Is there a way to answer it with out using the geometry
#help-0
sleek fog
tacit arch
wut
tight pier
Triangle
tight pier
i am fried too gn
sleek fog
Lmao gn
tacit arch
the trig way is easiest
sleek fog
the trig way is easiest
Ik it is but i wanna know an algebra way if possible
Like an idea
sleek fog
Nvvvvm tri sound way better after seeing that
99% of whatever in there we did reach yet
tacit arch
yea no shit
lone heartBOT
sleek fog
yea no shit
Goat
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vague glade
The function
f:R→R defined by f(x)=4^x+4^|x| is
a.) One-one and into
b.) Many one and into
c,) One-one and onto
d.) Many-one and onto
lone heartBOT
The function
f:R→R defined by f(x)=4^x+4^|x| is
a.) One-one and into
b.) Many o...
@vague glade Has your question been resolved?
vague glade
<@&286206848099549185>
jagged imp
What do you think?
copper sigil
Well, I'm not sure what the answers mean.
lone heartBOT
@vague glade Has your question been resolved?
jagged imp
you're not even op but if you don't know what they mean maybe look them up or read about them in your class notes xd
if you have questions about the definitions after having done that i'm sure someone can help but
rose sigil
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@vague glade Has your question been resolved?
glass silo
it's a combinatorics problem. please heeelp
glass silo
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glass silo
combinatorics problem again help
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hybrid mountain
How do I do this I am so lost and this homework is due in 2 hrs
hybrid mountain
<@&286206848099549185>
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@hybrid mountain Has your question been resolved?
hybrid mountain
Ok
versed lark
in those points are the asymptotes
hybrid mountain
It might take me a bit I’m new to this
versed lark
just in ordet to help
csc(3x)=1/sin(3x)
so you have to find the points where sin(3x)=0
grave basin
You can also just transform the parent function, csc(x)
versed lark
yea
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glacial fossil
Hello can I get help with this trigonometry question please
lone heartBOT
Hello can I get help with this trigonometry question please
limpid heart
sketching it out always helps
glacial fossil
Yeah but Im just confused on what to even do Im sorry
limpid heart
its asking for the distance traveled to reach its highest point
shrewd prism
Yes!!
glacial fossil
so I should use Sine ?
shrewd prism
Wait I thought you needed help but ok lol
sour mica
wait what? since when is projectile motion not parabolic?
cerulean zealot
discurs travelled hypotenuse or horizontally?
sour mica
What grade of studies are you in rn?
shrewd prism
wait what? since when is projectile motion not parabolic?
Since this problem was created
They would have to give the equation if it wasn’t a straight line
glacial fossil
What grade of studies are you in rn?
Its highschool math but Im in college rn
sour mica
So you should use equations of motion to find the path.
Use this kind of stuff, with gravity and everything
glacial fossil
So you should use equations of motion to find the path.
Trigonometry is the topic
sour mica
ffs, idek what kind of person designed this question then
glacial fossil
Thank you everyone I figured out the answer.
glacial fossil
ffs, idek what kind of person designed this question then
lol its okay
im studying sports kinetics so the word the questions weird ig idk
sour mica
🤷🏽♂️ If you feel like the answer you got is the answer they want, its fine ig
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brisk ruin
? what is this?
ok what are the variables?
x,y,z,lamda,mew?
a 5 variable system?
@cerulean grove
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cerulean grove
<@889542917759320175>
Ooh sorry my internet delayed i didn't see your message
brisk ruin
it is ok
cerulean grove
Yesss I solved
brisk ruin
nice
cerulean grove
Ty!!
brisk ruin
np
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marsh ridge
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marsh ridge
can someone explain what's going on here
I get that (126-3×39) was subbed into 9
but after that I don't get how it got to 13×39-4×126
how did line 4 turn into line 5
yeah
no that's not what happened
marsh ridge
wait
I realized I asked the wrong question
I meant to ask line 3 to 4
hold on let me process what u wrote
.close
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marsh ridge
???
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novel spear
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novel spear
Please help im in the middle of an exam
uneven isle
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@novel spear Has your question been resolved?
nimble anvil
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small lance
which question?
proven depot
25
lone heartBOT
@nimble anvil Has your question been resolved?
nimble anvil
which question?
25
lone heartBOT
@nimble anvil Has your question been resolved?
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timber nimbus
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modern skiff
u can find the value of simx+sin^3x and use it maybe
mossy jasper
Have you tried taking a factor of sin(x) for the first one?
