Draw a free body diagram
#help-13
cedar kilnBOT
@latent fox Has your question been resolved?
bright shadow
cedar kilnBOT
bright shadow
How can solve this with just two vectors given?
I know I can take cross product to find the area, and idk what else to do from there
sharp lotus
I know I can take cross product to find the area, and idk what else to do from t...
i guess you can think of 0, 0 (0 vector) as one of the points, a vector, b vector give 2 more and a + b gives the far corner
bright shadow
bright shadow
i guess you can think of 0, 0 (0 vector) as one of the points, a vector, b vecto...
Ooooooooooo
Right!
Easier then
cedar kilnBOT
@bright shadow Has your question been resolved?
bright shadow
i guess you can think of 0, 0 (0 vector) as one of the points, a vector, b vecto...
One more doubt, how can I find the midpoints? The separate diagonal midpoints does not match this way
lavish plank
need some arthimetic help
cedar kilnBOT
need some arthimetic help
tropic oxide
lavish plank
sorry just getting pic
i have this
tells me energy consumption in wh/km
im modelling it in 5 min chunks
tropic oxide
and your question is...?
lavish plank
i want to know the formula to know usage per 5min chunk
duration= tripdistances(j)/fivemindist;
endtriptime= round(departure_time_window + duration);
for departure
x=temperaturesinterval(k);
% tripusage(k)= (p1x^2 + p2x + p3)/12
% work out new soc
like i know trip distance and also average distance travelled in 5min
tropic oxide
usage of power per 5 minutes...? that depends on the speed, does it not
lavish plank
ive assumed speed constant as fivemindist
is average distance travelled in five minutes
only thing that changes this is if temp changes
think its ok
tropic oxide
sorry, i got a bit lost.
cedar kilnBOT
@lavish plank Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
turbid trout
Just a quick question
I'm doing "binomische Formeln" and have problem with this. I have to remove the brackets
turbid trout
I just multiplay everything with -5t first?
so -3r will be 15rt?
vagrant elbow
yes
vagrant elbow
I just multiplay everything with -5t first?
so -3r will be 15rt?
yup
plucky dagger
cedar kilnBOT
plucky dagger
How i can solve this question?
plucky dagger
Square š„²
plucky dagger
Sinx
clear berry
isn't that the power series for e^x
nah, I think it is sinx
plucky dagger
Ys
frosty thicket
probably
vagrant elbow
$\sum_{n =1}^{\infty} (-1)^n\frac{x^{(2n + 1)}}{(2n + 1)}$
Doesn't sin x involve factorials
also what
clear berry
$\sum_1^{\infty} (-1)^n\frac{x{^{2n + 1}}}{(2n + 1)}$
wraith daggerBOT
NEONPerseus
vagrant elbow
wellp
plucky dagger
But they're asking about first 4 terms.... š„²
clear berry
Doesn't sin x involve factorials
yeah, this isn't sinx
frosty thicket
also I think that's arctan
frosty thicket
Just square it carefully
also as numbpy suggested you can just write the same series side by side and go term by term
remember that they're ordered by increasing powers of x
vagrant elbow
Bingo it is arctan
So you just derive the Taylor Series for arctan squared
Have fun I have stuff to do
cedar kilnBOT
cedar kilnBOT
Available help channel!
lilac chasm
Is using 6 for lowest term okay here?
cedar kilnBOT
Is using 6 for lowest term okay here?
livid hound
30/6 isn't 4
livid hound
yes, it's ok to divide the numerator and denominator by the same amount
(and will aid in simplification if said value is a factor of both)
livid hound
in Q1, 5/15 can be simplified
lilac chasm
Oooh
livid hound
the rest seems ok
livid hound
nope
livid hound
yeh
lilac chasm
okay no need to drop it to lowest term then xd
livid hound
it's a lot easier to identify whether there are common factors when observing the unsimplified form
i.e whether 8 has a common factor with 5 or 7 (other than 1)
cedar kilnBOT
@lilac chasm Has your question been resolved?
candid wharf
cedar kilnBOT
candid wharf
this is what I understand but It's completely wrong lol
earnest socket
this is what I understand but It's completely wrong lol
use radians
adding 90 is wrong
candid wharf
why?
earnest socket
because trigonometric functions assume inputs in radians
wraith daggerBOT
tushar
candid wharf
oh so 27.266 is actually in radians not degrees?
cedar kilnBOT
Please read #āhow-to-get-help
earnest socket
oh so 27.266 is actually in radians not degrees?
