yea
#help-27
woven radishBOT
jan Niku
gentle thunder
-18/3 x^3... I dont really know
I dont understand why it's to this point, why did the -18 go outside of the integral? And why is it only x^2 within it?
timber pebble
so constants can move out of the integral
this is just a general rule
its because they are linear
its the same reason we can integrate this polynomial term-by-term
but im just using it to make the result easier to see, the result would be the same if you left it inside
gentle thunder
Could you show me what it looks like inside of the integral? I'm sorry for the trouble
Wait, this is just for -18x^2?
timber pebble
yea
timber pebble
its -6x^3
maybe youre messing up the math in your head which is a common mistake
,calc -18/3
woven radishBOT
Result:
-6
Haha yes because i got the 5 wrong earlier too
devout snowBOT
timber pebble
tame plover
(f/g), f(x) = 4x-1 and g(x) = x-4
tame plover
Ok thanks
timber pebble
heavy current
the denominator becomes (q/p)x^(q/p - 1) * x = (q/p)x^(q/p)
the extra x in the denominator is the result of differentiating the numerator, logx
,, \lim_{x \to \infty} \frac{\log(x)}{x^{\frac{q}{p}}} = \lim_{x \to \infty} \frac{1}{\frac{q}{p}x^{(q/p) - 1} \cdot x}
oh goodness that is ugly 
that's right!
woven radishBOT
higher!
heavy current
q and p are fixed
they are fixed numbers that cannot change
x is the one that is changing
oh, I see what you mean
hold on
you're asking about the case where p larger than q?
let me see
oh wait, I'm dumb lol
every single function x^a is growing for a > 0
oak smelt
I believe it still grows the denominator. Since p > q the x standalone in the denominator still out grows the x^(q/p-1)
oak smelt
You're so right, im so dumb
heavy current
@cosmic wind you are correct btw
if p > q then this explodes to infinity
there might be an extra condition in your problem statement?
you'll have to post the original problem for me to be sure though
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@cosmic wind Has your question been resolved?
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solid osprey
let a,b,c be distinct positive reals, $\frac{a^2(b+c)+b^2(a+c)+c^2(a+b)}{abc}$ would be
devout snowBOT
let a,b,c be distinct positive reals, $\frac{a^2(b+c)+b^2(a+c)+c^2(a+b)}{abc}$ w...
woven radishBOT
Skill_Issue
solid osprey
a.greater than 4
b.greater than 5
c.greater than 6
d.none of the above
ans is c apparently
!status 1
devout snowBOT
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
torn bane
alright well first notice that we can scale a,b,c by anything we want and the expression stays the same
so one thing you could do is assume that a+b+c = 1 or anything you want
also since it is symmetric you could assume that a<b<c
oh maybe we can apply jensen's inequality
polar chasm
Do you know muirhead's perhaps?
polar chasm
a.greater than 4
b.greater than 5
c.greater than 6
d.none of the above
also, greater or equal I suppose, right?
polar chasm
Do you know muirhead's perhaps?
muirhead's is just AM-GM on steroids btw, so you could do this with AM-GM as well
solid osprey
also, greater or equal I suppose, right?
no its just greater
polar chasm
no its just greater
then c doesn't look true
solid osprey
if your thinking of using am-gm, it wont be equal cus a,b,c is distinct
weak cove
AM-GM always works
polar chasm
place some constant k on the right side and multiply by abc
polar chasm
AM-GM always works
indeed
solid osprey
$$\frac{a^2(b+c)+b^2(a+c)+c^2(a+b)}{abc}>k$$
$$a^2(b+c)+b^2(a+c)+c^2(a+b)>kabc$$
woven radishBOT
Skill_Issue
torn bane
now you can apply am-gm on inner sums and the entire sum
solid osprey
do you want it to be equal?
polar chasm
do you want it to be equal?
eh, they are distinct so AM-GM says they will never be equal
so not necessarily
solid osprey
ok
polar chasm
but yeah, now it's just AM-GM
solid osprey
how so exactly? sorry im not really catching on
polar chasm
try expanding the LHS
it might make it more obvious
and if you wish to, divide both sides by the n.o. terms on the LHS
solid osprey
and if you wish to, divide both sides by the n.o. terms on the LHS
after expansion or before expansion
torn bane
,, 2a^2\sqrt{bc}+ 2b^2\sqrt{ac} + 2c^2\sqrt{ab} > 6\sqrt[3]{a^3b^3c^3}
woven radishBOT
Bair
torn bane
,, a^2(b+c)+b^2(a+c)+c^2(a+b) > 2a^2\sqrt{bc} + 2b^2\sqrt{ac} + 2c^2\sqrt{ab}
woven radishBOT
Bair
polar chasm
double application looks unnecessary, but ig it works too
solid osprey
$$a^2b+a^2c+ab^2+b^2c+ac^2+bc^2>kabc$$
$$a^2b+a^2c+ab^2+b^2c+ac^2+bc^2>kabc$$
woven radishBOT
Skill_Issue
woven radishBOT
MæthIsAlwaysRight
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
solid osprey
yea
solid osprey
press the trash
polar chasm
**MæthIsAlwaysRight**
Compile Error! Click the <:errors:504266556054962196> reac...