Since the sin^3(x) is the tricky part to get in terms of cos
sin(x)(1 + 3sin(x) + sin^2(x) )= 3 maybe?
nimble fern
u can find the value of simx+sin^3x and use it maybe
try to use this hint @timber nimbus
nimble fern
cos^2 x is still in terms of sin^2 x
with this
mossy jasper
Actually, hold on, wait a minute, there's a way simpler method I think
Are you allowed to use a calculator?
timber nimbus
nope
mossy jasper
Ah, that's sad
timber nimbus
try to use this hint <@895192019046117416>
sinx(1 + sin^2 x) = 3cos^2 x
thast what i come to
proven depot
sin^2(x) = 1-cos^2(x)
proven depot
sin^2(x) = 1-cos^2(x)
sinx(2-cos^2(x)) = 3cos^2(x)
timber nimbus
cos^2 x comes out to be (-3 + 5 root3)/16, (-3 - 5 root3)/16
proven depot
we have this
timber nimbus
yup
proven depot
square both sides
proven depot
I'm squaring bc I want to convert everything in the equation in terms of cos
nimble fern
I'm squaring bc I want to convert everything in the equation in terms of cos
Alaska so good at trigo
timber nimbus
8cos^4 x -3cos^6 x -4 = 0
timber nimbus
yes and then write sin^2 x = 1-cos^2 x
proven depot
yea
timber nimbus
then multiply and simplify
proven depot
yea
then you would get this, maybe some mistake in multiplication
simplify RHS and send LHS terms to RHS except the 4
send me a pic of what you have done
timber nimbus
dont have a phone rn
proven depot
oh
timber nimbus
and my working is too messy
proven depot
multiplication mistake then
timber nimbus
i doont get it sometimes 🥲
proven depot
goodluck
timber nimbus
then you would get this, maybe some mistake in multiplication
yup got that
timber nimbus
4 = 8cos^2 x - 3cos^6 x +4cos^4x
proven depot
4 = 8cos^2 x - 3cos^6 x +4cos^4x
you would get 4 = cos^6(x)+ 4cos^4(x) +8cos^2(x)
timber nimbus
😢
timber nimbus
okk
proven depot
^ thats the final answer
timber nimbus
multiplication mistake
proven depot
yea
timber nimbus
i really need to atart working neatly
ty
oh and
if i need ot ask another q do i opena new channel or just post here as a folow up
proven depot
if you have the question now you can ask it here
if you want to ask it later then close
timber nimbus
right
its another one with algebraic manipulation
but i cant seem to get it as one of the options
timber nimbus
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strange edge
I am working on proof with epsilon-delta definition. And the specific case that I am stuck with is to proof lim(x->2) x^2 = 5 is false. When x^2 = 4 I can factor it to (x+2)(x-2) but in this case I can't. Other solution I got from the internet is by providing a value of epsilon which makes the statement fail, but I don't really get how they get those epsilon values.
cerulean zealot
what about (x+sqrt5)(x-sqrt5)
strange edge
It wouldn't work since it has to be related with 0 < | x - 2 | < delta
tardy stag
hmm what if you wrote down x² - 4 - 1
strange edge
That is what I tried but it was a mess when I got into absolute values
tardy stag
what are you trying to show?
strange edge
I am trying to show that lim(x->2) x^2 = 5 is false by using the definition of limit
strange edge
By definition I believe its
for all epsilon > 0 there exist delta > 0 such that 0 < | x - 2 | < delta does not imply | x² - 5 | < epsilon
tardy stag
hmm that doesn't seem right
strange edge
How?
tardy stag
that's not how you negate qualifiers
strange edge
Oh wait
for atleast epsilon > 0 there does not exist delta > 0 such that 0 < | x - 2 | < delta implies | x² - 5 | < epsilon
Is this better?
tardy stag
the qualifiers can be kind of a mess but consider the intuitive idea: you can show that no matter how tight of a circle you draw around x=2, you can find points inside that circle where f(p) is nowhere near 5
tardy stag
for atleast epsilon > 0 there does not exist delta > 0 such that 0 < | x - 2 | <...
it would be something like
there exists an ε > 0 s.t. for all δ > 0, there exists an x in (2-δ, 2+δ) where f(x) is not in (5-ε, 5+ε)
strange edge
Oh
tardy stag
"as you get closer to x=2, you don't get closer to f(x)=5"
cerulean zealot
i never understood these epsilon deltha thing....
strange edge
Then how am I suppose to find the ε
tardy stag
well, it may help to look at a graph
tardy stag
i think that would work!
you don't need to describe every answer though, one example is good enough
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formal ginkgo
i need help with this integral
formal ginkgo
yoo can i get help pleaseee
vale anvil
formal ginkgo
send your problem in another channel
vale anvil
send your problem in another channel
Why any specific reason
formal ginkgo
Why any specific reason
because this channel is taken
vale anvil
Ok
strange edge
@formal ginkgo Ping Helpers
formal ginkgo
@craggy dagger
i'm left with this integral
which is impossible to integrate
$\frac{2}{\sqrt{3}}\int_{-1}^{1}\left(\int_{0}^{\sqrt{\frac{2}{3}}}e^{\left(u^{2}+v^{2}\right)}dv\right)du$
ocean sealBOT
RulzerFly
formal ginkgo
any idea to make this solvable
mabye switch to another coordinates system will help no ?
lone heartBOT
yo how to calculate such an integral
ocean sealBOT
caffu
cedar juniper
Whats the derivative of lnx?
ocean sealBOT
caffu
hot needle
Whats the derivative of lnx?