,w arccos(4/4.5)
wraith daggerBOT
candid wharf
then I add 90?
candid wharf
oh i add 1/2pi
candid wharf
why is doing it in degrees wrong tho it's just different units
wraith daggerBOT
tushar
earnest socket
,w tan(pi)
wraith daggerBOT
earnest socket
,w tan(pi degrees)
wraith daggerBOT
earnest socket
these are not the same
candid wharf
earnest socket
the result your calculator gives you will assume that the input is in radians unless specified otherwise
,w tan(117.3 degrees)
wraith daggerBOT
candid wharf
wha?
oh so tana should be 2.047 right?
the mark scheme has somethin else going on 
earnest socket
your answer is correct
you can ignore what i said about radians vs degrees because it seems your calculations correspond to using degrees for inputs
,w -8/sqrt(17)
wraith daggerBOT
earnest socket
this is the same as your answer
earnest socket
they probably want an exact form
candid wharf
i felt like i was doing something wrong because the ms does some weird calculations while i did it in like 2 steps
earnest socket
which you can get using their method
using decimals will only give you an approximate answer
candid wharf
:(
earnest socket
best to study their answer
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
How do I figure out sum & Difference angles identity formula?
calm agate
You just need to find the value, right?
glad kestrel
so use them
you're not looking to prove that the angle sum identity is true
you're just looking to answer your question
right?
"figure out the formula" could have different meanings so i was just clarifying
hint: -180+15 = -165, 15 = 45-30
crimson sedge
Iām just trying to figure out the exact value of sin(-165 degrees). I tried to combine the values on the Unit Circle but itās confusing to translate it, let alone remember it.
glad kestrel
hint: -180+15 = -165, 15 = 45-30
these are the values you should be using to figure it out
180, 45, and 30 are common angles
glad kestrel
just means you'd use -180 instead of 180 (which is the same exact value)
negative angles just move clockwise around the unit circle instead of counter clockwise
crimson sedge
I donāt understand how I would apply that to my equation. And how did you get 15? From the -180 + 15?
Is there a rule iām missing out
glad kestrel
it's just a matter of figuring out what angles you can use to get to the angle you want
i chose -180 because it's close to -165
crimson sedge
hint: -180+15 = -165, 15 = 45-30
I understand that but I donāt understand how you figure out which angles to choose. And what rule is this called?
glad kestrel
it's not a rule, it's just choosing numbers to figure out your question
crimson sedge
i chose -180 because it's close to -165
Is that degrees?
crimson sedge
Iām trying to find 165 on my unit circle
glad kestrel
it's not there
crimson sedge
Canāt I do 150 instead
glad kestrel
that's why you're using the sum and difference formulas
you could do 150, that's a 30 degree reference angle
you'd want -150 though
-180 is a tad bit easier though since sin(-180)=0 and cos(-180)=-1
crimson sedge
Why is that the case though?
glad kestrel
why is what the case
crimson sedge
Is that the reciprocal?
glad kestrel
?
crimson sedge
of 180 on the unit circle?
glad kestrel
what is that
-180 is just going 180 degrees around the unit circle clockwise
normally you'd go counter clockwise
crimson sedge
Oh
glad kestrel
it's the same distance but clockwise
which incidentally is in the same place as 180
crimson sedge
So sin(-180) is 0 since youāre going 180 counterclockwise?
glad kestrel
i guess that's one way of explaining it but it's not a particularly clear way of understanding it
if it helps to convert to positive angles that you know, you can do that
which is easy here since sin(-180) = sin(180)
crimson sedge
Ok, why would you choose 180 if itās bigger than 165?
Wouldnāt you choose something smaller?
Wait you just explained why
nvm
glad kestrel
it's just picking an angle close to the one you're trying to find and seeing a way to get there
if you're given one of these problems that you can't use a calculator on, there will be a way to get there with common angles
glad kestrel
but 45-30 = 15
45 and 30 are common angles
you're going to be using these formulas twice in this problem
once for -180+15, once for 45-30
-180+(45-30)=-165
crimson sedge
Ok, so you use angles on the graph to get to your ideal number.
