What are the other intervals?
#help-17
tame wadi
leaden scroll
[5,7] , [8, inf]
tame wadi
Now how about concave down?
tame wadi
Where?
leaden scroll
[5,7] , [8, inf]
here
tame wadi
Yes [5,7] is concave up
tame wadi
For every x, Whenever f' changes direction from + to - or - to +or rather the slope changes, x is called inflection point
For which values of x the slope changes in the graph?
leaden scroll
0,2,4,6, 7, 9 ?
tame wadi
The point when slope changes..
Take a look at the curve at x=1. Before 1 the curve is downwards and after 1 the curve is upwards
So 1 is inflection point
Find more inflection points like that..
leaden scroll
1,4,5/6?, 7
tame wadi
No.
Take a look at x=4. Before 4 the curve is upwards or downwards?
leaden scroll
down
tame wadi
Okay
After 4 the curve is ...?
leaden scroll
up
tame wadi
No the curve is still going down till 5
leaden scroll
oh
leaden scroll
before 5 is down and after is up
leaden scroll
would 3 be inflection
leaden scroll
1, 3, 5 ,7 ?
tame wadi
How about 8?
leaden scroll
oh yeah 8
tame wadi
So you got your answers..
leaden scroll
i put them in and this happened 😭
tame wadi
In the first one you did mistakenly put ] instead of ) near infinity
leaden scroll
what about the rest
tame wadi
Oh yes I did mistake in local minima and maxima part.
Okay do you see when f' is zero.
tame wadi
The values of x at which f' is zero.
According to second derivative test,
We make first derivative zero and find the sign of second derivative, if it's positive then local maxima or if it's negative then local minima exists at that point x.
Can you stat the points when f' is zero?
leaden scroll
would it = 0 whenever its 0 on the y axis?
tame wadi
f' is zero Whenever curve touches the x axis
leaden scroll
2,4,6
tame wadi
Okay
Now we need to find whether at 2 minima exist or maxima right?
leaden scroll
yes
tame wadi
Okay look at the graph at x=2. It's negative before 2 and becomes positive after 2 right?
leaden scroll
yess
tame wadi
So if direction changes from negative to positive, minima exists at that point.
So at x=2 we get local minima
What do we get at x=4?
leaden scroll
a 0 ?
tame wadi
Yeah you get f' to be zero at x=4.
How the direction changes before and after 4?
leaden scroll
isnt it down ?
tame wadi
I mean the sign changes from positive to negetive right?
leaden scroll
oh yeah
leaden scroll
yuh
tame wadi
Now what (minima or maxima) exists at x=6?
leaden scroll
minima?
tame wadi
Try putting 9] instead of inf
leaden scroll
that fixed c but a is still wrong
tame wadi
You did enter incorrect answer.
tame wadi
No put ) near inf
full vector
The line ends at 9 so change infi to 9
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frail mantle
hello
frail mantle
I'm trying to figure out how I factor an equation to find the vertical asymptotes
the equation is (x+2)/((x^2)+25
I was told I had to use the equation where the denominator was equal to 0
but x^2+25=0 doesnt result in a real number
frail mantle
since there is no square root of -25
hard valve
Correct! This function has no vertical asymptotes
frail mantle
hard valve
And your justification is correct as well
frail mantle
oh
i'm an idiot
It's asking for intercepts
the past 2 have asked me for asymptotes
so i got used to looking for asymptotes lmao
hard valve
Haha I see
hard valve
Yeah so for y-intercept you do the usual thing and set x=0
For x-intercepts you now want the numerator is 0 instead of the denominator
frail mantle
so -2 is the x intercept
k i def did this wrong i got 50
for my y intercept
i cancelled out one of the x's so i got 2/x+25
rocky wyvern
If x=0 then you get ((0)+2)/((0^2)+25)
rocky wyvern
Np
frail mantle
I had a coding project due so I pulled an all nighter
and i'm running off 2 monsters, a cup of coffee, and a peach redbull
Also a cup of ramen
so it's 2/25?
rocky wyvern
Yup
hard valve
Yeah, looks right
frail mantle
@hard valve i've one more quesiton
How do I find the horizontal asymptote here
would there be one at 0?
since it's the leading factors cancel out eachother?
rocky wyvern
Find f(x) as x goes to infinity I think
frail mantle
How do I figure that out exactly?
The book says to compare the leading factors
But I feel like I’m missing a step
rocky wyvern
So, if x was an unimaginably huge number, only the highest degree x would matter
Therefore we can ignore lower degree terms
And the problem becomes what does x^2/x^2 equal
frail mantle
0
Wait
No
1
I was doing it wrong in my head
The book showed them cancelling out the x when dividing
But I realize that only works when there are other factors
I think I’m really starting to understand this now
frail mantle
One final question, to find the x intercept I do x^2-x-20=0 so I add 20 to both sides and now I have x^2-x=20 where do I proceed from here?
