Take the limit as x approaches -infinity
#help-38
long basin
oblique meadow
please may you explain what you mean. im not sure
long basin
$\limit{3 + 4e^{0.5x}}{x}{- \infty}$
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Umbraleviathan
long basin
Well e^(-infinity) = 1/e^(infinity) = 1/infinity = 0
So it becomes 3 + 4(0)
Which equals 3
oblique meadow
1/5
long basin
1/5 or 1/67
long basin
As the denominator gets real big, that 1 ends up being nothing in comparison
oblique meadow
Also, is it the same as saying "how many infinities go into 1? 0"
long basin
No
long basin
Infinity is more of a concept number
It's not a real number
It has properties to it
oblique meadow
ok
thanks
also why is e so special
something to do with growth but i dont get it
long basin
Tbh, not real sure. It just kinda governs growth and probability
The real special thing about it is that the slope of e^x is itself
oblique meadow
yeah
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oblique meadow
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steep yacht
because you only measure out so many decimal places.
saying the area is infinite is kinda like saying pi = infinity, since as you solve for new decimals the number gets bigger, and there are an infinite number of decimals. However, you can be certain that pi < 4, so its uncountable infinity as opposed to countable infinity, which I think you were confused with.
oblique meadow
so does y=e^x cross the x axis
oblique meadow
so how is the area not infinite
steep yacht
thats the difference between countable and uncountable infinity.
as you move farther to the left on the graph, you get diminishing returns in area to the point where you can calculate out the total area close enough to the answer to be correct.
in practice, the area is technically infinite.
But for the purpose of your calculations, only calculate it out to a max of 4 decimal places unless otherwise instructed.
The area given is 2.718...
but it could be 2.718483058304830385038403903029204390859216508761340856
but at that point all those decimals only make your job harder, so avoid them.
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dull mountain
thats the difference between countable and uncountable infinity.
No, this isn’t what’s happening here.
What we’re really looking at is the difference between infinitely large and infinitely precise
The number e is not infinite because there are finite numbers bigger than it, for example 3. It’s true that the area keeps growing the further we go out, but the amount it grows by shrinks so much that we remain underneath an upper bound
steep yacht
What we’re really looking at is the difference between infinitely *large* and in...
That... is the difference.
dull mountain
Nope, countable and uncountable infinities have to do with cardinality
A countable set is one whose elements can be paired with natural numbers in a one-to-one fashion
And an uncountable set is one with more elements than natural numbers
But this doesn’t have much to do with limits or area under a curve
Maybe the terminology means something else in another part of the world but it’s pretty standardized afaik
lean lodge
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lean lodge
How would i find the steady state temperature in the box
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thorny adder
Help me!
thorny adder
<@&286206848099549185>
solar sequoia
<@&286206848099549185>
yes?
solar sequoia
are you trying to solve a system of equations?
thorny adder
Thank you so much!!
thorny adder
Thank you sooo much @solar sequoia
solid kilnBOT
tribal fractal
i need help. no idea where to start
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stable drift
prime shoal
$f(x,y,z)=2y^2-3z$
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$f(x,y,z)=2y^2-3z$
solid kilnBOT
Senoune
frosty sleet
hi
prime shoal
I wanna know what would be thought process towards graphing this function
quartz yoke
fix each variable and graph
of course if its a multivariable function I recommend just plugging it into wolfie
prime shoal
yeah it's a multivariable function but it's an exercise in the book where it's asking to draw this
quartz yoke
without a calc?
prime shoal
ya
quartz yoke
sure yeah
light crystal
Set x = f(x, y, z). I think the best you could do now is see what the graph looks like on selected x planes, e.g., x = 0, x = 1, etc.
solid kilnBOT
light crystal
On each plane x = k, for some k, you get a parabola and they're all connected.
I'll make you a better plot.
light crystal
light crystal
One with the mesh too.
This is the surface x = 2y^2 - 3z. For x = 0, z = 2/3y^2, so it would seem as though the parabolas should be arcing the other way doesn't it.
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prime shoal
yeah quite weird
snow bone
Let $K$ be a field and $A \in K^{n\times n}b$, where $A\neq 0$. Prove or disprove:
rank(A) = 1 is true iff vectors $x, y \in K^n$ exist, so that $xy^T = A$ is true.
solid kilnBOT
Levens
snow bone
What dimension would xy^T have in the first place?
digital bison
nxn
digital bison
do a few examples, see if you can figure that out
digital bison
Think about what it means to be rank 1 matrix and what it means to multiply xy^t
if rank(A) = 1, then A is just multiples of the first row.