By either subtracting or adding two angles
crimson sedge
Ok but what would I do with those 2 numbers in the formula?
So I only use 45-30 & -180 + 15 to get angles close to my given angle?
And what about the formula?
glad kestrel
plug numbers into your formula
sin(A+B) = sin(A)cos(B) + cos(A)sin(B) where A= -180 and B = 15
then sin(A-B) = sin(A)cos(B) - cos(A)sin(B) where A = 45 and B = 30
crimson sedge
So I have to substitute those values 2x in 2 different equations?
glad kestrel
you'll actually need to find cos(15) as well so cos(A-B) = cos(A)cos(B) + sin(A)sin(B) where A = 45 and B = 30 too
crimson sedge
Did I ask why were trying to get 15 by itself?
glad kestrel
because you need that to get to -165
-180 + 15 = -165
but 15 isn't a common angle
so you need to find out exactly what that is
in your formula to find -165, you'll be using the the sum formula with your first angle equal to -180 and your second angle equal to 15 (since these are easiest)
with the sum formula, you need to know sin(-180), cos(-180), sin(15), and cos(15)
-180 is a common angle, so you can find that value on the unit circle
15 is not a common angle though, so you need to use the difference formula to find sin(15) and cos(15)
which you can do using common angles 45 and 30
crimson sedge
So I need to find a number that can go into the numbers question which is -165. The second number is what I need to find with angles?
glad kestrel
not always, but sometimes
crimson sedge
How would I always find it?
glad kestrel
i'm just saying you don't always need to do it more than once
crimson sedge
And why is 11pi/4 easier to solve than sin(-165)
glad kestrel
because 11pi/4 is just 12pi/4-pi/4
both of which are common angles
so you'd just need to use one formula once
crimson sedge
Ok, so I kind of understand the thought process of using random numbers to equal -165.
But how would I know what to substitute for equations like this?
glad kestrel
by thinking about the common angles and what you can do with them
crimson sedge
I was referring to Cos A, B & Sin A,B. My bad
glad kestrel
A and B are your two angles
if you were finding sin(75), note that 45+30 = 75. so you could use the sum formula to find this
sin(A+B) = sin(A)cos(B) + cos(B)sin(A) where A=45, B=30
sin(45+30) = sin(45)cos(30) + cos(30)sin(45)
crimson sedge
if you were finding sin(75), note that 45+30 = 75. so you could use the sum form...
Thatās easier, but why would I need to use 2 different equations for this particular question.
glad kestrel
because 15 is not a common angle
crimson sedge
sin(45+30) = sin(45)cos(30) + cos(30)sin(45)
And how would I even simplify that?
glad kestrel
45 and 30 are common angles
sin(45), sin(30), cos(45), and cos(30) are all values found on your unit circle
crimson sedge
So for the 2nd part of the formula, I would have to memorize all angles of the unit circle including degrees, coordinates, and positions?
Because I need to get rid of Cos and Sin
glad kestrel
if you're not given a unit circle, then yes, values must be memorized
it's not as difficult as it sounds
you could derive them if it helps
for a 45-45-90 triangle with length of legs = 1, pythagorean's theorem states that the hypotenuse is $\sqrt{(1)^2+(1)^2}=\sqrt{2}$
wraith daggerBOT
a disappointing son
crimson sedge
This is very tedious if you donāt have this memorized
glad kestrel
memorizing them is not as difficult as it sounds though
muted bear
also true
crimson sedge
I have to memorize all of this
glad kestrel
yes but it's a lot easier to memorize than you'd think
muted bear
mainly, memorize this portion and the rest can be derived
glad kestrel
at the least, you could memorize sin(30), sin(45), cos(30), and what they said
crimson sedge
I donāt know what to say, I havenāt brushed my teeth yet so iām just going to do that and study.
You can close it
muted bear
you can close it if you want
crimson sedge
How do I do that?
glad kestrel
.close
crimson sedge
Thank you guys, if you have any advice for studying sin, cos, tan, csc, sec, cot, & unit circles besides staring at a piece of paper for hours then DM me.