What’s the rule on that?
rocky wyvern
No keep it as x^-x-20=0, instead factor it
frail mantle
I’ve heard the term to factor stuff quite a bit
How do I factor
I’m very sorry for all the hassle btw, I haven’t had any algebraic math since senior year highschool
It’s been around 2 years
Maybe even 3
The only math I’ve done recently was statistics applied for stem and it required a lot of coding and essay writing instead of math lmao
rocky wyvern
Oh lmao
frail mantle
And that class I really understood
Didn’t have any trouble there I was actually super confident in my ability to do the work there
rocky wyvern
You did do factoring tho at one point right?
frail mantle
But I’ve had a bit of trouble when it comes from algebra due to a sequence of negative experiences in math classes that really ruined my math career lmao
frail mantle
You did do factoring tho at one point right?
I actually don’t know for sure
rocky wyvern
So u wanna get x^2-x-20=0 in the form (x+constant) (x+constant)=0
To find the constants, you need to figure out what 2 numbers at to -1 and multiply to -20
rocky wyvern
Ok for example x^2+x-6=0
Factors to (x+3)(x-2)=0 because 3x-2x=x and 3•(-2)=-6
And x•x=x^2 of course
Does that make any sense?
rocky wyvern
Np, tbh I have calc 2 homework but I'm kinda addicted to helping on this dc now lmao
frail mantle
Np, tbh I have calc 2 homework but I'm kinda addicted to helping on this dc now ...
I just wish I was allowed to pick my college courses ngl
Whoever decided to put me in pre calc AND introduction to scripting should be arrested
I told my advisor my biggest concern was math
And they paired me learning a new coding language with learning what is essentially a numerical language aswell
I feel like math has even more rules than a traditional language
rocky wyvern
I took calc 2 online last year and it was TERRIBLE so I'm retaking it
frail mantle
I took calc 2 online last year and it was TERRIBLE so I'm retaking it
My main problem is I excel at literally anything but math because I kinda got bent over and screwed on my highschool math
I don’t like blaming the school and I will admit it’s part my fault too
But I went from being an AP math student to struggling in the regular courses
rocky wyvern
I'm still in highschool anyway and I have extra class slots for whatever i want so I'm also gonna take calc 3
frail mantle
My ap math teacher got sick mid semester and rather than move over an actual math teacher they just gave us substitutes
rocky wyvern
Ah yeah
frail mantle
Subs who didn’t know how to do the math themselves
Which sucks but I could just go down to regular class and be fine right?
rocky wyvern
I got lucky with math teachers
frail mantle
The next semester I got a teacher who was barely out of college
He didn’t understand the concept of punishment
The class was a monkey bin
rocky wyvern
But my school has a really bad science department
frail mantle
There was no control only chaos
Kid you not I’ve got videos from that class those kids were on some crazy nonsense
rocky wyvern
💀 you got no idea
frail mantle
We shorted out an electrical outlet by putting a coin in between the prongs on a wall outlet
Nobody ever got in trouble
rocky wyvern
My chemistry class teacher did LITERALLY nothing all year
frail mantle
Shit you not one kid even sprayed cologne on a girl, caused her to have an athsma attack and didn’t get in trouble
rocky wyvern
He just gave us online worksheets to fill out and taught morning
rocky wyvern
Shit you not one kid even sprayed cologne on a girl, caused her to have an athsm...
💀💀💀 that's pretty bad
frail mantle
And it upsets me because I’ll be nearing my junior year soon with my 4.0 gpa intact
And if I can’t get caught up in math
I’ll lose that
And I’m a computer science major
Which means I think I’ll go up to calc 4
rocky wyvern
And I’m a computer science major
I wanna be but my comp sci teacher went on a sebatical last year
frail mantle
I wanna be but my comp sci teacher went on a sebatical last year
Tip, get a part time job at Walmart
rocky wyvern
So I've been struggling to find time to do my own programming stuff
frail mantle
They fully cover any costs for a computer science degree
Nothing out of pocket for me
rocky wyvern
Oh cool!
rocky wyvern
Lmaoooo
rocky wyvern
I don’t actually like computer science
I'm honestly the opposite
rocky wyvern
I learned to program on scratch
frail mantle
rocky wyvern
That was a mistake in my opinion
frail mantle
Lepidoptera my beloved
rocky wyvern
frail mantle
Scaley winged insects
frail mantle
Can’t recall if dragonflies are orthoptera or another classification
rocky wyvern
Idk why the camera didn't capture it
frail mantle
Wait nah Diptera I got it mixed up
rocky wyvern
What programming languages do u know?
frail mantle
What programming languages do u know?