anyway, that's the AM-GM
try applying it on the LHS
solid osprey
mhm
polar chasm
and see what you get on RHS
solid osprey
**Skill\_Issue**
for this?
polar chasm
yep
solid osprey
$$a^2b+a^2c+ab^2+b^2c+ac^2+bc^2>6\sqrt[6]{a^6b^6c^6}=6abc$$
woven radishBOT
Skill_Issue
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solid osprey
omg bruh im so stupid 😭
there was an explanation literally under the question bruhh
soft umbra
🔥
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lost laurel
Prove that $\frac{a}{b}= \frac{ac}{bc}$
devout snowBOT
Prove that $\frac{a}{b}= \frac{ac}{bc}$
woven radishBOT
ƒ(why am I here)= MATHS
lost laurel
so I started by multiplying the fraction on the right by c^-1, and (c^-1)^-1
so $\frac{acc^{-1} (c^{-1})^{-1}}{bc}$
and $c^-1 and {c^{-1}}^{-1}$ are multiplicative inverses of one another
woven radishBOT
ƒ(why am I here)= MATHS
lost laurel
which proves that this is the same as a/b
woven radishBOT
ƒ(why am I here)= MATHS
lost laurel
is this fine
raven leaf
for $b,c \neq 0$ I assume
uncut crow
a = 0 is fine
woven radishBOT
Xetrov
raven leaf
lol
chrome isle
**ƒ(why am I here)= MATHS**
just guessing are u doing analysis
uncut crow
i don’t really see how that proves it
lost laurel
<:wut:1269167408896016394> just guessing are u doing analysis
Worse, spivak for a calc 1 course
lost laurel
i don’t really see how that proves it
well cc^{-1}=1
and c^{-1} \cdot (c^{-1})^{-1}=1
lost laurel
thanks
weak cove
well cc^{-1}=1
You weren’t aware of inverses @uncut crow ?
uncut crow
well cc^{-1}=1
you should be proving a * b^(-1) = ac * (bc)^(-1)
i don’t understand what your argument was before
weak cove
you should be proving a * b^(-1) = ac * (bc)^(-1)
Stop concern trolling.
uncut crow
do you want to go back on my block list
elfin atlas
laughing my ass off
uncut crow
even this is doing too much. the last line is true because c * c^(-1) = 1. don’t need to go through all the stuff before
woven radishBOT
ƒ(why am I here)= MATHS
uncut crow
are you done with the previous one
lost laurel
yea
uncut crow
you should be proving a * b^(-1) = ac * (bc)^(-1)
did you understand this, and that this has a simple, very short proof? or if you don’t want to answer and want to move on, also fine
lost laurel
you should be proving a * b^(-1) = ac * (bc)^(-1)
Hmm, I get this too
lost laurel
**ƒ(why am I here)= MATHS**
so $\frac{add^{-1}}{b} + \frac{bcb^{-1}}{d}$
woven radishBOT
ƒ(why am I here)= MATHS
lost laurel
so this is the same as $\frac{a}{b}+ \frac{c}{d}$
woven radishBOT
ƒ(why am I here)= MATHS
lost laurel
**ƒ(why am I here)= MATHS**
Is this proof wrong?
uncut crow
what does it prove
lost laurel
**ƒ(why am I here)= MATHS**
This
chrome isle
Worse, spivak for a calc 1 course
dam gl
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digital willow
Help
olive snow
You want to do g/h ?
digital willow
You want to do g/h ?
yep
olive snow
So (x^2-2)/(x^2-4)
digital willow
So (x^2-2)/(x^2-4)
oh alright
digital willow
So (x^2-2)/(x^2-4)
what's the next step
olive snow
what's the next step
You can't go further
digital willow
You can't go further
oh ok
olive snow
What would it be for the second one ?
digital willow
What would it be for the second one ?
Like this?
olive snow
More like $\frac{x^2-2}{x^2-4}$
woven radishBOT
YakuBros
digital willow
More like $\frac{x^2-2}{x^2-4}$
Like this?
digital willow
You are dividing
wait it's not?
olive snow
You didn't divide
olive snow
Like this?
Here
Just let as the fraction, yiu can't simplified it more
Dont use the / symbol, i think its confusing u
digital willow
Oh thanks
olive snow
What would be the 5) ?
devout snowBOT
@digital willow Has your question been resolved?
digital willow
What would be the 5) ?
Is 5 also the same?
devout snowBOT
@digital willow Has your question been resolved?
ebon aurora
How can I prove that the expression (n^5 - n) is divisible by 5 for any natural n? I assume I should use mathematical induction and consider all possible cases for n?
My inital attempt was to express it as:
5m
5m + 1
...
5m + 4
and prove that it is indeed divisible by 5 by solving for each. However, this approach seems a bit redundant to me.
devout snowBOT
How can I prove that the expression (n^5 - n) is divisible by 5 for any natural ...
winter patrol
don't need the separate cases if doing induction
topaz axle
ebon aurora
Don't they represent all possible cases for n?
