whats the power of x before you diff
#help-10
quartz idol
deep kraken
Then differentiation rule is?
keen stream
u times the coefficient by it
deep kraken
$ax^{a-1}$
keen stream
and add one to power
warm shaleBOT
Minλ
deep kraken
and add one to power
You are mixing it with integration
obtuse pebbleBOT
deep kraken
No worries 
obtuse pebbleBOT
Available help channel!
deep kraken
test
obtuse pebbleBOT
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deep kraken
!volunteers
obtuse pebbleBOT
Helpers are just people volunteering their time to help you. Be polite and patient.
deep kraken
!trigs
obtuse pebbleBOT
#geometry-and-trigonometry - euclidean geometry, coordinate geometry, trigonometry
trim portal
is !trigs new or sth
deep kraken
!trig
obtuse pebbleBOT
#geometry-and-trigonometry - euclidean geometry, coordinate geometry, trigonometry
deep kraken
they are the same
trim portal
ive never seen either of those
deep kraken
talks and γ dont work
deep kraken
!elliptic curve meme
obtuse pebbleBOT
🍎 = 154476802108746166441951315019919837485664325669565431700026634898253202035277999
🍌 = 36875131794129999827197811565225474825492979968971970996283137471637224634055579
🍍 = 4373612677928697257861252602371390152816537558161613618621437993378423467772036
deep kraken
!cohomology meme
obtuse pebbleBOT
H*(🌭, 🍔) ≅ 🍔[🍉]/(🍉ⁿ⁺¹)
deep kraken
.close this was fun
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
trim portal
<@&268886789983436800>
brave bramble
<@&268886789983436800>
Scam bot
sly elm
good question
obtuse pebbleBOT
Available help channel!
pulsar terrace
can someone tell me where i went wrong
obtuse pebbleBOT
can someone tell me where i went wrong
pulsar terrace
question: find x+2y
high lily
on the left side, you effectively only multiplied the second term by 2sqrt(2)
you need to multiply the WHOLE side
also why did the = sign turn into an arrow
pulsar terrace
you need to multiply the WHOLE side
oh i thought so
pulsar terrace
also why did the = sign turn into an arrow
habit
i should have just took whole term in common denominator
high lily
and if the end goal is to isolate
x + 2y,
you shouild only multiply using 2
obtuse pebbleBOT
obtuse pebbleBOT
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alpine igloo
how do i know which one to put as u and dv? I used LIATE and it didn't work!
slate shoal
this is a "go with your gut" kinda question tbh, but lemme see which combination yields the least calculation
alpine igloo
this is a "go with your gut" kinda question tbh, but lemme see which combination...
i'm pretty sure it's making xe^2x as u
since I did the opposite and it led me nowhere
slate shoal
yea e^(2x)/(2x+1)^2 is nasty to integrate
and reducing the (2x+1)^2 to (2x+1) could help out
actually you could sub and do some nice algebra but ill let you do the ibp for now
alpine igloo
awesome, so im just kinda supposed to try and see with ibp which works out better
slate shoal
basically
liate works on simpler problems
you should visit the bprp video on liate (and why he dislikes it like i do haha)
tabular just helps me out more
obtuse pebbleBOT
@alpine igloo Has your question been resolved?
lost plank
i've got an issue with diverging and converging sequences; the traduction is pretty easy
obtuse pebbleBOT
i've got an issue with diverging and converging sequences; the traduction is pre...
lost plank
ik know it but I can't proove it
pseudo swift
i've got an issue with diverging and converging sequences; the traduction is pre...
C'est un vrai/faux je suppose?
pseudo swift
Bha faut y aller un par un de tte façon
lost plank
oui
pseudo swift
T'as 0 idée des réponses là ?
lost plank
bah pr moi la 1ere est vraie
et pareil pr la 3eme
mais je sais pas si les autres le sont ou pas
pseudo swift
Bha la 4eme c'est l'inverse de la 3eme en vrai
Ok ils ont échangé un et vn mais ça reste suite convergente + suite divergente
lost plank
oe pas faux
pseudo swift
Ouais donc la 2 alors
pseudo swift
Pas forcément tu peux avoir des trucs à la (-1)^n aussi qui oscillent
pseudo swift
.close
warm trail
this isn't exactly a math question but I am looking for any insights on how to study for a math accuplacer
obtuse pebbleBOT
this isn't exactly a math question but I am looking for any insights on how to s...
warm trail
I do have study sheets but it seems underwhelming for an engineering school to have pre-algrebra questions
quartz idol
am i tripping or did a certain discord server pop up
pseudo swift
this isn't exactly a math question but I am looking for any insights on how to s...