Currently learning python
rocky wyvern
I consider myself a late beginner in both Python and JavaScript
I had this really cool linear regression algorithm
frail mantle
I know enough python to make graphs and calculate statistics outside of that I’m a complete beginner
Shoutout to my advisor for scheduling my Python based statistics class before my actual introduction to scripting class
rocky wyvern
Ah yeah
frail mantle
I may not know basic fundamentals of Python, but I can make a graphs
But yea the plan is to add “computer science major” to my list of certifications I’ll never use
rocky wyvern
I have been trying to code a Zelda like game but I keep getting hung up on small things like sprites and how to animate
frail mantle
Along with my welding certification, my osha certification, and my HVAC apprenticeship license
rocky wyvern
I think in another dimension I'm already an engineer
I was always good at robotics
But then I joined my highschool robotics team and they were horrible so I quit and haven't done it since
frail mantle
Lmao
I was in a robotics team
I got paired up with the worst person ever for our first event and I never went back
rocky wyvern
Yeah, way back in like elementary school I remember taking a robotics summer camp, and got paired with a kid with anger issues
He got so mad that I was trying to contribute that we never finished programming our robot
Wow, I feel like I just told my life story lmao
rocky wyvern
One final question, to find the x intercept I do x^2-x-20=0 so I add 20 to both ...
Have you tried factoring yet?
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@frail mantle Has your question been resolved?
frail mantle
Have you tried factoring yet?
gonna sleep on it and tackle it in the morning
frail mantle
it's 2:30 already
rocky wyvern
It's 12 30 for me
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solar forge
hello, i have this problem, that states: find basis of subspace for orthogonal complement
vocal sleetBOT
hello, i have this problem, that states: find basis of subspace for orthogonal c...
solar forge
i got the basis as
but now they want me to find a projector to X comp
since I already have the basis of the space, I can just find the projector P (without I-P) but i dont understand, how the choose to use orthogonal matrix
as this
can i just take any vector, normalize it and use it to have easier equation for the projector?
because the X^orth basis is not orthogonal itself (BB^T \neq I)
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quartz beacon
Suppose f : R → R is continuous and has no zero point. Suppose that F is a primitive function of f. Show that F has at most one zero point.
vocal sleetBOT
Suppose f : R → R is continuous and has no zero point. Suppose that F is a primi...
quartz beacon
How do you prove this without using an example
mild flower
you could show the contrapositive
hybrid flicker
you can show F is either increasing or decreasing for example
hard atlas
if F is a primitive of f, then f is a what of F?
quartz beacon
f is the derivative
hybrid flicker
f is the derivative
the derivative has no zero points and is continuous
does this tell us something maybe about ||the sign of || f?
quartz beacon
well its either strictly negative or strictly positive
so F will always be increasing or decreasing depending on the sign of f
@hybrid flicker what can i do after?
you also know F will be continuous because differentiating implies continuity
hybrid flicker
<@246787399991033858> what can i do after?
F is continuous and strictly monotonic
corollary of IVT...
or you can either do this distinction:
if F has no zero points, you win
if F has at least one zero point, name x that point such that F(x) = 0
now that you know that F is strictly monotonic, can there be another zero?
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vast shale
Why 1++2+3+4+...... infinity=-1/12
vocal sleetBOT
Why 1++2+3+4+...... infinity=-1/12
gentle oriole
Why 1++2+3+4+...... infinity=-1/12
it's not
you can find a lot of videos online on this topic
vast shale
But some people on YouTube prove it by some series by ramanujan
merry shuttle
thats a divergent series man it aint equal -1/12
gentle oriole
Why 1++2+3+4+...... infinity=-1/12
this happens when you redefine the rules of mathematics
vast shale
Yeah then how Ramanujan proved by using two other series
gentle oriole
Yeah then how Ramanujan proved by using two other series
ur not supposed to add/subtract infinities like that
gentle oriole
I was confused when i saw sum of all natural number equals -1/12
analytic continuation and complex analysis is involved if i am not mistaken
gentle oriole
And one more thing why circle is not a n sided polygon
well a circle is what happens when n approaches infinity
merry shuttle
bro asking all the controversial ones
gentle oriole
lmfaoooooooo yea
vast shale
bro asking all the controversial ones
😅 my teacher taught the polygon one last week i asked my friends but they said does circle has sides
vast shale
well a circle is what happens when n approaches infinity
Now i think my friends don't know anything
flat ermine
poor numberphile
vast shale
Hey does it mean our earth is also a polygon
flat ermine
this happens when you redefine the rules of mathematics
Ramanujan surely knew this, and yet he added 2 divergent series. I think he was just shitposting when he said the sum of all natural numbers is -1/12.
vast shale
Ramanujan surely knew this, and yet he added 2 divergent series. I think he was ...