.close
cedar kilnBOT
glad kestrel
also just realized you could do 225-60 which are both common angles
but good practice because you will probably need to do this a lot :)
cedar kilnBOT
Available help channel!
crimson sedge
but good practice because you will probably need to do this a lot :)
Wait wdym?
cedar kilnBOT
Wait wdym?
glad kestrel
chances are you'll need to use the formula more than once eventually
but my small brain didn't see 225-60 = 165
well in your case -225+60 = -165
so you only need to use the sum formula once
glad kestrel
lol
it all comes with practice
and i have not done trig in a while
so yknow
im proof that you need to practice
crimson sedge
How would I study these formulas besides flash cards?
I just ran out cards to write on
crimson sedge
What if I said, I need to get ready to study for my SAT and I didnāt have much time.
Time to pull an all-nighter
glad kestrel
byeah 
crimson sedge
Iām fucked
Let me get out of here, somebody else probably needs this channel.
Iāll be back later
the SAT doesnt have much formulas
mainly intuition
cerulean star
You need to get your own help channel
bb!howtogethelp
(I'm not so good with bunnybot)
@smoky fox you have a lot of different expressions on this paper
What are you concerned about
smoky fox
should I not be able to take the reciprocal on both sides
on the 3 * sqrt(4) expression
cerulean star
Answer in the box is wrong
smoky fox
is it???
smoky fox
that's just the value of x I found
smoky fox
I think maybe my brain just isn't working but like
I should be able to flip both sides, no?
cerulean star
Sure it does
The fractions just end up on opposite sides if you do it manually by multiplying and dividing each term through
Same thing
They are paired the same
smoky fox
but wouldn't it then become
and then if u multiply that
with 0.015
that's completely wrong
cerulean star
$\frac{dx}{.015} = \frac{2}{3\sqrt{4}}$
wraith daggerBOT
Disorganized
smoky fox
yeah so now
smoky fox
I can't multiply the 0.015
cerulean star
That is 2/6 = 1/3
cerulean star
Oh, you got a typo
cerulean star
No biggie
smoky fox
ššš
cerulean star
Welcome to math
smoky fox
this has been bugging me for the past hour
cerulean star
Yup
smoky fox
lmfao
cerulean star
It be that way sometimes
cedar kilnBOT
cedar kilnBOT
Available help channel!
marsh pond
cedar kilnBOT
marsh pond
How do you prefer writing your arrows for limits?
dull oxide
2
crimson sedge
2
crimson sedge
last is an abomination and if you write it like that, i am blocking you
marsh pond
If instructor saw these on an exam would they take marks away?
crystal raptor
unless it made something you were doing unclear, then no
marsh pond
First is easier for me to write
crimson sedge
if your teacher is taking marks off for u drawing an arrow a little bit off then they should've went for an art major
crystal raptor
just write the second, you'll live
wraith daggerBOT
Modus
crystal raptor
your $\vec{\phantom}$ could look like a minus if you get lazy and that could be problematic
upper garnet
just do xo
crystal raptor
i give up
marsh pond
just do xo
xoxo š
upper garnet
real
long arrow
$\rightarrow$
wraith daggerBOT
Modus
wraith daggerBOT
Ī£AC
marsh pond
Writing limit out each and every time might be my least favourite thing about Calculus so far.. would you rather see a symbol for this?
crystal raptor
yeah maybe a symbol like $\lim$
wraith daggerBOT
Ī£AC
wraith daggerBOT
Modus
upper garnet
chad
dull oxide
Writing limit out each and every time might be my least favourite thing about Ca...
My proposal
upper garnet
whattt
wraith daggerBOT
Modus
upper garnet
$^{\sum}f(a)^{\Pi}_{\int}$
wraith daggerBOT
Fucktalogist
marsh pond
Is Newton the inventor of ālimā syntax?
dull oxide
Is Newton the inventor of ālimā syntax?
doubt
I've read his principia mathematica
It's like math notation didn't even exist back then
The wording was all so confusing
zenith sail
Newton didn't even really have limits
The formal definition of the derivative and such using limits came later
upper garnet
i only dont know g h hardy
marsh pond
i only dont know g h hardy
To quote Wikipedia, G H Hardy wanted to:
4) be the first man at the top of Mount Everest; (5) be proclaimed the first president of the U. S. S. R. of Great Britain and Germany; and (6) murder Mussolini."[27] .
upper garnet
š
marsh pond
But instead he invented the arrow under the limit
upper garnet
he really wanted to go hard
marsh pond
.close
ruby stag
Consider the function y=x2āx+7. What is the equation of the tangent line at x=2
?