Any number could be expressed by one of these 5 cases.
*any natural number
pls correct me if I got this wrong
winter patrol
depends which method you want to use to solve this
the basic induction approach would already prove it for all integers after n=1, without needing to separate it into 5 cases
ebon aurora
I thought if I tried substituting each of these cases for n in the initial expression I would spot some pattern that would help me prove it. But I don't want to calculate the power of 5, it feels like too much work.
I see, sorry I am just getting into this topic.
winter patrol
if you're doing case work like that, induction isn't needed
ebon aurora
Then how should I go about this? I am curios how both the case approach and induction would work.
winter patrol
both would involve binomial theorem
you can leave stuff in exponent form, no need to evaluate fully
ebon aurora
if m>=0, we cover all possible natural numbers, right? with the cases
winter patrol
yes
ebon aurora
ok
let me show you what I get if substituted now
maybe we can spot some pattern
winter patrol
to reduce the amount of work,
do the expansion using
5m + c
ebon aurora
ok I will do that now)
@winter patrol
sorry my connection was slow
so
it seems like everything is a factor of 5 except the last term which we need to prove
for 5m + 1 the 1-s cancel out
2^5 gives us 32
Yeah I think we proved it this way ...
@winter patrol
I am curious, why this can't be considered induction? How would you do it the other way?
ebon aurora
i forgot the powers here lol
winter patrol
the basic process of induction is
using a base case e.g. n=1
then showing that if the statement holds for n=k, it'll also hold for n=k+1
thus creating a staircase effect showing it'll be true for n=2, and from that n=3 etc... true for all positive integers
(may differ slightly depending on what you're trying to show)
ebon aurora
I see, thank you for the detailed explanation!
So, how would we prove it that way? Substituting with k I get, k^5 - k
if I pick 1 as the base case, we get 0 which is indeed divisible by 5.
sorry I just want to make sure I get it this time
I am just not sure how we can prove that this holds true for every k without considering all of its cases
like we did with our initial approach
Or for example here:
n^(4k+1) - n is divisble by 10 for any natural n, k
How would I prove this using induction
the fact that now the power is 4k + 1 confuses me even more, we proved that it is divisible by 5 if k = 1 tho
@winter patrol (if you do not want to get pinged pls tell me I'll stop)
winter patrol
Substituting with k I get, k^5 - k
here you're going to make an assumption that'll be divisible by 5,
you can represent that as
k^5 - k = 5p
and that use that in some way to show that
(k+1)^5 - (k+1) is also a multiple of 5,
i.e. can be expressed in the form 5q
ebon aurora
I see, so we start with hypothesis like is done here https://math.stackexchange.com/a/350680
ebon aurora
Or for example here:
n^(4k+1) - n is divisble by 10 for any natural n, k
how would you prove this example? @winter patrol
now we have two variables (
<@&286206848099549185>
chrome isle
how would you prove this example? <@220517274845577216>
U need to prove that by induction right?
ebon aurora
Yeah) or by cases ig like I did with (n^5 +1) 🙂
chrome isle
First show that is true for the base case
Then assume it's true for n
Then prove it for (n+1) ^4k+1 - (n+1)
By expanding ( n+1) ^4k+1
ebon aurora
what value should I choose for k?
chrome isle
what value should I choose for k?
? Wdym
chrome isle
what value should I choose for k?
For the base case n = k = 1
ebon aurora
Ok
starting with the base base:
0 is divisible
now we assume that n^(4k + 1) - n = 10a, is that correct?)
ebon aurora
now we do the same for n+1 and k+1
so we get
(n+1)^(4k + 5) - n - 1
chrome isle
now we do the same for n+1 and k+1
so we get
(n+1)^(4k + 5) - n - 1
Yes but 4k+1 and 4k+5 are equal in the modulus world so won't matter if u choose 4k+1 or 4k+5
ebon aurora
ok so k doesn't matter got it)
so we have
(n+1)^(4k+1) - n - 1
what should we do now
chrome isle
ok so k doesn't matter got it)
so we have
(n+1)^(4k+1) - n - 1
Yes and now u can expand n+1^4k+1
chrome isle
Now the one would cancel out
ebon aurora
yes
n doesn't tho, right?
or no we get 4k*n sorry
or maybe we can keep it in the end and express the last two terms as 10a as we defined previously
(n)^(4k+1) -n
chrome isle
n doesn't tho, right?
Hmm i was thinking a little different
Don't cancel the n
cause we know n^4k+1 - n is divisible by 10
So now we have the task to show that the latter is also divisible by 10
ebon aurora
yeah
devout snowBOT
@ebon aurora Has your question been resolved?
ebon aurora
here's a more expanded version lol
might help us see sth we didn't see before
chrome isle
Hmm try this
Can i say u have to prove n+1^4k+1 -(n^4k+1 + 1)
So we can prove this no will be even for all n and k
And then u can take cases
First when n is of the form 5y
Second when n is of the form 5y +1
...