Maybe he was doing something else and we got something else
arctic mantle
Ramanujan surely knew this, and yet he added 2 divergent series. I think he was ...
no
it's a way of assigning finite values to div. series
through a neat trick of analytic continuation
it's a thing from complex anaysis
arctic mantle
😅 my teacher taught the polygon one last week i asked my friends but they said ...
no
arctic mantle
Hey does it mean our earth is also a polygon
also no, polygons are 2D
it isn't equal in the typical sense
but you can "assign" a value that agrees with other values
flat ermine
it's a thing from complex anaysis
but the proof that ramanujan allegedly wrote had nothing to do with Analytic continuation or complex analysis
flat ermine
do you realize what proof im talking about?
arctic mantle
and if you complete the analytic continuation of the riemann-zeta function, you get -1/12 at s = 1
flat ermine
im not talking about that
flat ermine
i haven't watched all of numberphile's vids yk
arctic mantle
oh NUMBERPHILE
i keep confusing this guy with mathologer.
don't like this guy at all
flat ermine
they claim this was the proof by ramanujan
and this proof has nothing to do with zeta funciton
flat ermine
which makes me think that proof is just a joke
arctic mantle
that proof doesn't even make sense
first off you can't even rearrange the series like that
it's not absolutely convergent
flat ermine
exactly
arctic mantle
lmao
his proof doesn't even work 💀
fairly certain ramanujan would've had a little more rigor
vast shale
... Why do i feel i am the lowest here 😢
arctic mantle
dw
flat ermine
dw about it you're still in highschool right
flat ermine
fairly certain ramanujan would've had a little more rigor
he probably did something else and it got lost or something
arctic mantle
yeah
vast shale
dw about it you're still in highschool right
11 grade
arctic mantle
yeah you don't need to know all this man
flat ermine
its highschool
arctic mantle
indian?
vast shale
Yeah
flat ermine
Why 1++2+3+4+...... infinity=-1/12
short answer, its not.
vast shale
How you know
arctic mantle
guessed
flat ermine
i've noticed this a lot
arctic mantle
long answer, it sort of is but not really
flat ermine
whenever indians meet each other online while being oblivious of the other persons nationality
arctic mantle
not in the usual sense of "is equal to" anyway
flat ermine
they somehow manage to figure out the other person is also indian
arctic mantle
lmao
gentle oriole
it's a thing from complex anaysis
aha i knew it
flat ermine
like some sort of spidey sense
arctic mantle
i was abt to say that lmao
vast shale
they somehow manage to figure out the other person is also indian
Then who is indian here
gentle oriole
you both indian?
flat ermine
ren and rin
vast shale
Offline is also the same like 14 lakh people give an exam this year to get good college
Ok that's it hmm hmm
.close
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quartz beacon
vocal sleetBOT
quartz beacon
Why isn’t 0 an absolute minimum
Because the lim for x->inf is 0
But zero actually reaches this point
hard atlas
well you cut off the page but are they actually saying anywhere its not the absolute min?
quartz beacon
they said its a local minimum
quartz beacon
ok is it in this case the absolute
hard atlas
yes
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spiral linden
3(5^2x)=6(4^3x), solve for x
vocal sleetBOT
3(5^2x)=6(4^3x), solve for x
spiral linden
sorry for constantly posting questions btw, im just really stuck on this unit
gentle oriole
take a log on both sides and apply product and power laws
you should end up with log3 + 2x log5 = log6 + 3x log4
spiral linden
ohh ok thx ill try that
im not sure how to solve 2x log (5) or 3x log4 because of the exponent
i might be an idiot though
gentle oriole
im not sure how to solve 2x log (5) or 3x log4 because of the exponent
uhhh what
there is no exponent
spiral linden
sorry i meant variable 2x and 3x
spiral linden
ok thx
gentle oriole
log3 + 2x log5 = log6 + 3x log4
log3 - log6 = 3x log4 - 2x log5
log3 - log6 = x(3 log4 - 2 log5)
x = (log3 - log6)/(3 log4 - 2 log5)
you could leave this as your final answer
but i do not recommend it
try to combine it all into a single logarithm
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plucky axle
Sam and Dean are 20 miles apart on seashore, Sam sees a ship N50°E and Dean sees the same ship N27°W Find their distance from the ship.
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Sam and Dean are 20 miles apart on seashore, Sam sees a ship N50°E and Dean sees...
plucky axle
@helper
arctic mantle
!15m
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
arctic mantle
HA get SNIPED south
plucky axle
Okok
bronze osprey
Sam and Dean are 20 miles apart on seashore, Sam sees a ship N50°E and Dean sees...
have you tried drawing it out?
plucky axle
Sam and Dean are 20 miles apart on seashore, Sam sees a ship N50°E and Dean sees...