Select one:
cedar kilnBOT
Consider the function y=x2āx+7. What is the equation of the tangent line at x=2
...
ruby stag
a. y=3(x+2)ā9
b. y=3(x+2)+9
c. y=3(xā2)ā9
d. y=3(xā2)+9
long arrow
$\TangentLine$
wraith daggerBOT
Modus
long arrow
x0 = 2, come on
ruby stag
so how do I solve -
ruby stag
x0 = 2, come on
will 2 be added or subtracted from 7
long arrow
where did you get 7
ruby stag
Consider the function y=x2āx+7. What is the equation of the tangent line at x=2?
what do you mean 'shift'
where did 7 go
why
so all numbers without variables have derivatives of 0?
then the equation should be 2x -
?
ok -
then how do I get to one of these answers a. y=3(x+2)ā9
b. y=3(x+2)+9
c. y=3(xā2)ā9
d. y=3(xā2)+9
2 minutes remaining
you're not supposed to plug them in - these are the possible answers a. y=3(x+2)ā9
b. y=3(x+2)+9
c. y=3(xā2)ā9
d. y=3(xā2)+9
1 minute remaining
what is it..
!?!
10 sec
idk the variables
fast
.close
tribal sonnet
cedar kilnBOT
tribal sonnet
0*(1(1+01)*000*)*
I got this as the answer after using arden's theorem
is this correct and can it be simplified further?
cedar kilnBOT
@tribal sonnet Has your question been resolved?
cedar kilnBOT
@tribal sonnet Has your question been resolved?
ripe sigil
Hi so I just wanna make sure I'm right
cedar kilnBOT
Hi so I just wanna make sure I'm right
cedar kilnBOT
@ripe sigil Has your question been resolved?
cedar kilnBOT
@ripe sigil Has your question been resolved?
wild belfry
wild belfry
I am saying that the red and the blue mean the same thing, my friend says they dont, who is correct
Like obviously the red one is correct but is the blue also correct or not?
lusty grotto
idk if im wrong but to me blue sounds like "there exist objects such that jack is happy only if the object is owned by jack and it is a computer" and red sounds to me like "jack is happy only if there exist objects that he owns and are also computers"
crimson sedge
Say I have a set $G$ that contains $1$ to $9$, $10$ to $90$ and $100$ to $900$ and say I want to write some natural $n$ as a sum of elements of $G$. So if $n=32$, I could write $30+2$, $10+10+10+2$, $5+5+5+5+5+5+1+1$, etc. How would I go about finding the number of different ways of getting $n$ by the sum of elements of $G$? Thanks in advance.
wraith daggerBOT
3317
crimson sedge
I guess one could say you could count:
1 + 1 + 1 ... n times (one way)
2 + 1 + 1 ... n - 1 times (another)
3 + 1 + 1 ... n - 2 times (a third)
But that doesn't seem like it would cover all possible ways.
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
.close
marsh pond
cedar kilnBOT
https://www.desmos.com/calculator/2lomp73get
violet night
why
half forge
yeah you're right the function shouldn't be continuous at 2
marsh pond
yeah you're right the function shouldn't be continuous at 2
is there a way to turn on discontinuity with Desmos?
obsidian coral
Don't think so
runic garnet
Hover over the point
half forge
is there a way to turn on discontinuity with Desmos?
well if you hover you're mouse over (2,4) it says (2, undefined)
marsh pond
which means there must be a hole there?
exact problem talked about here: https://youtu.be/OEE5-M4aY4k?t=967 at this timestamp
obsidian coral
But if you know where the hole is, you hover/click and it'll say unf
violet night
Hover over the point
this lists it as undefined
marsh pond
well if you hover you're mouse over (2,4) it says (2, undefined)
lol needle in a haystack
I didn't even see that
runic garnet
Yea Desmos does that
cosmic steppe
But if you know where the hole is, you hover/click and it'll say unf
You have to slide over it
marsh pond
would there be a better graphing alternative for limits?