might wanna go in #study-discussion there's more ppl looking in there
pseudo swift
am i tripping or did a certain discord server pop up
At least they're automodded now
So many fkin spammers these days
quartz idol
At least they're automodded now
yeah
warm trail
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fading vine
hi i wanna know the idea of solving this derivative problem
obtuse pebbleBOT
hi i wanna know the idea of solving this derivative problem
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
quick nova
Let the point of tangency on the graph (C) be P(x_0, y_0), since P is on the curve y = x^3 + 3x^2. You can use this to find an equation of the tangent line at x_0
once you get that, you can substiute M(m,0) as well
formal island
Also, what is the relation between the slope of two perpendicular lines?
fading vine
k₁.k₂=-1
formal island
once you get that, you can substiute M(m,0) as well
Quick question for MxRgD, kind of a spoiler: ||Arent there infinite solutions?||
quick nova
Quick question for MxRgD, kind of a spoiler: ||Arent there infinite solutions?||
||I don't think so?||
fading vine
Let the point of tangency on the graph (C) be P(x_0, y_0), since P is on the cur...
it would be
Δ: y = (3x₀²+6x₀)(x-x₀) + x₀³ + 3x₀²
Δ is the equation of the tangent to (C) at x₀
right..
tardy epoch
hi i wanna know the idea of solving this derivative problem
Do you not have any information on graph C?
fading vine
Do you not have any information on graph C?
noo, the problem only provides these info, i cannot use web to create and see the graph c
quick nova
it would be
Δ: y = (3x₀²+6x₀)(x-x₀) + x₀³ + 3x₀²
Δ is the equation of the tang...
looks right
fading vine
sooo M(m;0) ∈ Δ
0 = (3x₀²+6x₀)(m-x₀) + x₀³ + 3x₀²
i understand this, what should we do next
quick nova
0 = (3x₀²+6x₀)(m-x₀) + x₀³ + 3x₀²
expand the bracket part
fading vine
0 = 3mx₀² - 2x₀³ +6mx₀ - 3x₀²
0 = -2x₀³ + (3m-3)x₀² + 6mx₀
quick nova
0 = 3mx₀² - 2x₀³ +6mx₀ - 3x₀²
0 = -2x₀³ + (3m-3)x₀² + 6mx₀
now you can factor out the x_0
which gives x_0 = 0 being one of the solutions. The other two points of tangency are roots of the quadratic
fading vine
how can i factor out the x₀
quick nova
$x_0 [-2x_0^2 + (3 - 3)x_0 + 6m] = 0$ like this
warm shaleBOT
MxRgD
quick nova
which gives x_0 = 0 being one of the solutions. The other two points of tangency...
Since one tangent is at x_0. What would the slope at x_0 = 0 be
fading vine
slope = 0
quick nova
it's a horizontal line
quick nova
Yep, but the two other tangents could be perpendicular to it
What does that also imply?
fading vine
im confused
quick nova
what are you confused about
fading vine
like the other two are perpendicular to the first one?
quick nova
like the other two are perpendicular to the first one?
yeah, the one at x_0
since the question says two tangents being perpendicular
quick nova
im stuck 🥲
okay if it's a horizontal line, and you have another line being perpendicular to it. What does it look like?
fading vine
it is a vertical line
fading vine
vertical... or two of them are perpendicular to each other.. i dont know how to answer 😭
quick nova
vertical... or two of them are perpendicular to each other.. i dont know how to ...
Yeah they are vertical
or two of them are perpendicular to each other
quick nova
but if it's vertical, what does that imply for the slope?
fading vine
but if it's vertical, what does that imply for the slope?
hmmm, the slope would go to infinity i guess
quick nova
hmmm, the slope would go to infinity i guess
eh sort of? But a better answer would have been it's undefined basically
the slope is undefined
but if the slope is undefined then its derivative is also undefined
fading vine
why though, my teacher didnt talk much about these things
oooohhhh x₂-x₁ will always be 0 right
quick nova
yeah
fading vine
but if the slope is undefined then its derivative is also undefined
yeppp
fading vine
y = f(x) = x³ + 3x²
fading vine
okay wait brb
okay
quick nova
alright I'm back
quick nova
but if the slope is undefined then its derivative is also undefined
but we said here the derivative has to be undefined
see the contradiction here?
fading vine
yea f'(x) = 3x² + 6x
quick nova
vertical... or two of them are perpendicular to each other.. i dont know how to ...
so then which one of these options is right
fading vine
the 2nd one
but im still so confused 🥹 cannot load
i still cant connect all of them together to fully understand here
quick nova
i still cant connect all of them together to fully understand here
Which part confuses you
fading vine
f(x) = x³ + 3x²
f'(x) = 3x² + 6x
Δ: y = (3x₀²+6x₀)(x-x₀) + x₀³ + 3x₀²
M(m,0) ∈ Δ
-> 0 = x₀.[-2x₀² + (3m-3)x₀ + 6m]
hmmm
fading vine
Which part confuses you
from the contradiction, x₀=0, where the slope is unidentified, all the things after, kinda new to me and hard to understand
quick nova
from the contradiction, x₀=0, where the slope is unidentified, all the things af...