Plss help
Yeah
bronze osprey
the question sucks cause it assumes the line between Sam and Dean is horizontal, or something
but it's an application of the sine rule
you want to find the two angles inside the triangle, where Sam and Dean are at
plucky axle
bronze osprey
Ahhh i minus it from 90°?
yeah
plucky axle
So 15 miles and 9 miles is the answer?
vast shale
Determine λ ∈ R such that the point A(0, 2, 1) is the orthogonal projection of the point B(3, 3, 3) onto the line p, whose direction vector is (3, λ, λ). How far is that direction from the origin? (λ=-3; closest point is (1,1,0), d=sqrt(2). I got λ correct, but i don't know how to get closest point and distance from the origin.
vocal sleetBOT
Determine λ ∈ R such that the point A(0, 2, 1) is the orthogonal projection of t...
gloomy wadi
Distance from the origin of what? The line or the closest point?
vast shale
of closest point on that line
gloomy wadi
(it should be the same anyways)
bronze osprey
Determine λ ∈ R such that the point A(0, 2, 1) is the orthogonal projection of t...
well that means AB is perpendicular to the direction vector
okay you found lambda
the closest point to the origin right?
gloomy wadi
The closest point is the intersection of the line and the orthogonal plane passing by the origin?
bronze osprey
so if you have say (1 + 2t, 2 + 3t, 3 + 4t)
you want to minimise the squared distance or just $(1+2t)^2+(2+3t)^2+(3+4t)^2$
twin meteorBOT
south's secret twin brother
bronze osprey
do you get it now?
vast shale
hmm not really haha, i know there are some formulas of x product for distance but i cant find them
bronze osprey
hmm not really haha, i know there are some formulas of x product for distance bu...
alternatively you can dot $(P - O)$ with the direction vector of the line and you get $0$
twin meteorBOT
south's secret twin brother
bronze osprey
well $P - O = P$ since $O$ is the origin
twin meteorBOT
south's secret twin brother
vocal sleetBOT
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vast shale
chem but idk if anyone help
tame wadi
Can't see the questions properly. Can you please send it again?
vocal sleetBOT
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onyx abyss
need lil help
vocal sleetBOT
need lil help
onyx abyss
let me translate the problem
Find all polynomials W(x) up to at most 3rd degree, such that ( W(x) % (x^2 - 1) = (x+2) ) and ( W(x) % (x^2 - 2x) = (x+1) ).
seems pretty simple but i'm not the shaperst tool
it's kind of urgent
<@&286206848099549185>
I would probably know how to do it if i was dividing the polynomial by a polynomial of 1st degree
wraith mist
Find all polynomials W(x) up to at most 3rd degree, such that ( W(x) % (x^2 - 1)...
On one hand, W(x) = (a x + b)(x² - 1) + x + 2
On the other hand, W(x) = (c x + d)(x² - 2x) + x + 1
wraith mist
Yes, this is close to what I mean
onyx abyss
Yes, this is close to what I mean
how do i solve it?
wraith mist
Expand the brackets in both cases and note that coefficients of x³, x², x, 1 in both cases should be equal
This will produce a system of equations
onyx abyss
so a=c and b=d?
onyx abyss
you're a life saver
i'll keep the channel open in case i'm dumb enough to not solve it with that info
@wraith mist sorry to bother you, i've calculated a,b,c,d and i need to answer but i'm not sure how to get all the polynomials that satisfy the problem out of that
nvm it works, not sure if i got it right
or if there's any edge cases
rose shard
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rose shard
Need help with backpropagation
I feel like im doing something wrong....
especially the last steps when computing for second hidden layer..
vocal sleetBOT
@rose shard Has your question been resolved?
uneven crag
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uneven crag
ok thanks
tame pasture
this may potentially not be a good question here, but are there any tricks I can use to make my handwritten us and vs distinct?
vocal sleetBOT
this may potentially not be a good question here, but are there any tricks I can...
tame pasture
they look like this (u is the first)
tame pasture
can you give an example please?
plucky trout
uh hold up
silk osprey
give the u a tail
twin meteorBOT
knief
tame pasture
oh, that's a good idea, thanks!
drifting jackal
they look like this (u is the first)
Make the v "sharper"
tame pasture
Make the v "sharper"
how do I do this without sacrificing speed?
drifting jackal
Practice
Plus a u is like one curved stroke while a v is basically two straight lines
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vast shale
Hello, my question is whether my rephrasing is accurate according to this definition: "TM M decides a language L if On every w, M accepts all words in the language and rejects all words that are not (i.e. all w that do not belong to the language of M reach q_{rej})"
vocal sleetBOT
Hello, my question is whether my rephrasing is accurate according to this defini...
vast shale
@graceful ibex
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@vast shale Has your question been resolved?
mighty cedar
If lets say I have y-18 = x (-0.5 - 4)
vocal sleetBOT
If lets say I have y-18 = x (-0.5 - 4)
mighty cedar
do i gotta then multiply the brackets by the x
like
will it be
-4.5x
or
x -4.5
kinda confused on this
terse ether
uhhh
vital sky
Make x alone right?