cosmic steppe
On desmos
Desmos tries to auto fill the hole unless you slide over it/trace the function
marsh pond
You have to slide over it
But there is no indication, and you have to be pixel perfect
obsidian coral
I wish Desmos made it more clear
It's definitely clear, you just need to explore software more to discover the features
marsh pond
lol
marsh pond
but a button to turn on would be great
cosmic steppe
And you're on mobile
:)))
Eh I usually can do it around the same on on PC
you can trace function with a mouse
marsh pond
violet night
exact problem talked about here: https://youtu.be/OEE5-M4aY4k?t=967 at this time...
I wasn't disagreeing either just wasn't sure on your reasoning, skipped back a bit on that video and he mentions the domain's which is the main bit for me , not because the limit is 4, (x^2-4)/(x-2) = x+2 for all x =/= 2
obsidian coral
https://twitter.com/desmos/status/436331176609849344?lang=en
That literally just shows how to plot a point where the hole is. It doesn't label the hole as a hole
marsh pond
It's not a feature of Desmos to show the hole
someone manually added the holes to their graph
violet night
holy moly
obsidian coral
someone manually added the holes to their graph
No, they made points for where the hole exists
obsidian coral
Those are just points, coordinate points to label where the hole is
marsh pond
All the work just to show these two holes
obsidian coral
If you click/hover/drag, it doesn't say (2, unf). It will say (2, 5/9)
marsh pond
Mine says 2, Undefined when I click and drag over the holes
But anyways, too bad it's not a feature you can turn on with a click of a button. Looks like some manual work to get them to always show up
obsidian coral
It's based on what graph/function was last plotted
marsh pond
Alright, well anyways, maybe WA offers something a bit better for this, I can check out what else is out there
Desmos seems good otherwise
obsidian coral
Actually it's based on what graph you trace on
marsh pond
Maybe we are talking about different things, I'm just looking for a graph that can show Holes rather easily, like turn them on with labels automatically
regardless of when or how they were created
obsidian coral
I was still referring to this stuff
marsh pond
yeah it requires manual work, no thanks
obsidian coral
It's based on what line you traced on
And as I stated, it's just coordinate points to depict the hole
marsh pond
They don't follow the graphs, if thats what you think?
the holes are manually added by the user
to show them as labels
obsidian coral
They were manually added as coordinate points
marsh pond
alright, well it's too much work for something so trivial.. i just wanna be able to see them easily after graphing
such as the original graph I posted
obsidian coral
If you know where the hole is, just trace it
old hare
cedar kilnBOT
old hare
20.5x+ 55= position of motercicle
t1 needs to equal t2
potion of motercycle equals 20.5x from x1-4
idk how to solve position of motercycle
runic garnet
What type of problem solving are u using for this
Physics or math
Kinematic eqns?
runic garnet
Can u use kinematic eqns
old hare
yea
yes
but idk how to do that with the change at t=4
this was what i tried
20.5x=20.5x+(1)/(2)6x^(2)-55
t=4.28
then i added 4 cause he acel at t=4
but 8.28 isnt right
runic garnet
Well ur eqn was right, but u donāt add 4, cuz thatās when the acceleration starts
runic garnet
If u add 4, that means ur starting 4 seconds before the acceleration and we donāt want that
crimson sedge
When proving a conditional statement p -> q, what needs to be assumed and what needs to be proved to justify the statement: using direct proof, proof by contraposition, proof by contradiction.
crimson sedge
So when using direct proof, assume p and prove q
For contraposition, assume not q and prove not p
and for contraposition assume p and not q and prove a contradiction
does this sound right?
gilded elm
i'll assume you made a typo for the last one
muted bear
and for contraposition assume p and not q and prove a contradiction
i think you used the wrong word here
crimson sedge
whats the typo?