Yeah I'm basically explaining why the 2nd option has to be true
which you would maybe need to do in a question like this (justifying why you rejected the 1st option)
fading vine
quick nova
so from here
warm shaleBOT
MxRgD
fading vine
okay
quick nova
since we know that x_0 = 0 implies the two perpendicular tangents cannot include the one at x_0
the other two points of tangency must come from the roots of this quadratic $$2x_0^2 + 3(1 - m)x_0 - 6m = 0$$
warm shaleBOT
MxRgD
fading vine
since we know that x_0 = 0 implies the two perpendicular tangents cannot include...
ohhhh alright read it again and somewhat understand this
not fully but better now
quick nova
cool
fading vine
the other two points of tangency must come from the roots of this quadratic $$2x...
yeaaa
quick nova
Let these two other points of tangency be x_1 and x_2
fading vine
alright
quick nova
what would the slopes of both of these tangents be
fading vine
the slope would just be the derivative right...
quick nova
y = f(x) = x³ + 3x²
That's incorrect since your original function is this
quick nova
Yeah and it's derivative is 3x^2 + 6x
and this is your derivative needed for tangents with point x_1 and x_2
fading vine
so 3x₁² + 6x₁ and 3x₂² + 6x₂
quick nova
yep
I'll rewrite this as $$k_2 = 3x_1^2 + 6x_1 = 3x_1(x_1 + 2)$$
$$k_3 = 3x_2^2 + 6x_2 = 3x_2(x_2 + 2)$$
warm shaleBOT
MxRgD
quick nova
so you know k_2 and k_3 are perpendicular
fading vine
ooooo
quick nova
so apply that and you get...?
fading vine
9x₁x₂(x₁x₂+2(x₁+x₂)+4) = -1
quick nova
cool
fading vine
do i have to use viete here
warm shaleBOT
MxRgD
quick nova
yep
you'll get everything in terms of m
and then you can solve for m
and that's your answer
quick nova
yeah that's right
quick nova
It's pretty long winded the problem 
fading vine
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
chilly crane
obtuse pebbleBOT
quick nova
,rccw
warm shaleBOT
quick nova
what's the original question?
chilly crane
chilly crane
what's the original question?
sorry, I was sending in the question
the part I am stuck on is c
quick nova
sorry, I was sending in the question
no worries
obtuse pebbleBOT
@chilly crane Has your question been resolved?
green lintel
Help my math or get terminated
obtuse pebbleBOT
Help my math or get terminated
green lintel
A - 7B + 3C = 2
2A - 6B + 4C = 8
A + B + C = ?
No decimals or fractions accepted in this
Only whole numbers
I hate this level
gloomy pelican
subtract
green lintel
I've been trying to solve by substitution for over 30 minutes
gloomy pelican
subtract equations
shut lagoon
Use elimination.
green lintel
A - 7B + 3C = 2
-(2A - 6B + 4C = 8)
crude oxide
u can subtract eqn 1 and 3, and the A's will cancel out
shut lagoon
You're better off the other way around
hardy widget
A - 7B + 3C = 2
2A - 6B + 4C = 8
A + B + C = ?
shut lagoon
A - 7B + 3C = 2
-(2A - 6B + 4C = 8)
Do this, but subtract the other way around.
crude oxide
oh nvm there is no eqn 3
green lintel
Should end up the same either way
green lintel
I ain't scared of negative numbers
shut lagoon
That's okay then. You can keep going.
crude oxide
after you do that you get −8B+2C=−4
then divide by 2
you get -4b+C=-2
solve for C
green lintel
-A -B -C = -6
crude oxide
C = -2 + 4b
shut lagoon
multiply the first eqn by 2
This is overkill, the equations are set up so that you get A+B+C if you subtract one from the other
green lintel
Bruh but now there's no coefficients left
shut lagoon
Wdym
crude oxide
A+B+C=(8−5B)+B+(4B−2)
green lintel
💀
shut lagoon
The coefficients are -1, you can just multiply through by -1
crude oxide
The Bs cancel out
green lintel
Yeah
crude oxide
and you get 6
hollow shuttle
how do i solve this
it says: the value of the expression 18-(-30):(-2)+(-2)*(-1)
(El valor de la expresion)
a) 9
b) -5
c) 5
d) 9
obtuse pebbleBOT
how do i solve this
it says: the value of the expression 18-(-30):(-2)+(-2)*(-1...
hollow shuttle
i thought it was simple arithmetic's but when i try to do it i notice is dividing from 0
is on my diagnosis to university : (
hollow shuttle
isnt multiply first?
parentesis, power, division/multiplication, add/sub
then (-2) * (-1)
minus * minus = +
so is 2
-2 + 2 on the numerator
hollow shuttle
also, we can speak in spanish too if you want
mejor, por que me cuestan algunos terminos
18-(-30) = 48 y ese es el numerador
formal island
Si, el orden es
- Resolver todo lo que este en parentesis
- Potencias
- Multiplicaciones y Divisiones
- Suma y Resta.
formal island
18-(-30) = 48 y ese es el numerador
Estas seguro?