And u can show that that no is a multiple of 5 for all values of n and k
And so as the no is a multiple of 2 and 5 for all values of n and k it must be a multiple of 10
chrome isle
here's a more expanded version lol
might help us see sth we didn't see before
Ok thanks
ebon aurora
That's a good idea
so take these cases?
5y
5y +1
5y +2 ...
chrome isle
That's a good idea
so take these cases?
5y
5y +1
5y +2 ...
Yes
Can't find of a better method other than taking cases rn il tell when I do
ebon aurora
ok lol
I always go with cases too so I'm fine with that) I am just lazy to do all the calculations
sorry can you please explain me the part where you proved that it is even for all cases of k and n?
you subtracted the one with (n) from (n+1)^ ...
did you subtract it from the expanded form?
chrome isle
did you subtract it from the expanded form?
Yes we had already proven that n^4k+1 - n is divisible by 10 and we needed to prove that the latter is
So I just took 1 and n^4k+1 to the other side to obtain the other form of the latter
chrome isle
ok lol
I always go with cases too so I'm fine with that) I am just lazy to do al...
I just took cases
When n is even
Then n+1 is odd so odd - odd = even
When n is odd
N+1 is even so even - even = even
Also for proving its divisible by 5 u will have to be clever and take advantage of the fact that it raised to the power 4k +1 (ie use cyclicity)
ebon aurora
I just took cases
When n is even
Then n+1 is odd so odd - odd = even
When n i...
oh
yeah that makes sense) ok I think I get it now, ty!
chrome isle
oh
yeah that makes sense) ok I think I get it now, ty!
Yw : )
ebon aurora
the only thing left is to prove that it is a factor of 5 using cases) which is a bit redundant but ig that's what the problem expects me to do too)
in the previous problem I proved that for any n (n^5 - n) is divisible by 5
could we use it here?
I guess we could
for k = 1 it is for example
ebon aurora
here
chrome isle
I guess we could
for k = 1 it is for example
What did u do in the previous one?
Also if u look closely this prob is just the generalization of the pervious one
ebon aurora
yeah ...
I took cases for n
but at first I just expanded it using some general variable c
everything is a factor of 5 except the last term which I proved using cases
so 2^5 - 2
3^5 - 3 etc )
chrome isle
yeah ...
I took cases for n
but at first I just expanded it using some general...
so u took cases anyways
chrome isle
I see, so we start with hypothesis like is done here https://math.stackexchange....
I feel like this approach can be used here
chrome isle
I feel like this approach can be used here
If we can show that n+1^4k+1 - n-1
Can be Factorized as ten consecutive no and another no which is a multiple of 10 we are done
ebon aurora
here's a more expanded version lol
might help us see sth we didn't see before
yes
we have to show that the ones I didn't cancel are a factor of 10 somehow
cuz cases with this one feels like too much work 🫠
chrome isle
cuz cases with this one feels like too much work 🫠
Tbh I did it and it isnt that diff 
ebon aurora
oh ok
then my brain exaggerates stuff lol
if you figure out how to do it with our initial approach, please let me know🤎
thank you so much for your help!)) I think the book I took this from expected me to use cases anyway, cuz there are no examples of that(stack overflow's) approach provided
I can close the chat now ig, have a great day!)
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fallow hull
Hello! I need a little bit of an explanation on this question in my assignment. (Its in danish) in question (c) i found -b ; opposite vector to b. And in question (d) i need to find the “difference triangle” a-b and i am so confused on which Numbers Im supposed to use and how to draw this vector.
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Hello! I need a little bit of an explanation on this question in my assignment. ...
fallow hull
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rotund kernel
help
somber mulch
is k a specific value?
somber mulch
k>1 can imply its always positive, i think you can simplify from this point by moving sinx from the right to the left by dividing sinx and getting 1/sin^2(x) =k
chrome isle
how to get k
?
rotund kernel
k>1 can imply its always positive, i think you can simplify from this point by m...
yes i did that
rotund kernel
?
chrome isle
not necessarily
Ahh ok it's a periodic function
somber mulch
yes i did that
whats the specific problem youre working on
chrome isle
cold bone
like whats it asking for
I suppose they are looking for the set of possible values of k
cold bone
possible values of cotx it says
cotx?
rotund kernel
yeah
give that cosec(x)=k/cosec(x) and k>1 find the possible values of cotx
😭
in terms of k
cold bone
give that cosec(x)=k/cosec(x) and k>1 find the possible values of cotx
should have told earlier
cold bone
give that cosec(x)=k/cosec(x) and k>1 find the possible values of cotx
I think you can use some trig identities to find that
chrome isle
in terms of k
hint - cosec²x = cot²x +1
chrome isle
I think you can use some trig identities to find that
Rather only one
rotund kernel
hint - cosec²x = cot²x +1
okok let me try wthis
ok got it guys
tysm
cotx= root k-1
+/-
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wet robin
is 13.937 irrational?
devout snowBOT
is 13.937 irrational?