gilded elm
and say ā anyway
gusty anvil
yo
crimson sedge
i'll assume you made a typo for the last one
urm not im not sure what the typo is
gilded elm
ehh it should be apparent
gusty anvil
can i get some help
gilded elm
!help
cedar kilnBOT
Please read #āhow-to-get-help
gusty anvil
with some slope work
gilded elm
not here
crimson sedge
and for contraposition assume p and not q and prove a contradiction
is this not right?
gilded elm
you gave me the strategies for direct proof and proof by contraposition
well the strategy is correct
what you called it is wrong
crimson sedge
alr I was just making sure I wasn't going about this wrong
gilded elm
your strategy was right
crimson sedge
Tysm!
gilded elm
np
crimson sedge
.close
random oyster
cedar kilnBOT
random oyster
it's zero ahlie
earnest socket
i was wondering y he multiplies by 1/x
because a common strategy with such limits is to divide both the numerator and denominator by the highest power of the variable present in either the numerator or denominator
brisk dirge
Same degree
random oyster
rlly
brisk dirge
Divide numerator and denominator by x
random oyster
so 1/x^3
frosty thicket
I don't think this limit exists
random oyster
I don't think this limit exists
Your supposed to multiply top and bottom by 1/x^3
and then simplify then sub in zero right?
dark silo
Why sub in zero?
frosty thicket
I'd multiply by 1/x^{3/2} because of that square root
random oyster
Why sub in zero?
cuz
1/0.0001
is just approaching zero
let me do it and show u guys
is this proper way to do it?
frosty thicket
you can't really conclude anything from a indeterminate form such as 0/0
try using 1/e^{3/2}
frosty thicket
yeah
frosty thicket
yes
random oyster
frosty thicket
see what that approaches as x approaches -ā
frosty thicket
so remember that we working over the real numbers
so it's really just 0/undefined
hence the limit does not exist
frosty thicket
yep
frosty thicket
L'hopital can be one for certain cases
random oyster
dk that one yet
so for this I used the same method
it has root so instead i just do 1/x
is this correct?
random oyster
how
frosty thicket
no
random oyster
x(x-1)
frosty thicket
close?
random oyster
x(x-1/x)
frosty thicket
it's alr
random oyster
x^2(1-1/x^2)
frosty thicket
yeah
random oyster
ok
frosty thicket
you can take out the xĀ² out of the root
frosty thicket
yeah but
random oyster
ok
frosty thicket
remember that for positive x, 1/x = sqrt(1/xĀ²)
and āa Ć āb = sqrt(ab)
a Ć āb = sqrt(aĀ²b)
random oyster
yes.
frosty thicket
so
random oyster
ok
frosty thicket
multiply 1/x with sqrt(xĀ²-1)
random oyster
fuck man why am i so slow
random oyster
remember that for positive x, 1/x = sqrt(1/xĀ²)
i dont understand this
frosty thicket
do recall that
frosty thicket
for positive x $\sqrt{xĀ²} = x$
wraith daggerBOT
biggboy
frosty thicket
nope it's okay
random oyster
ok
right
so it's the opposite operation your trying to say
so xāx^2 = x
inverse of x is 1/xx
so 1/x multiplied x^2 is x^3?