terse ether
it would be -4.5x right?
mighty cedar
.close
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dull bear
(Wait, as in the "self" inner products here, you mean?)
if so, then yea, <u, u> and <v, v> are always nonnegative real (even in complex vector spaces)
dull bear
(be very careful, the notation is sus, and these aren't numbers but vectors)
twin meteorBOT
gmdn
dull bear
But $\ip{u + v}{u - v} = \ip{u}{u} - \ip{u}{v} + \ip{v}{u} - \ip{v}{v}$, sure
twin meteorBOT
@dull bear
you're learning after all 
vocal sleetBOT
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tranquil shuttle
i know how to deal with the differentiation here, but what do i do with the information that y(0) = 8 once i have the general solution?
vocal sleetBOT
i know how to deal with the differentiation here, but what do i do with the info...
sick flax
plug it in to figure out what ur constants should be
tranquil shuttle
do i plug it in before or after i differentiate
tranquil shuttle
no question it just says “solve the differential equations” at the top of the whole worksheet
tranquil shuttle
ok
sick flax
because ur solution for y will have constants
sick flax
the equation will equal 8 yeah
tranquil shuttle
cool
sick flax
if you put 0 in ye
tranquil shuttle
ty
sick flax
have a go
tranquil shuttle
how does this look
vocal sleetBOT
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zinc grove
Im trying to solve this equation using variation of parameters but im lost on what functions to use in my Wronskian determinant. Right now im using e^xcosx and e^xsinx, but im getting something kinda ugly
vocal sleetBOT
Im trying to solve this equation using variation of parameters but im lost on wh...
zinc grove
this is my work so far
ive realized im incapable of multiplication
revisited my work and got this:
not sure what im doing wrong <@&286206848099549185>
vocal sleetBOT
@zinc grove Has your question been resolved?
zinc grove
no
vocal sleetBOT
@zinc grove Has your question been resolved?
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@zinc grove Has your question been resolved?
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@zinc grove Has your question been resolved?
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@zinc grove Has your question been resolved?
steep inlet
When i tried this, i got to the conclusion that month 1 is 4% then month2: 5%, m3: 6%, then shouldn't m4 be 7%?
vocal sleetBOT
When i tried this, i got to the conclusion that month 1 is 4% then month2: 5%, m...
steep inlet
Or is it based on 4% +1 for every 80,000 sales
Will my Rate of commision will be 8% or 7%?
Oh bruh, is it capped at 6%?
Idk, maybe my sir did a typo on 5% around 80k-160k
vocal sleetBOT
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@steep inlet Has your question been resolved?
chilly mason
vocal sleetBOT
chilly mason
How do I integrate this function?
ebon sand
hybrid flicker
How do I integrate this function?
You should try euclidian division
t^2 = ...(1-t) + constant
since 1/(1-t) is easy to integrate
vast shale
How do I integrate this function?
divide t^2 by 1-t using long division method
chilly mason
Understood, thanks a lot!
vast shale
do u need futher help?
chilly mason
No need, thank you
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vast shale
I NEED A GOOD RESOURCES TO STUDY ANALYSIS ON YOUTUBE PLZ IM ON MY TEARS RN
steep crater
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fallen palm
Need help with trigonometry
vocal sleetBOT
Need help with trigonometry
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weary fjord
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
% Set the line color and thickness
\draw[blue, line width=2pt]
(-1,1) -- (1,-1) % Diagonal line from top left to bottom right
(-1,-1) -- (1,1) % Diagonal line from bottom left to top right
(0,1.5) -- (0,-1.5) % Vertical line from top to bottom
(-1.5,0) -- (1.5,0); % Horizontal line from left to right
\end{tikzpicture}
\end{document}
twin meteorBOT
nick
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
weary fjord
man this did not come out right
think of a coordinate plane
that goes like this
is that a function
vocal sleetBOT
@weary fjord Has your question been resolved?
weary fjord
its not a function
thank god
i just had my quiz
everyone thought it was a function
rain cypress
if you draw a vertical line at any place and it cuts the graph at 2 or more points its not a function
weary fjord
thank you
vocal sleetBOT
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rain cypress
snow hedge
It has no meaning
As far as I've studied
I've never came across such thing
Once it also came in my mind but when I looked at the internet, it says it has no meaning
Which I think is true
plush summit
State whether the statement is false or correct:
if f′′(x) > 0 for x < 4 and f′′(x) < 0 for x > 4, then f(x) needs to have a turning point at x = 4.