acoustic leaf
no. any number with a finite number of decimals is rational
wet robin
thanks
how will I do this question I don’t have much information
its fine now
for some reason
my brain didn’t realise the centre was (0,0) of the circle as i’m so use to always seeing a version of (x-a)^2 + (y-b)^2 = r^2
.solved
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dapper reef
for B can someone please expain why we do 2sin first?
devout snowBOT
for B can someone please expain why we do 2sin first?
dapper reef
sonic sphinx
do you know the power rule formula in differentiation ?
pale patio
You can imagine sin^2(x) as (sin(x))^2 with the chain rule you first have to take the derivative of the outside ( )^2 so that would be the 2sin(x) and than multiply it by the derivative of the inside sine(x) and that would bo cos(x) so it equals 2sin(x)cos(x)
oblique granite
You can imagine sin^2(x) as (sin(x))^2 with the chain rule you first have to tak...
Jsem Shaco explains it very well here, in a general way the derivative of the fiction f•g (the notation to name the function where x associate f(g(x)) ) is
g’(x) * f’(g(x))
dapper reef
I do know the power rule formula but I wasn't sure if it applied to sin cos and tan
tysm for the expanation
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north goblet
can some explain to me where did the 'd' go in the development opf the formula? AP
devout snowBOT
can some explain to me where did the 'd' go in the development opf the formula? ...
north goblet
talking about the part with the n^2
cold bough
north goblet
it should be 0.5dn^2
shouldnt it?
???
oh
they took out the d
thanks
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leaden plinth
ik this is chem but can any1 explain why Ms are equal?
devout snowBOT
ik this is chem but can any1 explain why Ms are equal?
@leaden plinth Has your question been resolved?
rigid python
hello
upper schooner
rigid python
i literally forgot how to do rate of change
and ummm how do i do interval positive and negatives
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solid cape
if i have the function for velocity 24m/s * sin(pi * t ), and want to derivate it to turn it into a function for acceleration using derivatives, how should i do it?
devout snowBOT
if i have the function for velocity 24m/s * sin(pi * t ), and want to derivate i...
wicked turtle
did you try taking the derivative? where did you get stuck
solid cape
what happens is that im a little bit confused as for how derivates work, im still learning, and i do not know the rules for trigonometric functions
wicked turtle
do you know the derivative of sine is cosine?
solid cape
i understand that, but i wanted to make sure if i skipped any other rule
solid cape
how does it work?
wicked turtle
first you take the derivative of sine, giving you cos(pi * t)
then you take the derivative of pi * t
which is?
wicked turtle
same as what?
solid cape
like, unchanged
wicked turtle
what's the derivative of 2t?
solid cape
pi
devout snowBOT
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warped tapir
Hey guys ! Im really lost and would appreciate any help. My teacher never went over this today and im struggling on HW. The first picture represents the original graph and the second is the trasnformation im supposed to do . What would my new set of points be ?
devout snowBOT
Hey guys ! Im really lost and would appreciate any help. My teacher never went o...
warped tapir
I think the x-2 would move the x values 2 units to the right but as for the -f, I dont know how to inverse the function
<@&286206848099549185>
fossil locust
I think the x-2 would move the x values 2 units to the right but as for the -f, ...
correct
then flip the function upside down, so a reflection across the x-axis
warped tapir
okay !
Let me try
and ill send a new picture
thanks for responding, im going crazy 😭
fossil locust
nwnw
(I would do it point by point, so find where (-2, 4) ends up after the transformation, then find where (0, 3) goes etc)
fossil locust
ok
fossil locust
yes
warped tapir
👍
okay done with all those ones
I also got this back side but
Its kinda hard to see the graphs
fossil locust
oh it's the same type of problem
warped tapir
kinda yea
fossil locust
the only new thing is that they have f(x/2)
that's a compression in the x-direction by 1/2, or a stretch by factor 2
fossil locust
and like f(2x)
that's still a compression
by factor 2
so it gets squished towards the y-axis
in both directions
warped tapir
Sorry for asking so many questions lol
fossil locust
it's okay
fossil locust
but this stuff is really important for working with functions in general
fossil locust
there's only translation,
warped tapir
towards the y axis
fossil locust
towards the y axis
yep, by a factor of 2
so if I had the point (4, -2) on the function
warped tapir
yea
fossil locust
yep
warped tapir
so would I just
pick any point
that is like a good point
to do my compression
fossil locust
oh yeah that works, you can figure them out by testing one point
warped tapir
the thing is
theo nly good point I see is
(0,2)
but zero divded by 2
wouldnt get me anything
*(0,1)
Im guessing the answer is B though
only one that looks decently right
fossil locust
Im guessing the answer is B though
yeah its B
warped tapir
👍
alright
then number 3 is a
units 2 to the left
and inverse
correct ?
cause (x+2), is 2 units to the left and then -f is reflecting over x axis
so G I think ?
fossil locust
so G I think ?