1/x
cedar juniper
What would happen if you sub ln x as u
dim garnet
Write it as $\int \ln(x) \cdot \frac{1}{x} \cdot dx$
ocean sealBOT
DeadTomato
hot needle
Write it as $\int \ln(x) \cdot \frac{1}{x} \cdot dx$
yeah so i gotta use the formula?
$\int {u'v}=\left[uv\right]-\int {uv'}$
ocean sealBOT
caffu
dim garnet
no
hot needle
oh i get it
dim garnet
But you have ln multiplied by its derivative
hot needle
$\int u \cdot u' \cdot dx$
ocean sealBOT
caffu
cedar juniper
Yea
cedar juniper
Then its basically the integral of $\int u \cdot du$
ocean sealBOT
Adarsh
dim garnet
so it's integral of ln(x)?
no
hot needle
🤦🏻♂️
dim garnet
It’s integral of u
cedar juniper
which is ln(x)²/2?
Yea thats correct
hot needle
It’s integral of u
isnt that what i said lol
dim garnet
Yea thats correct
False reasoning tho xd
cedar juniper
Yup
hot needle
yeah i got it thanksssssssssssss
cedar juniper
One more thing
hot needle
so it's integral of ln(x)?
yeah idk why i said that
i mean i get it but idk how to say it
hot needle
One more thing
?
hot needle
why so
cedar juniper
Cause its usually lenghty
dim garnet
I mean you can use by parts here I think
cerulean grove
If f(x)<a for all x then lim f(x)<a ?
lone heartBOT
If f(x)<a for all x then lim f(x)<a ?
fickle heath
"lim f(x)" doesn't mean much, you need to specify the limit point
If you include lim_{x -> inf} f(x), then no
cerulean grove
"lim f(x)" doesn't mean much, you need to specify the limit point
0
cerulean grove
If you include lim_{x -> inf} f(x), then no
why?
fickle heath
Well basically it depends what you include in "for all x"
You can't just say "for all x", you need a set
If you mean "for all x in R", then +inf and -inf aren't in R
If your function's domain does not include 0, but for all x =/= 0 (in R) f(x) < a, then the limit at 0 can still equal a
ocean sealBOT
Nel
fickle heath
but arctan(x) < pi/2 for all x in R
cerulean grove
@fickle heath what about at x->0?
fickle heath
-x^3/x < 0 for all x in its domain (R without 0), but the limit at 0 is 0
cerulean grove
-x^3/x ?
fickle heath
Yes
cerulean grove
-x^2 you mean?
fickle heath
-x^2 except not defined at 0
cerulean grove
If f(x)<a for all x then lim f(x)<a ?
so this statement doesn't hold for all x in R? only in a specific domain?
fickle heath
Well you could build a function to disprove it entirely
f(x) = {x=0: -1, -x^2}
(-1 at 0 but -x^2 everywhere else)
This is < 0 everywhere (and the domain is R)
Yet the limit at 0 is still 0
This is a case where the limit does not equal the value at that point (discontinuity)
If you specify that f must be continuous, then I don't think you can build a counterexample
In other words, if f is continuous on R and f(x) < a for all x in R, then for any l in R, lim{x -> l} f(x) < a, simply because lim{x -> l} f(x) = f(x)
Note that l cannot be +inf or -inf here
However you can easily build a non-continuous function for which that isn't true
cerulean grove
Yet the limit at 0 is still 0
Since it's a constant or?
fickle heath
?
The limit of -x^2 at 0 is 0
Yeah
Limits care about neighborhoods
which is why you can have a limit at a point where the function is not even defined
cerulean grove
Why is it 0?
fickle heath
I don't know where you got that from
fickle heath
This is the definition of the derivative
It uses a limit, it isn't the definition of the limit...
cerulean grove
Lmao sorryyyy my brain is rusty today
cerulean grove
so this statement doesn't hold for all x in R? only in a specific domain?
So this statement hold only for continuous f on R?
cerulean grove
In other words, if f is continuous on R and f(x) < a for all x in R, then for an...