Estas empezando con sumas, y ya se ven varias multiplicaciones y divisiones.
hollow shuttle
Estas empezando con sumas, y ya se ven varias multiplicaciones y divisiones.
deberia empezar con (-30):-(2)?
formal island
Si, y te queda tambíen pendiente la multiplicacion.
formal island
Listo
hollow shuttle
eso gracias : DDD
formal island
Si te tengo que dar una explicacion facil
Podes hacer esto
,tex $18 - (-30) : (-2) + (-2) \cdot (-1)$\par
$\underline{18} - \underline{(-30):(-2)} + \underline{(-2) \cdot (-1)}$
warm shaleBOT
formal island
Fijate que dividis los terminos en cualquier lugar que veas un mas o un menos cuando no este entre parentesis.
hollow shuttle
que es que este subrayado abajo?
formal island
Para que sepas cuales terminos se separan
18 es un termino
-(-30):(-2) es otro
+(-2) * (-1) es otro
hollow shuttle
entiendo
ya entendi, voy a separar los terminos para hacer este tipo de ejercicios gracias : DD
formal island
.close cuando no tengas mas dudas
hollow shuttle
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dark cairn
How do I find the horizontal intercept here?
obtuse pebbleBOT
How do I find the horizontal intercept here?
proud geyser
do you know what defines a horizontal intercept?
dark cairn
do you know what defines a horizontal intercept?
the position where the line touches the X axis?
proud geyser
right. and at the x-axis, what is necessarily true?
dark cairn
right. and at the x-axis, what is necessarily true?
Y=0
proud geyser
mhm. so set y = 0 and find x.
dark cairn
6/5?
proud geyser
looks correct.
proud geyser
um.
(5, 6) implies your horizontal intercept is at x = 5, y = 6.
didn't we agree earlier that the horizontal intercept occurs at y = 0?
have a look at how you wrote the coordinates for the vertical intercept.
follow that method, but change it to fit the concept of a horizontal intercept.
proud geyser
sure. all the best.
obtuse pebbleBOT
@dark cairn Has your question been resolved?
dark cairn
.closed
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
burnt hearth
Okay. I do not know how to prove linear independence or dependence. I have no familariaty with complex numbers.
obtuse pebbleBOT
Okay. I do not know how to prove linear independence or dependence. I have no fa...
burnt hearth
I tried with the usual definition of linear dependence
burnt hearth
can you show your progress?
i am about to do that
uhm, uh. I deleted it
for a), $a_1, a_2 \in \mathbb{R}$ such that $a_1(1 + i) + a_2(1 - i) = 0$ with not all $a_i = 0$
warm shaleBOT
andre
burnt hearth
$a_1(1 + i) + a_2(1 - i) = 0 \implies a_1(1+i) = -a_2(1 - i)$
warm shaleBOT
andre
keen scroll
what do you want to show ?
burnt hearth
Okay. I do not know how to prove linear independence or dependence. I have no fa...
(a)
first
keen scroll
$a_1(1 + i) + a_2(1 - i) = 0 \implies a_1(1+i) = -a_2(1 - i)$
sure but here what is your goal ?
burnt hearth
sure but here what is your goal ?
Show that 1+i, 1-i is linearly independent
$a_1 + a_1 \cdot i = a_2 \cdot i - a_2$
warm shaleBOT
andre
worn yoke
so if you have an equality of two complex numbers like this, is there any equalities you can extract from it?
i'm not sure where you got that from?
burnt hearth
so if you have an equality of two complex numbers like this, is there any equali...
I don't know
worn yoke
well if you had a + bi = 3 + 4i, what are a and b?
burnt hearth
a = 3 and bi = 4i
worn yoke
yes, so the real and imaginary parts must separately be equal
burnt hearth
yes, so the real and imaginary parts must separately be equal
why
how is a = 3
and bi = 4i
Is there something I can see that proves it?
Normal algebraic manipulation would mess with me, I think
warm shaleBOT
Lin Xia
worn yoke
your textbook defines complex numbers as being pairs of real numbers (i.e. a + bi is notation for (a,b)), and pairs of numbers can be equal only if each member of the pair is equal
burnt hearth
your textbook defines complex numbers as being pairs of real numbers (i.e. a + b...
I did not see that
LADR books do that??
worn yoke
it's the first thing in the entire book
burnt hearth
it's the first thing in the entire book
Omg
I am dying
I must have forgotten about it
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
spring oar
obtuse pebbleBOT
spring oar
I dont even know where to start this
tardy epoch
Try ratio test
spring oar
yeah i think it is the ratio test but im not sure how to get it into that form
tardy epoch
What do you think the coefficient is
spring oar
x?
tardy epoch
x?