yep
fossil locust
the max of the function is transformed to x = 0 then reflected upside down
one sec
fossil locust
and then a reflection
well you do f(-x) first so the reflection
fossil locust
let me see
the confusing thing is f(2x): 2 f(x) is much easier
for f(2x) imagine the function playing 2 times faster, like 2x speed
warped tapir
👍
4 is so weird 😭
would it be
like
it needs to be a graph on the left side
so either F or I
fossil locust
so either F or I
yes those are the two correct options
fossil locust
however with a stretch, that means the slope of the graph is being increased, cause it's stretched
yeah it's F for that reason
warped tapir
Alr lets go
fossil locust
so now you can figure out f(-x) + 2
warped tapir
hes probably going to clarify all this tommorow
he just gave us this today
without any context
fossil locust
omg that's so sad
warped tapir
so hopefully tomorrow i understand it better
we did easy stuff today like this
it was a lot easier
warped tapir
so now you can figure out f(-x) + 2
alr let me try
so u said to do
reflection first
and then
since its
+2
I go up
2
so its
isnt it I ?
thats the only other one on the left
fossil locust
isnt it I ?
yep
fossil locust
so f(x) is that a reflection over the
no, it's f(x)/2 or 1/2 * f(x)
glad drift
My phone is glitching
fossil locust
it's this rule
fossil locust
So where do I go fr hell
fossil locust
yeah
fossil locust
ok
warped tapir
?
fossil locust
no
well actually you can eliminate a lot of the options cause it's negative f(x/2)
so it's flipped upside down
fossil locust
no D is not upside down
warped tapir
E
fossil locust
yep
warped tapir
💀
fossil locust
so it was a stretch by factor 2 (compression by factor 1/2)
warped tapir
yea
warped tapir
because of the
well
im guessing its
D
Since thats my last
option lol
I used all the other
ones
fossil locust
yep D looks right
warped tapir
Im done bro
fossil locust
if you're wondering why the top didn't move, it's cause y = 2 * 2 - 2 = 2
warped tapir
👍
Hopefully tomrrow he goes over this
I got a quiz but all the topics on the quiz I already know
so I should be good 👍
warped tapir
Than ku so much for the help
upbeat marten
Is what I did okay or do can I not include the -3
devout snowBOT
Is what I did okay or do can I not include the -3
topaz beacon
youre not supposed to include the -3 since that gives you 0/0
you should pick x vales that get close to -3
devout snowBOT
devout snowBOT
Available help channel!
brisk jacinth
my teacher break down this integration on 1 but i dont know why
devout snowBOT
my teacher break down this integration on 1 but i dont know why
iron sun
The probable reason is to be able to instead reason with the second term, which hopefully can be compared with an integral of the form 1/x^p from 1 to infty
(the first term is trivially convergent)
rapid blaze
I want to start learning Calculus but I don't know where to start from, any suggestions
devout snowBOT
I want to start learning Calculus but I don't know where to start from, any sugg...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
@brisk jacinth Has your question been resolved?
brisk jacinth
The probable reason is to be able to instead reason with the second term, which ...
So it is ok to break down on any number like 2 or 3?
devout snowBOT
So it is ok to break down on any number like 2 or 3?
iron sun
So it is ok to break down on any number like 2 or 3?
Sure, but you want to make sure each piece is convergent
Which they will in this case
devout snowBOT
@brisk jacinth Has your question been resolved?
brisk jacinth
Sure, but you want to make sure each piece is convergent
why the comparison test in two x range should be different? one is x^a and the other is x^a/x^b
devout snowBOT
why the comparison test in two x range should be different? one is x^a and the ...
@brisk jacinth Has your question been resolved?
jolly anvil
Is there a way for me to calculate arugment for complex number without a calculator?
devout snowBOT
Is there a way for me to calculate arugment for complex number without a calcula...
jolly anvil
like this
upper schooner
In the case you have, draw a picture and make a triangle 
From where you can use trig/sohcahtoa to figure out what the argument is, if you remember the “special values”…
jolly anvil
what does trig/sohcahtoa mean?
neat solstice
,w atan(sqrt(3)/1)
woven radishBOT
solid osprey
what does trig/sohcahtoa mean?
neat solstice
Sin cos tan is what you wanna use, afaik sohcahotoa is how they are defined (soh:sine=opposite/hypothenus
jolly anvil
ohhhh thanks
neat solstice
In your case, you have a triangle with one point in the origin, another on your point, the last on the x axis. Thus you wanna use tan
So:
tan(arg)=opposite/adjacent=Im/Re
Therefore
atan(Im/Re)=argument
Im and Re being imaginary and real parts
upper schooner
(Be careful if the real part is negative though, you’d then need to add/subtract pi to get the correct argument)
jolly anvil
those i know (i hope)
cold bone
those i know (i hope)
okok nice
devout snowBOT
devout snowBOT
Available help channel!
steel fiber
Can anyone help me with this
devout snowBOT
Can anyone help me with this
brittle inlet
I dont understand why they’re doing this
They're probably equaling tangents
steel fiber
How can dc/db be equal to db/ad though
brittle inlet
How can dc/db be equal to db/ad though
If the angles are equal, it then follows that their tangent must be equal
If I were you, I'd start by calculating as many angles as possible
That should clear up a lot of confusion
steel fiber
How can i get whether angles are equal
Yes but in order for me to determine angles i would need to know how angle b is splitted
teal grotto
Yes but in order for me to determine angles i would need to know how angle b is ...