Is this false simply when f isn't defined at x = 4?
vocal sleetBOT
State whether the statement is false or correct:
if f′′(x) > 0 for x < 4 and f′′...
rain cypress
It has no meaning
But you get the right answer
snow hedge
But you get the right answer
And many more says its meaning less,
It either might be some typing mistake or some assumption by Physics guys
vocal sleetBOT
rain cypress
https://www.google.com/amp/s/www.edaboard.com/threads/integration-of-1-dx-please...
Man
It doesn't make sense yeah
But it somehow mathematically works out
To solve the differential eqn
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heavy palm
Can someone explain 64 to me on what’s wrong with the equation?
vocal sleetBOT
Can someone explain 64 to me on what’s wrong with the equation?
silk osprey
Can someone explain 64 to me on what’s wrong with the equation?
is there any discontinuity?
in the interval -1 to 2
heavy palm
is there any discontinuity?
How could I check?
silk osprey
well, is 4/x^3 continuous on -1 to 2
first commandment
thou shall not divide by zero
heavy palm
thou shall not divide by zero
Well I don’t believe none of these divide by zero do they
Unless I’m wrong
ok uh wait
heavy palm
Oh sorry I looked at 63 instead ☠️
heavy palm
is 0 \in [-1,2]?
I’m gonna assume the answer is probably yes because you’re asking me this, but I don’t see where the denominator is zero
heavy palm
Yes
Sorry I was only looking at the two values
I didn’t take in account for that
Thank you 🙏
silk osprey
you’re welcome
vocal sleetBOT
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livid void
Im trying to think of how to define this. 😅
Is it getting x/y direction from magnitude?
vocal sleetBOT
Im trying to think of how to define this. 😅
Is it getting x/y direction from m...
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undone pier
vocal sleetBOT
undone pier
I figure i need to show 3 things here:
- non empty, it has the zero vector. that's pretty clear to me. since W1 and W2 are both subspaces, they each have the 0 vector, so their intersect must also have the 0 vector, so this is trivial
- closed under addition
- closed under scalar mul
i'm not sure how to show the last 2 things
quick crag
closed under scalar multiplication should be fairly straight forward. give it a go.
If w in W_1 n W_2, then ||w in W_1 and w in W_2||. Therefore kw in ...
hushed pewter
2. closed under addition
Consider two arbitrary elements $x,y\in W_1\cap W_2$. Consider what you need to show about $x+y$
twin meteorBOT
SWR
undone pier
hmmm
undone pier
If `w in W_1 n W_2`, then ||`w in W_1` and `w in W_2`||. Therefore `kw in ` ...
so w is in both W1 and W2. a scalar muliple of w in W1 is still in W1 by definition, since its a subspace of V, and a scalar multiple of w in W2 by definition, since its a subspace of V
since its in both, kW exists in W1 n W2 ?
quick crag
yep
undone pier
now for addition
quick crag
$$w \in W_1 \cap W_2 \implies \begin{cases} w \in W_1 \ w \in W_2 \end{cases} \implies \begin{cases} kw \in W_1 \ kw \in W_2 \end{cases} \implies kw \in W_1 \cap W_2$$
twin meteorBOT
Shuba
quick crag
now for addition
addition should follow very similarly
undone pier
so lets consider two arbitrary elms for W1 N W2
x is in both W1 and W2
y is in both W1 and W2
x+y is defined in W1 by definition since its a subspace of V
x+y is also defined in W2 by definition since thats also a subspace of V
x+y is in both; x+y is contained in W1nW2
quick crag
ye 🙂
undone pier
now all 3 properties are fulfilled, and we can say W1 n W2 is subspace of V also
okay, thank you to the both of you ! :)
.close
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sullen elm
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oak magnet
What have you tried ?
vocal sleetBOT
@sullen elm Has your question been resolved?
kind forge
can you solve for x
what have you tried till now ?
tidal dock
hint: ||simplify the numerator||
jagged slate
anyone wanna help me
vocal sleetBOT
anyone wanna help me
languid sparrow
Sure what do u need help with
robust hemlock
what specifically
jagged slate
just how to do this problem in genreal
robust hemlock
run is how much the x value changes
jagged slate
its our first day learning this topic
jagged slate
so how can i solve this
robust hemlock
so for triangle ABC
you have to start at the leftmost point
so in this case, it would be point B
now you have to count how many steps it takes in the x axis and y axis to get to point A
jagged slate
ohhh
robust hemlock
which gives you your run and rise values respectively
robust hemlock
run is 1 but rise should be 4
robust hemlock
slope is defined as rise divided by run
jagged slate
thank u so much
robust hemlock
and then you can do the same for the other triangle
jagged slate
ok thanks so much
robust hemlock
👍
jagged slate
.close
vocal sleetBOT
robust hemlock
oh keep in mind that you read graphs left to right
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zealous pebble
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flat whale
,w [[0.84, 0.43], [0.16, 0.57]]^2 * [[948, 252]]
twin meteorBOT
flat whale
i don't understand how i'm wrong
you rounded incorrectly
zealous pebble
nearest integer...?