How do you multiply xy^t, you'd just multiply each entry of x times the whol vector of y to get a row in A.
for example
$\begin{bmatrix} 1 & 2\ 2 & 4\end{bmatrix}$ is a rank 1 matrix.
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Zybikron
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digital bison
,w {{a},{b},{c}}{{x, y, z}}
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snow bone
so then it should be true right?
since that would mean all columns are linear dependent on one other column
which basically means it has the rank of 1
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snow bone
<@&286206848099549185>
wraith hinge
<@&286206848099549185>
whats the question
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strong horizon
For context, this is the problem:
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For context, this is the problem:
strong horizon
I'm being asked: What is Terry’s opportunity cost of risotto (in terms of pie)? What is Terry’s opportunity cost of pie
(in terms of risotto)?
This is my answer, but I'm unsure if my thought process is correct: "Terry's opportunity cost of producing one unit of risotto is 2 units of pie, as his PPF is given by P = 4 - 2R. This means that for every unit of risotto he produces, he must give up 2 units of pie production.
Terry's opportunity cost of producing one unit of pie is 1/2 unit of risotto, since the equation of his PPF can be rearranged to R = 4/2 - P/2. This means that for every unit of pie he produces, he must give up 1/2 unit of risotto production."
Can anyone let me know if I'm correct?
<@&286206848099549185>
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strong horizon
<@&286206848099549185>
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gritty zodiac
Can I get some guidance on the last step?
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Can I get some guidance on the last step?
inland orbit
Now that you've simplified all the ugly stuff, you can evaluate the limit
Just allow h to approach 0
zinc wagon
more of a physics thing but i am confused about the math so i am asking here, i just wanna confirm that the velocity v = -v_max.sin(wt) here comes from differentiating the component/tangent that is made in the direction equaling Acos(wt) right?
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more of a physics thing but i am confused about the math so i am asking here, i ...
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quaint lynx
part B i understand
but idk how to get OC
guys is this solvable
i made the question
pls anyone help
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north mirage
you...made the question?
why would you not know how to solve a question you made
for a hint, let OC = x + iy, and notice CB is parallel to OA
quaint lynx
what do u mean
quaint lynx
yes
north mirage
so let point C be x + iy
sorry, i wrote the one before wrongly
and the idea is to find x and y
quaint lynx
yep
north mirage
you have to use B somehow
and so we notice OCB is a triangle
so what is OB, as a vector, equal to?
quaint lynx
AC ?
quaint lynx
3+8i
north mirage
i want to represent OB as OC plus some other vector
tell me what that vector is, in terms of the letters of the diagram
quaint lynx
OB = OC + CB
north mirage
right
and now we know OC, but we have no idea what CB is
luckily, we know that, as a vector, CB = OA
because they have the same length and are parallel
quaint lynx
yep agreed
north mirage
so now the question is what is OA
and to find OA we can notice that OA is precisely a 90 degree rotation of OC
can you fill in the rest?
quaint lynx
so OA = i x OC ?
north mirage
the rotation is backwards, so i think it's -i, no?
quaint lynx
i thought multiplying by i is anticlockwise
north mirage
sure, but you have OC: x + iy, and you want to get OA, which is 90 degrees clockwise from OC
north mirage
then this is where you tell me what you get and what you think you should be doing
north mirage
sure, it'll just be in terms of x and y
north mirage
and that's fine, because we still need to look back at what we did to find x and y
quaint lynx
rip need to change the questipn
waht one value would make OC solvable
in terms of integers
quaint lynx
But i need to create a question
quaint lynx
that will work for part b
north mirage
then good luck lol
lucid raven
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lucid raven
At point P, the orbital arms of the Earth and comet intersect Find the component of the comet's velocity that is tangent to the Earth's orbit at that point Hint: Consider the comet's angular momentum
Does anyone have an approach for me?
north mirage
sounds like physics #old-network
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short star
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short star
This is a T/F question
The contrapositive of this statement is: If $(a_n)$ is bounded, then there exist $M$ for all $N$ such that if $n \ge M$, then $|a_n| \le N$
short star
But that just seems like a stronger statement for this
subtle lava
but yes thats right
short star
oh yeah, ty
solid kilnBOT
KN
subtle lava
the dependence on N is the difference, you can use that definition to show it's unbound for $n\in (N, \infty)$
solid kilnBOT
Max..
short star
not sure
solid kilnBOT
Max..
short star
yeah, so the contrapositive part matches with the definition for bounded. But that is just when n > N, right?
and they should be logically equivalent
so the problem is when n < N
Is that wrong?