No. Review definition 10.1.1
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/10%3A_Power_Series/10.01%3A_Power_Series_and_Functions
spring oar
so would it be the n^2 if so, when we seperate the x^(n+1) into x and x^n what do we do with that extra x
tardy epoch
so would it be the n^2 if so, when we seperate the x^(n+1) into x and x^n ...
That's the incorrect coefficient
tardy epoch
so would it be the n^2 if so, when we seperate the x^(n+1) into x and x^n ...
That extra x tells you the radius and part of the interval of convergence
See example 1 for a worked problem very similar to yours
https://tutorial.math.lamar.edu/classes/calcii/powerseries.aspx
spring oar
See example 1 for a worked problem very similar to yours
https://tutorial.math.l...
thank you this helped, im trying it now
I don’t get how to get rid of the n at the bottom
Would that be right?
keen scroll
i'm not sure if that is what you wrote but $\frac{n^2}{(n+1)^2}$ isn't equal to $\frac{1}{2n+1}$
warm shaleBOT
Lin Xia
spring oar
oh wait yeah oaky thank you
oaky thank you both I think i have it now
I really appreciate the help
.close
hollow moon
can anyone explain me spans as subspaces in linear algebra
obtuse pebbleBOT
can anyone explain me `spans as subspaces` in linear algebra
old lily
do you know span
hollow moon
no
old lily
do you know vector space
hollow moon
idk the technical terms very much
but i have just started
i know matrices
subspace is the part of the bigger vector?
old lily
do you know what's R^3
old lily
subspace is the part of the bigger vector?
subspace is a vectorspace
it's a subset
not a vector
hollow moon
R^3 means no. of 3 vector elements
again idk much technical terms...that's why i am here
uneven schooner
R^3 means no. of 3 vector elements
space would be a better word here rather than no. of
old lily
R = set of real numbers
hollow moon
*space* would be a better word here rather than *no. of*
how do i write it
hollow moon
R = set of real numbers
ok
hollow moon
yes
hollow moon
can vector space be on xyz plane?
hollow moon
i read that span is all the sets of linear combinations
hollow moon
R^3 = xyz space
ok
old lily
if you have 2 vectors in R^3 and look at their span u get a plane (if the vectors are not in the same direction)
what's the span of (1,0,0) and (0,1,0)?
gtg
old lily
personal reasons
restive gorge
i dont think that was what the why was directed at 🙏🏻
old lily
i dont think that was what the why was directed at 🙏🏻
huh
brave bramble
what's the span of (1,0,0) and (0,1,0)?
This is a good question to answer though. Feel free to guess if needed. What's the set of all linear combinations of (1,0,0) and (0,1,0)?
hollow moon
doesn't there need three vectors
old lily
no
brave bramble
Yes, that's true
obtuse pebbleBOT
restive gorge
nvm...i think gpt helps better than this server....
You are the wizard gng
old lily
<@&268886789983436800>
steel night
I dont know how to answer the last box
obtuse pebbleBOT
I dont know how to answer the last box
steel night
little stuck
winter cargo
I dont know how to answer the last box
the easiest way would be to calculate using the smallest h mentioned in the question here
can you see how you can get the value of this expression for h = 0.08 from here
steel night
the easiest way would be to calculate using the smallest h mentioned in the ques...
isnt the smallest h -0.62
winter cargo
you found f(π+h)-f(h) = -0.62
thats not a value of h
you check for the smallest h in magnitude here for the best approximation
steel night
you check for the smallest h in magnitude here for the best approximation
yea h =-0.67 is the largest followed by h=0.08 then -0.23
steel night
but $(\pi+h)-f(\pi)$ doesnt correlate with each other because h=-0.62 -> -0.62, h=0.23 -> 0.23, h=0.08 -> -0.08
warm shaleBOT
ø
steel night
i might be overthinking
winter cargo
it's curved so the values you get for small h would still be a bit off
as the magnitude of h becomes smaller you get a better value for the slope asked in the last question
steel night
what is curved?
winter cargo
the curve you experimented with in the question
it's just very slightly off from a straight line
steel night
yeah I agree
winter cargo
the smallest h in magnitude discussed in the question is 0.08
steel night
only if i zoom in, it will look like a straight line
winter cargo
yeah
obtuse pebbleBOT
@steel night Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
sand night
would prefer using divisibility, instead of modular arithmetic or something like that, did arrive at a few conclusions like x+j | y-x, feel like this is important but cant make any use of it
obtuse pebbleBOT
would prefer using divisibility, instead of modular arithmetic or something like...
sand night
maybe i gotta use the condition that if a|b and b is not equal to 0 then |a| <= |b|
but
dont see how i can use it either, help is appreciated
🩷 dont want the exact method to prove this either, any hints or leads would help
uneven schooner
hint: construct such $x,y$
warm shaleBOT
Annie Maqionde
uneven schooner
though not sure if it will work 
, use with discretion
sand night
**Annie Maqionde**
construct as in ? like assume some values of x and y ?
i tried to express y as a multiple of j
and i succeeded in that too but
i couldn't use it further
sand night
yh x and y in terms of j
okay i did express y in terms of some jf where f is an integer
expressing x in terms of a j
hmmm
uneven schooner
there's a solution which i found; so it does work.
sand night
there's a solution which i found; so it does work.