frosty thicket
and $\sqrt{a}\cdot \sqrt{b} = \sqrt{ab}$ and $a \cdot \sqrt{b} = \sqrt{aĀ²b}$
wraith daggerBOT
biggboy
frosty thicket
so it's the opposite operation your trying to say
kinda
random oyster
so ok
frosty thicket
I am trying to tell you that shen taking something insixd of a squreroot, you square it to keep the value same
that's kinda it
you are dividing everything by x inside the square root
random oyster
ok
frosty thicket
when you should divide by xĀ²
random oyster
but u did 1/x^3/2 earlier
but why can't i do the same here
instead of x^2 just x
to preserve the shit in the root
frosty thicket
you see
random oyster
that's where im confused
frosty thicket
it's that we square when it's inside the squareroot so that 1/x^{3/2} becomes 1/x^3 and cleanly divides the polynomial inside the squareroot
we square that too
so like
random oyster
so your saying
we did that earlier to kill the x^3
so that we don't get the intermediate form 0/0
frosty thicket
$\frac{1}{x} \cdot \sqrt{xĀ²-1} = \sqrt{\left(\frac{1}{x}\right)Ā² \cdot (xĀ²-1)}$
wraith daggerBOT
biggboy
frosty thicket
so that we don't get the intermediate form 0/0
yeah
frosty thicket
kind of like that but we would actually get 0/sqrt(-inf) there
random oyster
ok
but since hefe
if it was āx-1
i can do 1/x
since that kills the x
but it's x^2 hefe
so it would be
1-1/x^2
so
1/1
frosty thicket
why
frosty thicket
it is
random oyster
the top is just x
frosty thicket
but we multiply x by 1/x
random oyster
bruh
frosty thicket
look
frosty thicket
we multiply the numerator with 1/x
frosty thicket
so that's 1/x ā¢ x = 1
and we also multiply the denominator by 1/x
that's $\frac{1}{x} \cdot \sqrt{xĀ²-1}$
wraith daggerBOT
biggboy
frosty thicket
right
random oyster
yuh
frosty thicket
and that's equal to $\sqrt{\left(\frac{1}{x}\right)Ā² \cdot (xĀ²-1)}$
wraith daggerBOT
biggboy
random oyster
but why not by 1/x^2
frosty thicket
that's leave the denominator as x
random oyster
because a common strategy with such limits is to divide both the numerator and d...
what he said here
is this false then
the highest powered is 2
frosty thicket
heighest power 2 inside a square root is like power 1
random oyster
just find the highest power that's not eooted
ah
that's true
cuz root and ^2 cancel out right
so ur just left with 1
random oyster
ok i get it here why it's 3 since u root it it's 3/2 that's the highest power here.
that makes sense why u said 3/2 and then 1 there
okok
frosty thicket
yep
frosty thicket
explaining -infinity with factoring out would be easier
frosty thicket
so
factoring xĀ² from xĀ²-1 again
you did that earlier
that's xĀ²(1- (1/xĀ²))
this is inside a square root
random oyster
yes
frosty thicket
but since our x is negative
we take it out of the square root as -x
does that make sense
for general x $\sqrt{xĀ²} = |x|$
wraith daggerBOT
biggboy
wraith daggerBOT
biggboy
random oyster
ok
frosty thicket
x's cancel out
random oyster
ye
random oyster
ok
so can I conclude
that I find infinity limit
negative infinity is just the negative of it?
frosty thicket
not always
frosty thicket
better to just solve for both
cedar kilnBOT
@random oyster Has your question been resolved?
pearl orbit
cedar kilnBOT
pearl orbit
upper garnet
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
i think 1 for both wasn't there the day of the lesson and videos haven't helped
livid hound
are you familiar with identities related to
sum of first n natural numbers
sum of squares of first n natural numbers
half forge
As in this
livid hound
considering the linearity of summation,
$$\sum_{k=1}^{20} (2k+5) = \br{2\blue{\sum_{k=1}^{20} k}} + \br{\red{\sum_{k=1}^{20} 5}}$$
wraith daggerBOT
āamonov
livid hound
would you be able to use the above to evaluate the blue and red
pearl orbit
would you be able to use the above to evaluate the blue and red
no i don't think i know how to solve
not really sure what to do
livid hound
do you see those identities above
pearl orbit
yes
livid hound
can you identify which of those the one in blue is related to
pearl orbit
2?
half forge
The blue one is just k instead of i, and 20 instead of n
pearl orbit
now how would you go about solving that
livid hound
identify the corresponding values and substitute into the identity/formula
half forge
You basically subb in n=20 (for the blue one)
livid hound
and the k in your question is the same as the i in that image
pearl orbit
so 400?
livid hound
how are you getting 400
pearl orbit
i subbed n for 20?
half forge
Umm
half forge
210 is write
half forge
**āamonov**
But just for the blue one
Now you need to find the red one
Using this
pearl orbit
5 x 20?
pearl orbit
ok
cedar kilnBOT
@pearl orbit Has your question been resolved?
weak python
does anybody how to solve this equation without using calculator?
weak python
it has bad solutions
Im thinking of making it a quadratic equation then factoring it
long arrow
does anybody how to solve this equation without using calculator?
square both sides
then solve
it will be polynomial equation
final mist
it will be polynomial equation
I think he's afraid that it will cause it to be a quartic polynomial
