pretty straightforward from there

[cobalt sentinel]

Using trig identity

[grizzled bobcat]

i don’t think they are familiar with this

[sour lantern]

sec2 x

[sour lantern]

nah its in my notes

[grizzled bobcat]

oh

yeah it’s just two pythag identities

[sour lantern]

ah ok

@cobalt sentinel thanks

[sour lantern]

bist du oesterreicher?
weil du hast die wappe als pfp

[cobalt sentinel]

I’m not Austrian

[sour lantern]

oh

[warm iron]

that is as simple as it can get
i sort of did exactly how the stack exchange showed
but this one is very elegant

[sour lantern]

well your pfp is the coat of arms of austria LOL

[cobalt sentinel]

Yes it’s related

: )

[sour lantern]

alright thanks though!

!close

.close

[marsh citrus]

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[marsh citrus]

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[rapid cosmos]

My teachr gave this question to find the value of probability (of success) in a binomial distribution which maximises the variance of the distribution

We have only just started differentiation so im not really sure how to find the maximum other then the derivative is = 0

I think I need to find where dv/dp = 0 but how do I get it into a form where I can actually differentiate it?

[rapid cosmos]

I’ve tried dv/dp = 1 - 2p = 0 and got 1/2 but idk if it’s right

Can I just disregard n?

[copper raven]

well dv/dp = n(1-2p)

it's not like n is really relevant here though

n is a positive integer anyway

it can't be 0

[rapid cosmos]

ohh yeah

[copper raven]

so if dv/dp = 0, you need to have 1-2p=0