Aah yea you said here
Got it now, tysm
.close
lone heartBOT
icy jewel
wait so is this channel open or not
alpine sable
no
icy jewel
ok
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alpine sable
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alpine sable
i don't understand how like
|a| - |x| <= |a-x| = |a-x| < |a|/2
|a| - |a|/2 <= |x|
i don't understand how there is = ?
isn't |a|/2 came to left from < |a|/2
lavish cave
this makes sense if you know the concept of absolute value as a distance
so |x - a| < |a|/2 means that x is less than |a|/2 away from a
alpine sable
yes
lavish cave
exactly |a|/2 away from a will be
alpine sable
know about that
lavish cave
$|a| - |a|/2$ or $|a| + |a|/2$
ocean sealBOT
south's secret twin brother
alpine sable
btw this technique gets used all the time
i should understand it good than
lavish cave
yeah just keep practicing
alpine sable
yeah just keep practicing
wait so
x <= y < c does that implies x<=c
lavish cave
wait so
x <= y < c does that implies x<=c
yes, you can chain inequalities which are in the same direction
alpine sable
yes, you can chain inequalities which are in the same direction
this is CRAZY i never did this in lower courses
😭
lavish cave
actually that implies x < c
alpine sable
💀
lavish cave
say 3 <= 3 < 3.1
alpine sable
oh
lmao
|a| - |x| <= |a-x| = |a-x| < |a|/2
im still not getting how
|a| - |x| <= |a|/2
isn't the inequality should be
just <
alpine sable
say 3 <= 3 < 3.1
like as this
how there is that =
even if u take the upper bound of |a-x| thats just gonna remove the equality sign from the inequality
|a| - |x| <= |a-x|
|a-x| < |a|/2
|a|-|x| < |a|/2
lavish cave
oh that's the reverse triangle inequality in action
lavish cave
the normal triangle inequality has <= (= is for a degenerate triangle)
so the reverse also must have <=
or >=
alpine sable
no no
i meant
now if u know the maximum value of |a-x| which is |a|/2 and u replace |a-x| with it in this case >= should become
just >
earnest chasm
guys I'm stuck on this one exercise, it says that function f is defined on R except Pi, and i need to prove that it's extendable by continuity to Pi, and the fact that it's a function with trigonometric functions makes it even worse, can I get some help with it?
alpine sable
show the problem
earnest chasm
f\left(x\right)=\frac{x\sin\left(x\right)-\cos\left(\frac{x}{2}\right)}{x-\pi}
dusk depot
put $ around it
$f\left(x\right)=\frac{x\sin\left(x\right)-\cos\left(\frac{x}{2}\right)}{x-\pi}$
ocean sealBOT
Merosity
earnest chasm
yeah that one
so pls can I get some help defining the limit on Pi
if u do it in a direct manner, it turns out as undefined value (obv)
sterile trench
L' Hospital allowed?
earnest chasm
L' Hospital allowed?
just show whatever u got mate I'm so desperate
it looks ez but made me suffer
and yes l'hopital allowed
earnest chasm
since its 0/0 form
obviously it was, but idk how to apply LH
dire cloak
wsg guys wats the Q
sterile trench
and differentiate denominator
earnest chasm
LH = L Hospital
yeah man I got what u mean but it's still confusing
earnest chasm
and differentiate denominator
I've been trying for 2 hrs...
splitting the limit, conjugue, denominator changing, value changing, trigo properties
nothing worked
dusk depot
I've been trying for 2 hrs...
show what you get when you differentiate the numerator and denominator
earnest chasm
$lim\ \frac{x\ \sin\left(x\right)}{x-\pi}-\frac{\cos\left(\frac{x}{2}\right)}{x-\pi}$
ocean sealBOT
YassTheLion
earnest chasm
I tried splitting it as I said
but still can't see any obvious property to simplify the function
dusk depot
don't split them, just take the derivative of the numerator and denominator
sterile trench
he meant show your work where you tried to use LH
earnest chasm
so as we said we'll take x-Pi as f(x) and the numerator as g(x)
and we'll take the g'(x) and f'(x) and calc their division
right?
but I'm not sure if we got the right to use the Derivative of the COS and SIN functions...
earnest chasm
are u allowed to use equivalent ?
yes the equivalence is allowed
earnest chasm
and do u know the answer ?
nope
alpine sable
i get (1-2 pi)/2 but not sure tho
earnest chasm
it says "define the continuity extension in Pi"
earnest chasm
i get (1-2 pi)/2 but not sure tho
IMMA TRY AGAIN OMG OMG
alpine sable
?
alpine sable
i did h= x-pi
earnest chasm
okay value changed
alpine sable
and used formula to make appear sin(h/2)
and with the equivalence of sin, the h simplify
sterile trench
i am getting 1/2-pi
earnest chasm
formula being 1-cos(x) divided by x?