flat whale
re-read the question
.
vocal sleetBOT
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kind kindle
how can I find the derivative of sin^2 (x/2) without using the chain rule
torn oracle
sin^2(x)=1/2(1-cos(2x))
kind kindle
why arent u using the chain rule anyway
question asks to solve without chain rule
sick flax
ah
kind kindle
thank you!
sick flax
learn the trig identities they are so helpful
untold arrow
Why if lim f- g >0, then f>g?
vocal sleetBOT
Why if lim f- g >0, then f>g?
mild flower
that's not true
untold arrow
Why?😭
prisma rain
x² < x for x in (0, 1), but x² > x for x > 1, so you need to be more precise
mild flower
,w graph x + 1, sqrt(-x) from -3 to 1
twin meteorBOT
untold arrow
In a small nbhd
mild flower
ah!
now we are getting somewhere
go back to the definition of limit
you can prove it
untold arrow
I can't😭
I'm new to that definition
I couldn't even understand it
I posted the question here bc I need help
If I can, i wouldn't even post here
mild flower
if lim f-g > 0 then lim f-g = L where L is some positive number
so as you zoom in closer to 0, f-g gets closer to L
untold arrow
Doesn't that mean f>g ? f-g is a positive number
mild flower
f > g means that the entire function f is greater than the entire function g
unless you clarify otherwise
untold arrow
Wait so f only > g in this small nbhd?
Specifically, for the x enough close to c, f>g ?
mild flower
what you have is that if you want f-g to be within a certain distance of L, you can zoom in and make that happen
mild flower
Wait so f only > g in this small nbhd?
yes
vocal sleetBOT
untold arrow
I see! Thanks!
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trail moat
Help
trail moat
spiral turtle
!da2a
vocal sleetBOT
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/
trail moat
I’m stuck on finding what multiplies to 112 and adds to -23
spiral turtle
It only multiplies to 56 though?
trail moat
Huh?
trail moat
Ye I was confused 😭
spiral turtle
Anyway 7 + 16 = 23
regal slate
-7 - 16
trail moat
So that’s why I’m confused
regal slate
well you’re still adding them, it’s just -7 + (-16)
regal slate
yes
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outer hemlock
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outer hemlock
can someone explain to me this infinity thing
why do we insert infity
when do we insert infinity
i really don't get it
torn oracle
You insert infinity when you have an expression that won't be undefined
So like the step you are up to
2/K as k--> infinity will become 0
Which gives you a defined value of 1/2
If you substitute earlier the value would instead be undefined
outer hemlock
so is infinity like a zero?
torn oracle
so is infinity like a zero?
No it's literal infinity
outer hemlock
damn really lmao
torn oracle
It's just 1/infinity is well known to be 0
1/K approaches 0 as K approaches infinity
outer hemlock
so then it becomes 1/2?
torn oracle
Ye
outer hemlock
so when do we insert infinity?
torn oracle
When the expression won't be undefined
torn oracle
Well you want to find a defined limit
So you want to simplify until inserting the limit creates a defined value
(or just show that it diverges off to infinity)
outer hemlock
ooh okay
also this limit thing
what does limit even mean?
i swear i do math without not knowing what these things mean
limit is like limiting an equation or what?
torn oracle
Basically infinity isn't a number
So you can't really substitute infinity into an equation
However
What you can do is observe how a function behaves as you input a value that gets closer and closer to infinity
What the limit means is that you are taking a value that is approaching so close to infinity that you can claim it will functionally provide the same result
It's like taking better and better approximations
outer hemlock
oooh
is this where these tests come in?
like telescoping, divergence test, root test?
or what are these tests for exactly?
torn oracle
To determine what the value will be as it approaches infinity
Some limits will just go to infinity
Others will converge to a number
Overall some require different tricks to solve and that's where the tests come in
prisma badger
why did my teacher use test points here?
vocal sleetBOT
why did my teacher use test points here?
@prisma badger Has your question been resolved?
prisma badger
like y = 1 and y = -1
gaunt sparrow
They are points of intersection of the two curves, not test points
prisma badger
but whats the point of them
and why did she use 1 and -1?
it it just above and below h.a?
gaunt sparrow
It's solving for the intersection.
If you equate p and q, you get (x-1)^4 = 1, so that (x-1)^2 = 1 or (x-1)^2 = -1
Then they show why -1 doesn't work
prisma badger
It's solving for the intersection.
If you equate p and q, you get (x-1)^4 = 1, s...
why but why do we need the poi
gaunt sparrow
Probably just want to identify them on the graph
prisma badger
you think its to graph the inverse?
gaunt sparrow
I suppose so
Unless the table they want you to fill requires finding the intersections
vocal sleetBOT
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