🐲 so i am on the right path it seems
uneven schooner
okay i did express y in terms of some jf where f is an integer
it dosnt necessarily have to be a multiple of j, but it can be.
sand night
it dosnt necessarily have to be a multiple of j, but it can be.
oh you meant express it in some sort of jq + r
nah it does end up being a multiple of j actually
uneven schooner
oh you meant express it in some sort of jq + r
well you see what works
i gave you a big enough hint
obtuse pebbleBOT
@sand night Has your question been resolved?
sand night
well you see what works
honestly actually i just noticed y can not be expressed as a multiple of j 😭 i made a small mistake
this just set me back for quite some time
obtuse pebbleBOT
@sand night Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
unborn ridge
This seems really hard to integrate
short crescent
(x^2-4)^3 is not x^6-64
short crescent
Remember the Pascal’s triangle coefficients if you’re stuck, 1 3 3 1
valid temple
You can simplify it to:
$$ \int_4^4 \big(1+\frac{(x^2-4)^3}{36}\big)^{(1/2)}$$
warm shaleBOT
S0S4
valid temple
is the upper bound 9 or 4?
valid temple
your reasoning was correct but the expansion of the (x^2-4)^3 is bad as krish said
you should get to $$ \int_4^9 \sqrt{1+ \big( \frac{(x^2-4)^{3/2}}{6}\big)^2}$$
warm shaleBOT
S0S4
valid temple
mmm
It's a bit unclear to me because I don't understand your caligraphy that much, but I don't think that's the easier way to go
obtuse pebbleBOT
@unborn ridge Has your question been resolved?
warm shaleBOT
pi_day
tardy epoch
just simplify this first before differentiating
unborn ridge
Oh
tardy epoch
$\sqrt{x^2-4}$ does not simplify further
warm shaleBOT
pi_day
unborn ridge
Oh
tardy epoch
you should test your calculations with some x like x=4 to see if it's even right
tardy epoch
i don't know what this last step is
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
steep inlet
Hey guys I just need help getting a quick explanation. Maybe I’m looking at Series wrong but for example, a series that’s (1/n)^3 how come the series converges to 1/2? Wouldn’t you be adding up an infinite amount of fractions and it would be divergent?
obtuse pebbleBOT
Hey guys I just need help getting a quick explanation. Maybe I’m looking at Seri...
steep inlet
I’ve been struggling fully grasping the concept, I can go through the motions and do the different tests but I really want to satisfy this itch of actually understanding what’s going on
formal island
The associated sequence (1/n)^3 converges fast enough for the series to not diverge.
There are "tests" for this condition
restive gorge
Imagine you have a chcolate bar and cut it in half and then cut the half into 2 new halves and continue
steep inlet
So the series is basically adding up to 1/2 because the fractions get super small fast enough that it’s not really increasing anymore?
restive gorge
Imagine you have a chcolate bar and cut it in half and then cut the half into 2 ...
Thats the same as the sum 1/2 + 1/4 + 1/8 + ...
formal island
Yea, basically. Youd have to be a little more refined with your statement, since 1/n could theorically still satisfy said condition, but it doesnt.
steep inlet
>Yea, basically. Youd have to be a little more refined with your statement, sinc...
Yeah I figured lol but thank you that’s really helpful
.close
obtuse pebbleBOT
frozen pike
Am I on the right track for 6?
formal island
By any chance, are you in the middle of a test?
obtuse pebbleBOT
Available help channel!
worn heart
hi
shut lagoon
Hi, do you need help with something in particular?
worn heart
Stop spamming in every channel
yo no ablos ingles
high lily
.close
torn wing
Hi there, im just doing problems on finding out if a vector field is conservative on a non-simply closed region and want to see if my work is correct
obtuse pebbleBOT
Hi there, im just doing problems on finding out if a vector field is conservativ...
torn wing
F(x,y) in top left, D is the region
circular with hole in the middle
r(t) is a parameterization that i chose enclosing the hole
does this look right?
i got not conservative
also don’t mind the random thetas, they should be t’s im just silly
snow trout
yes but x² + y² should be 36
obtuse pebbleBOT
@torn wing Has your question been resolved?
torn wing
yes but x² + y² should be 36
thx for catching that
snow trout
i got not conservative
oh i also wanted to remark that you can add and subtract vector fields v such that \int v \cdot dr = 0, so in particular the constant vector field (-10, 1)
obtuse pebbleBOT
oh i also wanted to remark that you can add and subtract vector fields v such th...
torn wing
oh i also wanted to remark that you can add and subtract vector fields v such th...