alpine sable
but i need to verify i did fast
alpine sable
formula being 1-cos(x) divided by x?
no just sin(a+b)
cos(a+b) and sin(2x)
im checking ill be slower
earnest chasm
no just sin(a+b)
wait wait so u didn't use the LH?
alpine sable
no
earnest chasm
wait I changed the value to h but still didn't see a way to apply the formula of sin(a+b) as sin(h+Pi)
alpine sable
imma send a pic
earnest chasm
thanks so much man
alpine sable
sin(h+pi) = -sin(h)
earnest chasm
and how exactly did u manage to make the sin(h/2) appear?
wait so we take sin(h)/h=1 and we're left with the other stuff?
ocean sealBOT
alpine sable
do u agree @earnest chasm ?
earnest chasm
do u agree <@1276507592037761068> ?
I hope u just be blessed and thanks u once more
thank*
alpine sable
np ive had the same experience ik how it is
earnest chasm
will it be the same even after using LH?
alpine sable
idk i never used lh
earnest chasm
np ive had the same experience ik how it is
how old are u btw cuz u damn smart fr
alpine sable
how old are u btw cuz u damn smart fr
i was lucky bc i didnt plan the thing to cancel out
im 19
earnest chasm
im 19
HOLY CRAP U HAVE THE BRAIN OF A 40 YO UNIVERSITY TEACHER
so I'm yass and I'm 17, it was very nice meeting u brother
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dire cloak
whats the Q
craggy idol
, \frac {p} {k}
bruh how we write it
How do we prove ((k-1)! / (k - 1 + p )! ) - ((k)!/(k+p)!) = p*((k-1)!(k+p)!)
idk how to put it in latex
ocean sealBOT
Kookiemon
waxen flame
Also --> #latex-help .
craggy idol
Also --> <#840667252793802752> .
alr thanks
ocean sealBOT
Alozens
craggy idol
so i need to prove this
and I don't know how to do that
One of my classmate recommendd me to use binomial coefficient but I still don't get it
tight marten
so i need to prove this
ok well first step is to make a common denominator
tight marten
why k-1
tight marten
what is (n+1)! in terms of n!
or perhaps phrased better can you think of a relation between these two things
craggy idol
is it (n+1)n!
tight marten
yes
craggy idol
we learned that in class yea
tight marten
so what is (k+p)! in terms of (k+p-1)!
craggy idol
hmm
tight marten
what is (n+1)! in terms of n!
use this
craggy idol
then i assume it's (n-1)n!
craggy idol
so would it be (n-1)! = n!/n ?
tight marten
yes !
craggy idol
i see
tight marten
so would it be (n-1)! = n!/n ?
which is just this rearranged
craggy idol
yes
tight marten
ok so far ?
craggy idol
yeah
craggy idol
so then we have (k+p-1)! = (k+p)! / (n + p)
therefore (k +p)! = (n + p)* (k +p-1)! ?
tight marten
if by n you mean k yes
craggy idol
well i thought k would then become n because it's product from k to n
we remove biggest value
tight marten
perfect
tight marten
**Alozens**
now can you use that to make a common denominator in this
craggy idol
so then we get $\frac{(k-1)!} { (k - 1 + p )! }$ - $\frac { (k)!} {(k+p)(k+p-1)! }$ = p* $\frac {(k-1)!} {(k+p)(k+p-1)! }$
ocean sealBOT
Alozens
tight marten
its going to be easier to focus on the first fraction
getting its denominator to be (k+p)!
craggy idol
yes that's true
so then we get $\frac{(k+p)!(k-1)!} { (k + p )! }$ - $\frac { (k)!} {(k+p)! }$
ocean sealBOT
Alozens
tight marten
not quite
craggy idol
oh yeah there no factorial
tight marten
yep
craggy idol
so then we get $\frac{(k+p)(k-1)!} { (k + p )! }$ - $\frac { (k)!} {(k+p)! }$
ocean sealBOT
Alozens
craggy idol
yes
tight marten
also you dont need the brackets around k, you can just write k!
its not wrong just not needed
ocean sealBOT
Alozens
craggy idol
so then we get this right
tight marten
drop that factorial on the top and yep !
tight marten
no you cant do that
craggy idol
yea
tight marten
i just mean (k+p) on the top instead of (k+p)!
tight marten
**Alozens**
like here
craggy idol
i just mean (k+p) on the top instead of (k+p)!