You can use trigonometry
steel fiber
And it doesnt say anything on this and im sure its not 45-45
brittle inlet
Can anyone help me with this
First of all, notice the BD segment is perfectly perpendicular to AD
steel fiber
You can use trigonometry
ohh ur right
cold bone
And it doesnt say anything on this and im sure its not 45-45
you don't actually need to find the value of angle
brittle inlet
What does this say about the angle between them?
steel fiber
you don't actually need to find the value of angle
then how do i do it
steel fiber
What does this say about the angle between them?
i dont remember tbh 😢
cold bone
then how do i do it
just assume it to be some variable then use the sum of angles of a triangle property
steel fiber
wait
yes i can do that
i would do alpha and theta
and get trigonometric values of them
right?
cold bone
i would do alpha and theta
assuming any one is enough
glossy shell
There's a harder way to do it without finding angles, but it's dumb, give me a minute to draw it
cold bone
There's a harder way to do it without finding angles, but it's dumb, give me a m...
similarity?
glossy shell
similarity?
Area of a rectangle, Heron's formula, and some addition
cold bone
Area of a rectangle, Heron's formula, and some addition
noice
devout snowBOT
@steel fiber Has your question been resolved?
steel fiber
Area of a rectangle, Heron's formula, and some addition
Dude there’s fr no reason to use heron’s formula lol i already got it thanks a lot to everyone
/close
.close
devout snowBOT
glossy shell
I did say it's a dumb way, also it might not be possible in the way I was thinking
devout snowBOT
Available help channel!
coral wraith
can someone please help me with this?
devout snowBOT
can someone please help me with this?
stone stump
what have you tried
coral wraith
what have you tried
im not sure what to try
devout snowBOT
@coral wraith Has your question been resolved?
coral wraith
@stone stump you there?
coral wraith
that is, the sufficiency part
im not sure how exactly this proof should go, because it seems rather obvious
restive river
Since A is invertible, write its inverse out, and there is only one reasonable way to use this matrix
coral wraith
Since A is invertible, write its inverse out, and there is only one reasonable w...
A^{-1}*b=x
restive river
so it is unique, isn't it
coral wraith
so it is unique, isn't it
right
because A^{-1} is unique
what about the other way around
@restive river you there?
restive river
let $x_i$ be the unique solution of $Ax_i=e_i$, and think about the block matrix $(x_1|\cdots |x_n)$.
woven radishBOT
worthless loser
restive river
This block matrix is n by n
devout snowBOT
@coral wraith Has your question been resolved?
coral wraith
Ik confused
restive river
why not play with a 2 by 2 matrix, find the corresponding x1 and x2, and see what A does to the block matrix
just to get a feel for it
For example A = ((0,1),(1,0))
devout snowBOT
@coral wraith Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
ruby rover
Any tips for time management in exam? My exam is in about 2hours, I only have one hour for the math test, I might not finish pre-calc
devout snowBOT
Any tips for time management in exam? My exam is in about 2hours, I only have on...
small jackal
Any tips for time management in exam? My exam is in about 2hours, I only have on...
Scan for the least time consuming and easy questions then answer them
Then do the others
Remember if all questions have the same mark don't waste too much time on a single question
ruby rover
So the moment I get the paper I should at least check pretty much everything first right
olive snow
Find the worth questions in terms of time/marks
ruby rover
Find the worth questions in terms of time/marks
ok ok
olive snow
How many marks ?
ruby rover
Atleast how many minutes should I spend on one question
ruby rover
How many marks ?
its over 80
olive snow
its over 80
120/80 ?
olive snow
No
ruby rover
Total score?
olive snow
120/80 = 1.5min per marks
olive snow
Atleast how many minutes should I spend on one question
Depends question therefore
If its 3marks the question, its supposed to be 4.5 or 5 min on it
olive snow
Don't be disturbed by the time tho
olive snow
Good luck !
devout snowBOT
devout snowBOT
Available help channel!
fallen rune
devout snowBOT
fallen rune
what did I do wrong
devout snowBOT
Show your work, and if possible, explain where you are stuck.
fallen rune
I plugged in the 9 into the equation but I still got the question wrong
devout snowBOT
@fallen rune Has your question been resolved?
devout snowBOT
@fallen rune Has your question been resolved?
fallen rune
.close
devout snowBOT
devout snowBOT
Available help channel!
mystic bloom
devout snowBOT
mystic bloom
how to do 10
upper schooner
Maybe first try factoring, to see if you get something a bit easier to deal with 
mystic bloom
Maybe first try factoring, to see if you get something a bit easier to deal with...