.reopen
here so it’s easier
torn wing
oh i also wanted to remark that you can add and subtract vector fields v such th...
ohh so you can see that it’s off center in a way
about the origin
snow trout
well not in the sense that you're saying it but in another sense yes it is off-center
but the point is that the computation is much simplified
torn wing
hmm okay
snow trout
so here it would suffice to instead consider the vector field (-7y/(x² + y²), 7x/(x² + y²))
torn wing
so it’s fine to not include the extra constants in the problem ?
snow trout
so long as you can justify why to your instructor
torn wing
Okay that makes sense
snow trout
in fact if you don't care about the actual number and only care about detecting if it's zero or nonzero you can do even more things
snow trout
like you could also ignore the 7
but this is maybe a bit too higher-maths-core for now
torn wing
yeah all i’m at rn is Linear Algebra and Calc3
i might take some more math courses in the future bc they’re pretty fun
but can’t stray too far off degree plan either so
snow trout
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
Sorry bro I js wanted help
proud geyser
you've already opened it. please send your question.
obtuse pebbleBOT
@frozen pike Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
round island
Does this look…like it’s going in the right direction? (Top part and bottom part are different things)
obtuse pebbleBOT
Does this look…like it’s going in the right direction? (Top part and bottom part...
inner sierra
,rccw
round island
The top part determined holes x-3 and x+2 but no VA or x int
warm shaleBOT
round island
The bottom part is an attempt to get the slant asymptote
potent beacon
what is the ques
round island
14
hardy widget
inner sierra
I believe you don't need to polynomial division this
round island
The degree on top is higher than the degree on the bottom
inner sierra
After you factorized from the top and bottom there's a $x^2 - x - 6$ common on numerator and denominator
warm shaleBOT
1 divided by 0 equals Infinity
round island
The degree on top is 6 while the agree on bottom is only 3….
Yes
So what are you implying here
I have x/-3 remaining
inner sierra
14
Im kinda confused here, the polynomial you wrote on your work and in this picture is really different
round island
So what problem did I write…
inner sierra
You wrote problem 8 💀
round island
Fuck
inner sierra
Into problem 14
round island
Let me write 14 then
inner sierra
Also are you supposed to simplify $f(x)$ or smth?
warm shaleBOT
1 divided by 0 equals Infinity
round island
Does this look any better?
round island
Also are you supposed to simplify $f(x)$ or smth?
I have to find….all of this
Horizontal or slant asymptote, vertical asymptote, holes, y and x intercepts and rnd behavior
inner sierra
🫡
round island
It’s not horrible once I get into a groove
round island
Right..
So to get the bottom to equal zero….
It’s x=3 and x=-1
Which of them works for a VA?
inner sierra
Does this look any better?
But here you can see the denominator's degree is greater
round island
So it’s 0?
inner sierra
Veritcal asymptote happens when the deno is 0
inner sierra
It’s x=3 and x=-1
So both of them works here
round island
Are you sure..?
inner sierra
Yea
inner sierra
I also graphed the function out here
round island
Oh ok
inner sierra
YES X INTERCEPT
X intercept happens when the graph intersects the x axis
Or at $y = 0$
warm shaleBOT
1 divided by 0 equals Infinity
inner sierra
So basically substitute $f(x) = 0$ and solve for $x$
warm shaleBOT
1 divided by 0 equals Infinity
round island
Also what do I do with the remaining top portion from the first part
inner sierra
The HA and SA?
inner sierra
I have to find….all of this
In this case the HA exists so i think that you should fill in the HA and probably state that SA does not exist in the SA spot
inner sierra
So what *is* the HA?
Degree of numerator < denominator
So it always exists at y = 0
round island
Ohhh
For x and y intercepts I got 4-
For both-
Are there any holes?
<@&286206848099549185>
dire moss
Are there any holes?
A hole happens when the same number makes the numerator and denominator equal 0
round island
So none
dire moss
End behaviour is basically what happens when x -> ±♾️
round island
Yeah ik
dire moss
And so, you figure that out by finding the horizontal asymptote
round island
I have that
dire moss
I have that
HA = 0 right?
round island
Yes
dire moss
So, what the means is the end behaviour is y -> 0
round island
I thought you used the vertical asymptote to find it…
That’s what my paper is implying at least
Since I only have one HA and 2 VA’s
dire moss
Since I only have one HA and 2 VA’s
VA’s tell you when the y value shoots off to infinity or negative infinity around a certain x value.
dire moss
VA’s tell you when the y value shoots off to infinity or negative infinity aroun...
HA’s tell you what the graph does as the x value approaches infinity or negative infinity
dire moss
That’s exactly what those are. None of those have anything to do with end behaviour though
dire moss
Are they correct?
Aside from the fact that the numbers are in the wrong place, it’s right, lol
dire moss
The numbers go underneath the sign.
3⁺ as an example
But that’s a TINY nitpick. Your answers are right
dire moss
I’m not gonna worry too much about that
Do you know how to tell what the HA is?
round island
It depends on the degree of the top and bottom
dire moss
Just out of curiosity
dire moss
It depends on the degree of the top and bottom
If they are equal?
round island
If the denominator has a higher degree it’s 0 if the numerator has a higher degree you have to do the weird dividy thing…
round island
If they are equal?