$\frac{(k+p)(k-1)! - k!} { (k + p )! }$
ocean sealBOT
Alozens
craggy idol
so this ?
craggy idol
nice
tight marten
k! = ?? in terms of (k-1)!
craggy idol
so (k-1)! = k! / k
Therefore k! = k(k-1)!
craggy idol
$\frac{(k+p)(k-1)! - k(k-1)!} { (k + p )! }$
ocean sealBOT
Alozens
tight marten
yep
craggy idol
oooh i think i see now
tight marten
yes
ocean sealBOT
Alozens
craggy idol
we end up with this
tight marten
\begin{align*}
\frac{(k-1)!}{(k+p-1)!} - \frac{k!}{(k+p)!} &= \frac{(k-1)!}{(k+p-1)!} \cdot \frac{k+p}{k+p} - \frac{k!}{(k+p)!} \
&= \frac{(k+p)(k-1)!}{(k+p)(k+p-1)!} - \frac{k!}{(k+p)!} \
&= \frac{(k+p)(k-1)!}{(k+p)!} - \frac{k!}{(k+p)!} \
&= \frac{(k+p)(k-1)! - k!}{(k+p)!} \
&= \frac{(k+p)(k-1)! - k(k-1)!}{(k+p)!} \
&= \frac{(k+p-k)(k-1)!}{(k+p)!} \
&= p \cdot \frac{(k-1)!}{(k+p)!}
\end{align*}
ocean sealBOT
Acman
tight marten
thats how id lay it out fyi
tight marten
nothing new there ! just what we did
craggy idol
yes
craggy idol
we got another question after that but i'll try working on it on my own before asking for help ^^
so everything's good for now
thanks
tight marten
cool good luck
craggy idol
.close
lone heartBOT
alpine sable
lone heartBOT
alpine sable
I'm a bit confused on which part i made a mistake in
cerulean zealot
is answer wrong?
earnest vigil
lone heartBOT
earnest vigil
not sure how to do this question
lone heartBOT
@earnest vigil Has your question been resolved?
earnest vigil
<@&286206848099549185>
earnest vigil
<@&286206848099549185>
earnest vigil
<@&286206848099549185>
earnest vigil
<@&286206848099549185>
earnest vigil
my bad, i thought it was every 15 minutes
earnest vigil
<@923026265005518860> similar triangles
how would u get that equation though, because ik that the stuff inside the root is the formula u use to find a side using cos and 2 sides, but im not sure how ur meant to get the fraction
torpid dirge
my bad, i thought it was every 15 minutes
its just once after 15 min. i dont believe it helps much because not many people have the role too.
u should be able to find the blue and yellow parts from the stuff u know
from there u should be able to form an equation for OP
but i believe it should be long. good luck
lone heartBOT
torpid dirge
npnp
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young light
how would you multiply a sqaure root variable with a whole number? like sqrt(x) * 3
charred jewel
how would you multiply a sqaure root variable with a whole number? like sqrt(x) ...
just do it?
young light
would it just be square root 3x?
lone heartBOT
lone heartBOT
Available help channel!
hasty saddle
lone heartBOT
hasty saddle
I calculate it and i get 0
But after drawing the function, I noticed that the end comes to 2/3, this is weird
lone heartBOT
Show your work, and if possible, explain where you are stuck.
@hasty saddle Has your question been resolved?
lone heartBOT
Available help channel!
drifting seal
Quick question:
Is there any general method to find the formula of a series?
alpine sable
what's the "formula of a series"?
subtle birch
Quick question:
Is there any general method to find the formula of a series?
no general method
drifting seal
oh...
subtle birch
however, you can be limited to a certain type of series
are you asking this question from curiosity or are you learning about them
beneficial to give more context
drifting seal
are you asking this question from curiosity or are you learning about them
From curiosity
I want to learn more about how to turn a series into a formula
drifting seal
into analytic continuation or maybe that's another story, lol
subtle birch
for example cosx is 1-x^2/2!+x^4/4!....
drifting seal
how about some polynomials?
drifting seal
for example cosx is 1-x^2/2!+x^4/4!....
but we cannot turn this series into some 'general form'...
subtle birch
how about some polynomials?
like?
drifting seal
E.g. 1 + x + x^2 + x ^3 + ... = 1 / (1-x)
Like this
subtle birch
but we cannot turn this series into some 'general form'...
how would you define general form
subtle birch
Like this
so basically, a polynomial series converted into a quotient of polynomials ?
drifting seal
ye
subtle birch
'series' = 'a single term'
well cosx is a single term
anyways
you can try to evaluate the following
x+2x^2+3x^3+4x^4...