OMG HI CHARTBIT
ur my fav ever
or second fav idk
upper schooner
Second who do I have to bury then 
upper schooner
i forgor his name like penfound or something like that
Right, hunting time then 
mystic bloom
OK I got (3x+1)/(x-2)
oki idk wat do from here
upper schooner
Any ideas what happens as you decrease to 2? Maybe play around with values slightly above 2 and see if that brings any ideas?
mystic bloom
idk do I just put in 2.1 or something
upper schooner
idk do I just put in 2.1 or something
You could, if you wanted, that's one way, stuff like 2.1, 2.01, etc etc 
(you could e.g. also consider what happens to the numerator and the denominator too!)
mystic bloom
(you could e.g. also consider what happens to the numerator and the denominator ...
wat
it gets super big right
I haven't used a calculator yet idk
upper schooner
The whole thing does get large, yep 
mystic bloom
so the answer is infinfity
upper schooner
(you could e.g. also consider what happens to the numerator and the denominator ...
For this one, the numerator is something positive but finite, whereas the denominator is positive but gets closer and closer to zero
mystic bloom
uwaa
upper schooner
Yep, dividing something finite (and positive) by something that gets smaller and smaller (but still positive)
As for the proof 
,w lim (3x^2 + 7x + 2)/(x^2 - 4), x to 2 from right
woven radishBOT
upper schooner
mystic bloom
Yayaya
how to do 12
do I use perfect chbe
cube
thing
that's like (a-b)(a^2+ab+b^2
rightr
upper schooner
Yep, that's it 
woven radishBOT
mystic bloom
Yayayaya
upper schooner
mystic bloom
how to do 15
do I change it to inverse of tan
then turn tan into sin over cos of wtv
then reciprocal it cuz ya
devout snowBOT
devout snowBOT
✅
upper schooner
don't know what to do for the 13 one?
mystic bloom
Fr
upper schooner
You can either, if you have/are allowed a calculator, play around with values that are slightly above pi, or, otherwise, try and figure out how the numerator and the denominator behave when you're decreasing to pi
mystic bloom
umm can u spawn in the unit circle
upper schooner
Well, I guess you could tbf, if you want to choose to relate cot to tan instead?
mystic bloom
IDK WHAT TO DO
mystic bloom
You can either, if you have/are allowed a calculator, play around with values th...
I can do the ladder by liek using unit circle to see where it's like for cos and sin righttt
upper schooner
I can do the ladder by liek using unit circle to see where it's like for cos and...
Well, I mean you could, or e.g. you can figure out that as you're close and decreasing to pi, what quadrant you're in, and what value you approach for tan, and then argue what happens to cot = 1/tan
mystic bloom
,w unit circle
woven radishBOT
mystic bloom
IDK
mystic bloom
Well, I mean you could, or e.g. you can figure out that as you're close and decr...
idkkkk
upper schooner
Have you seen CAST diagrams before? (they may be called something different for you)
mystic bloom
No
upper schooner
Anyways (stolen, thanks mathsisfun 
), we're decreasing to pi, right, so going clockwise from quadrant 3...
If you wanna consider cot as cos/sin, then thinking about what cos gets closer to, and what sin gets closer to...
upper schooner
Yep, sure, but also sin is negative and gets closer to zero, whereas cos is negative and increases to -1 
so what happens to cos/sin?
mystic bloom
is the answer liek neg infinity
upper schooner
Not negative, no 
upper schooner
Of course, that should be a big hint, not negative
upper schooner
Yep, you have your numerator negative and going to -1, but your denominator negative but getting closer to zero, so you have a positive fraction and its value gets larger and larger
There you go
mystic bloom
light work
mystic bloom
There you go <:SCgoodjob2:750436894915166321>
I got 1 for 14.
upper schooner
I got 1 for 14.
Yep
mystic bloom
Yay
gloomy lily
Hello?
upper schooner
Can I ask for help?
!occupied also
devout snowBOT
Can I ask for help?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
upper schooner
Yep, you can find each sided limits separately that way
mystic bloom
Yep, you can find each sided limits separately that way <:SCgoodjob2:75043689491...
wat should I do for the second one
liek
0.9
upper schooner
Same thing 
you can set x as 1 for the second half too, "because"
(as each separate half is continuous, the limits for them are literally just the same as putting in what you're taking the limit to)
mystic bloom
okii
so like
does it not exist
cuz like it's diff for each side
@upper schooner
upper schooner
does it not exist
Yep, it doesn't, they're not the same on either side, so the overall limit is nonexistent
mystic bloom
easy
wat Abt the last one
also there's like 30 questions on the next page😔
they are short though
upper schooner
The last one is just a matter of expanding and simplifying stuff
mystic bloom
The last one is just a matter of expanding and simplifying stuff <:happyCat:5363...
omg i have to expand it
grr
I tried simplifying but nothing happened
upper schooner
What did you get when you expanded?
woven radishBOT
mystic bloom
omg i can factor out an x
upper schooner
Remember that this is all divided by h, of course
mystic bloom
Remember that this is all divided by h, of course <:pikathink:972100841748185208...
this the final page
do I just like
plug it in
for the corresponding thing
upper schooner
Pretty much (just notice that the limits ones are slightly different than the function value ones as where you're meant to put things, otherwise it's quite chill imo 
)