I don’t know- and my next problem has tha
(Context the next problem is 15)
dire moss
I don’t know- and my next problem has tha
Lucky for you, I would say it’s probably one of the easiest cases to find the HA
signal hollow
dire moss
Lucky for you, I would say it’s probably one of the easiest cases to find the HA
If the degree of the numbers for is equal to the degree of the denominator, you just divide the coefficients of the highest degree term
round island
Oh
dire moss
So for 15, what would you do?
round island
Well idk if I can factor that….
So just…set the denominator equal to zero?
Cus I don’t think anything cancels either
dire moss
Cus I don’t think anything cancels either
Nope. So, what would your VA be then?
round island
-2?
dire moss
Yessir!!
dire moss
And the HA is…. 2?
That’s correct!!!! 😊
dire moss
No holes
round island
Since nothing cancels
dire moss
x, and y-int’s are pretty easy too
dire moss
And x is 0 as well
Yessir. Both your x, and y intercepts are located at (0, 0)
round island
Ok ok
dire moss
Are you told to do rough sketches of graphs? Or just to find these values
round island
I was told I can use the fancy calculator but I don’t have one on me
Hold on one sec
,w graph (2x)/(x+2)
warm shaleBOT
round island
Huzzah
So I think it’s…. Positive infinity
For both
Cus you can’t have positive and negative zero
dire moss
So I think it’s…. Positive infinity
For what?
round island
X-> +/- 0?
dire moss
X-> +/- 0?
Huh?
dire moss
The limits
Limits as x approaches what?
round island
0
Oh siad
Wait
Wrong thing
Mb I was looking at the intercept
-2?
Or ig 2 and -2
dire moss
-2?
So, the limit as x approaches -2 from the left is +♾️. And the limit as x approaches -2 from the right is -♾️
round island
So…. X -> -2^+ is inf and x-> -2^- is -inf?
dire moss
So…. X -> -2^+ is inf and x-> -2^- is -inf?
Other way around
dire moss
So, the limit as x approaches -2 from the left is +♾️. And the limit as x approa...
If you actually wanna calculate which ones which, if you’re allowed calculators, plug really really close values to -2 into your calculator. From the left, plug in smth like -2.0001. And from the right plug in -1.9999
round island
I’m allowed to for that and that alone
But…I’m just telling her I put it in the calculator
RIGHT NEW PROBLEM
I factored it
dire moss
Alr. So, you’ve factored properly!! Now just find your VA, and HA
round island
I could go more though…
dire moss
I could go more though…
You’re right. I would’ve stoped there because I could figure out my values from there
But you’re right
round island
Ok
dire moss
But you’re right
Not the numerator and denominator can be factored even more
round island
Ok I got 2 for VA
dire moss
Ok I got 2 for VA
Is 2 the only one
dire moss
Cus I square rooted it-
I think it might help you to be able to factor a difference of squares
round island
Wut
dire moss
Do you know how to do that?
round island
I don’t see how you could get another answer besides that
I can show my work
But the square root of 4 could be 2 or -2
dire moss
But square rooting smth gives you both a positive and negative answer
round island
That’s what I said
dire moss
I don’t see how you could get another answer besides that
If you have :
a² - b² -> (a - b)(a + b)
dire moss
Ok I got 2 for VA
^
round island
Teehee
dire moss
Now, is there any HA for this one?
round island
And the degree on top is larger than the one on the bottom-
So you have to do the weird dividy thing right?
dire moss
So you have to do the weird dividy thing right?
Yep. So you know that there isn’t an HA. But there might be an SA
dire moss
Yep. Just make sure to account for every term when you do it
What I mean by that
Is if you have a missing term, add it with a 0 coefficient
x³ + 0x² - 16x + 0
round island
Your way is…confusing me
So I went back to what I new
Knew*
And now I’m also confused
dire moss
So I went back to what I new
How do you do it then?
round island
I just don’t put in the extra terms
dire moss
I just don’t put in the extra terms
Do you leave spaces to account for them?
round island
No…
dire moss
Idk that’s just how my teacher showed me how to do it
I’m sure your teacher wouldn’t show you an incorrect method
round island
She would.
dire moss
She would.
As long as the answer is correct, is there really a “correct” method?
dire moss
And the 12 doesn’t matter?
Remainder doesn’t matter for the slant asymptote, no
round island
So it’s just… -1/2x?
dire moss
Exactly
round island
Wait do you not have to fix that to make it x= 1/2?
dire moss
Wait do you not have to fix that to make it x= 1/2?
No
The asymptote itself is the line y = -0.5x
dire moss
No holes? Eight
In this case, no
warm shaleBOT
round island
I got x as 16…idk if that’s right
round island
Find x and y intercepts…