subtle birch
E.g. 1 + x + x^2 + x ^3 + ... = 1 / (1-x)
these are basically a modded version of this exact series
I reckon you are interested in these so called AGPs
arithmetico geometric progression
drifting seal
oh
subtle birch
the general idea for such series is to multiply the sum by the common ratio and then subtract it from the original series term by term excluding the first term of the original series. so a1-A2, a2-A3 and so on where a_i represents the original series and A_i represents the new series
subtle birch
arithmetico geometric progression
honestly this is hard to explain in theory
drifting seal
the general idea for such series is to multiply the sum by the common ratio and ...
ah ok
subtle birch
I'd suggest watch some videos on it
subtle birch
arithmetico geometric progression
search this up on youtube
lone heartBOT
lone heartBOT
Available help channel!
spring dawn
I need help in simplifying this log
lone heartBOT
I need help in simplifying this log
crystal garnet
guys
i need help i have an exam tmrw
i need someone to 1 by 1 with me with all my questions
pls
lone heartBOT
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).
manic wyvern
I need help in simplifying this log
can you send the options too?
mossy jasper
I need help in simplifying this log
Do you know your log rules?
spring dawn
Do you know your log rules?
I forgor 😭😭😭😭
mossy jasper
log_a(b^c) = clog_a(b)
mossy jasper
Yep
mossy jasper
np
lone heartBOT
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pliant estuary
proof, that if m < n and matrix A has a full rank, the system of equations has infinitely many solutions
pliant estuary
so I know, that rank A = min{m,n}, m<n -> Rank A = m and Rng A = R^m
but the next step states, that it has infinitely many solutions, because A has a non-trivial space, can somebody please tell me, how to know if the space is non-trivial?
i have like the intuition in my head, if you have more variables than equations (m<n), than you will have infinitely many soultions, just dont know how to say it formally
lone heartBOT
@pliant estuary Has your question been resolved?
sinful flame
Hello , I need help in linear algebra, particularly in the jacob canonical form
sinful flame
oki
I have this
first of all, we know that the eigenvalue is -3 with multiplicity 4.
Now we are looking for the eigenvectors so we compute (A - lambda I)v=0.
I found only 1 eigenvector, that is v = (1 ; 1 ; 1 ; 1).
so we are looking for 3 power vectors such as (A - lambda I) w = v.
I found 2 power vectors : w1 = (2 3 0 1) and w2 = (0 0 1 0).
we are looking for a last power vector. We compute (A - lambda I) y = w1. But now there is a probleme because we have the matrix
(1 0 0 -1
-1 1 0 0
-1 1 0 0
3 -1 0 -2)
and we get the system
y1 - y4 = 2
-y1 + y2 = 3
-y1 + y2 = 0
3y1 - y 2 -2 y4 = 1
it's incoherent for row 2 and row 3.
So how can we find the Jordan canonical form for this matrix ??
pallid scarab
you might need to use a combination of w1 and w2 to find a last power vector, as now you found from which rows an incoherent system may arise
sinful flame
oh ok ! how can I write my system with a combination of w1 and w2 ?
pallid scarab
since you already know w1 and w2 satisfy (A - lambda I) w = v
any combination aw1 + (1-a)w2 will also satisfy that
now time to find an appropriate value of a such that (A - lambda I) y = aw1 + (1-a)w2 is not incoherent
sinful flame
why aw1 + (1-a)w2 ? 🤔
pallid scarab
why aw1 + (1-a)w2 ? 🤔
oh, it's just that you're gonna look at combinations of w1 and w2 that also satisfy (A - lambda I) w = v
so w = aw1 + bw2
but if you want the left hand side to equal v
you need b = 1-a
pallid scarab
try out this method for now
we can get more into the specific of why it works afterwards
lone heartBOT
@sinful flame Has your question been resolved?
sinful flame
not yet
lone heartBOT
@sinful flame Has your question been resolved?
iron shale
lone heartBOT
cedar juniper
Which one?
mystic swallow
we don't speak whatever langugage that is. provide a translation and explain where you are stuck and why.
lone heartBOT
@iron shale Has your question been resolved?
obsidian ember
heyy
obsidian ember
$\lim_{x \to a} \frac{x^2 - (a - 1)x + a}{x^2 - a^2}$
ocean sealBOT
Vicho
obsidian ember
there
me and my friends all got different results
idk which one is right
i wrote the numerator as (x-a)(x+1) + 2a and the denominator as (x+a)(x-a)
(x-a) cancels out leaving me with
$$\frac{(x+1) + 2a}{x+a}$$
ocean sealBOT
Vicho
jagged cobalt
thats not how that works
obsidian ember
why not?
jagged cobalt
if you sub in a
you get (a^2-a^2+a+a)/(a^2-a^2)=2a/0
provided a is non zero, what would that mean
obsidian ember
i have to fsctorize it in some way?
obsidian ember
the function is not continuous at that point?
jagged cobalt
uh, sure, that would be the case no matter what a is
lone heartBOT
jagged cobalt
(doesnt exist)
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Available help channel!
lilac jolt
identify the quadrant where theta can be found, and find the exact value of the specified trig functions
a.) cos theta = 2/5 and sin theta < 0, tan theta = ?
lilac jolt
what i did was
a.) focused on the sign, since (cos,sin) is (x,y), therefore (+ , -) is in quadrant IV.
b.) used sin²x + cos²x = 1 and sub cos(2/5), and then finding sinx we get -sqrt(21)/5
c.) sub sin and cos in tan = sin/cos, we get -sqrt(21)/2
is this correct
silk lintel
what i did was
a.) focused on the sign, since (cos,sin) is (x,y), therefore (+ ...
yes
lilac jolt
yes
ok but how would i do it with:
cotx = 3 and cosx > 0, sinx = ?
same process?
im trying and i cant get it
lilac jolt
cosx/sinx
lilac jolt
yes
silk lintel
so
lilac jolt
but how is 1/tanx more helpful here
silk lintel
we have 1/tanx = 3, which is also the same as tanx = 1/3 yeah?
silk lintel
but how is 1/tanx more helpful here
youll see
silk lintel
what i did was
a.) focused on the sign, since (cos,sin) is (x,y), therefore (+ ...
personally i have a diff method on solving this which i personally find it easier to do
silk lintel
oh
we know now that tanx is postive and the qn tells us cosx is postive too, thus it must be in the first quadrant
lilac jolt
qn?
silk lintel
yes
lilac jolt
whats qn
silk lintel
um
silk lintel
cotx = 3 and cosx > 0, sinx = ?
this....?
lilac jolt
oh u meant question, sorry
silk lintel
its okay nws!
silk lintel
we know now that tanx is postive and the qn tells us cosx is postive too, thus i...
does this make sense so far
lilac jolt
if the cosx in tanx is positive, then the sinx must also be positive is what i got from your statement
am i correct?
silk lintel
if the cosx in tanx is positive, then the sinx must also be positive is what i g...
yuhhhh
silk lintel
am i correct?
yuh
silk lintel
from here im going to approach it in a way u may or may not have done before but ill try to explain it
do yk how like tanx = opposite/adjacent, with a right angle triangle
lilac jolt
soh cah toa yes
silk lintel
yeah!
hold up let me draw smt
you could use pythagorus to find the length of the hypotenuse
in this case hyp = root( 3^2 + 1^2) = root10
so you can say to find sinx, sinx= opp/hyp = 1/root10
silk lintel
if the cosx in tanx is positive, then the sinx must also be positive is what i g...
and itll be postive 1/root10 from this
and thats how i would solve qns like these
does it kinda make sense?
silk lintel
yuh
lilac jolt
but the radical on the denominator
i just multiply both top and bottom by root10 right
silk lintel
sure
lilac jolt
so i get
lilac jolt
thats just 10?
silk lintel
mhmm
lilac jolt
oh, so just root10/10 then
silk lintel
mhmm
silk lintel
i got the question wrong
like u typed it wrong?
silk lintel
but i get the idea now
yayyy thats great
lilac jolt
cotx = 3 and cosx < 0, sinx = ?
cos is negative
ill try answering it on my own, wait a min
silk lintel
okay!
lilac jolt
nvm i cant
i have an answer key and it is quadrant 3
how so?
i found that sinx is still the same as earlier
am i wrong
silk lintel
i have an answer key and it is quadrant 3
if its in quadrant 3, what is the signs for sin
silk lintel
mhmmm
lilac jolt
so how would i know
silk lintel
but i wouldnt know it was quadrant 3 if not for the answer key
how come?
hmmm
have u heard of the rule
ASTC
or all stations to central
lilac jolt
nope
silk lintel
um
lilac jolt
pls explain
lilac jolt
yh
silk lintel
lemme draw hold up
these r the 4 quads yeah?
the first quad is the top right and then u go in like a C shape to get to the last quad
lilac jolt
yhhh
silk lintel
ASTC
this rule essentially stands for, all sin tan cos, where it follows the same order of the quadrants, so like the first quad ALL is positive, second quad ONLY SIN is positive, third quad ONLY TAN is positive, fourth quad ONLY COS is positive
lilac jolt
ohh
silk lintel
so that means eg, the seocnd quad ONLY SIN is POSTIVE, so the other 2, cos and tan has to be negative
and vice versa
so in this qn, we first know tan is postive, thus it could be in EITHER FIRST or THIRD, since those 2 quadrants will allow tan to be postive
but next we find out cos is negative, which eliminates the option of the first quadrant
so it MUST be in the THIRD quadrant
so since its in the third quad, if we want to find sin in it, it will be negative