Or maybe if I just negate the definition for bounded
Ok. I think I have some idea
Ty
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normal marten
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https://giphy.com/gifs/theoffice-xXbwgiIjYaZJC86YCk
mellow hull
Ehh
slow swallow
https://giphy.com/gifs/theoffice-xXbwgiIjYaZJC86YCk
please close the channel if you don't need help in math
tepid rock
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reef walrus
help
reef walrus
EN; 1. Cn is the sum of the squares of the first n non-zero natural numbers, where n belongs to N*.
C4 = 1² + 2² + 3² + 4² = 1 + 4 + 9 + 16 = 30.
Define the sequence (Cn) by recurrence.
- Un = n(n+1)(2n+1)/6
A. Calculate U1
B. Express Un+1 as a function of n.
C. Deduce that Un+1 - Un = (n+1)².
D. What can be said about the sequences (Cn) and (Un)?
FR; 1. On note Cn la somme des carrés des n premiers nombres entiers naturels non nuls, où n appartient à N*.
C4 = 1² + 2² + 3² + 4² = 1 + 4 + 9 + 16 = 30.
Définir la suite (Cn) par récurrence.
- Un = n(n+1)(2n+1)/6
A. Calculer U1
B. Exprimer Un+1 en fonction de n.
C. En déduire que Un+1 - Un = (n+1)².
D. Que peut on dire sur les suites (Cn) et (Un) ?
FR;
-
La définition de la suite (Cn) par récurrence est: Cn = Cn-1 + n², avec C1 = 1.
-
A. U1 = 1 * 2 * 3 / 6 = 1.
-
B. Un+1 = (n+1)(n+2)(2n+3) / 6 = (n+1)^2 (2n+3) / 6 + (n+1)(n+2) / 2.
EN;
-
The definition of the sequence (Cn) by recurrence is: Cn = Cn-1 + n², with C1 = 1.
-
A. U1 = 1 * 2 * 3 / 6 = 1.
-
B. Un+1 = (n+1)(n+2)(2n+3) / 6 = (n+1)^2 (2n+3) / 6 + (n+1)(n+2) / 2.
who can help me for Deduce that Un+1 - Un = (n+1)².
i have issue in the calcul
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sage anvil
To derivate this , do i apply the rule f'(x) * g'(x) =f' (x) * g(x) + f(x) * g'(x)* ?
sour quest
Yes, you have to use the product rule here.
trim lichen
do i apply the rule f'(x) * g'(x) =f'* (x) * g(x) + f(x) * g'(x) ?
this rule is incorrectly written
on multiple counts
but yes, to take the derivative of your function, the natural choice of rule is product
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slim forge
Can someone explain how the top and bottom parts of C turn into what it turns into?
slim forge
<@&286206848099549185>
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lone mauve
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lone mauve
I got two different answers here.. did I not factor the conjugate correctly?
trim lichen
0/0 is not an answer
only an indication that direct substitution does not work as is
lone mauve
But it lead me to 0/0
chilly bobcat
maybe L'Hopital's rule is useful here?
lone mauve
When I kept it as factor it led me to 2
vagrant marsh
why did you foil is step 3
lone mauve
maybe L'Hopital's rule is useful here?
Haven’t learned that yet
vagrant marsh
you couldve done the cancellation already
lone mauve
you couldve done the cancellation already
How so?
vagrant marsh
only foil the bottom line, keep the top line in factor form
lone mauve
only foil the bottom line, keep the top line in factor form
Yeah but my point is when I foil I get 0, when I leave numerator in factored form I get 2
That’s normal? Or weird
vagrant marsh
show
lone mauve
So this sort of stuff happens all the time?
vagrant marsh
try this: lim x-> 4 (x^2-16)/(x-4)
sour token
when you take limit x -> 1, that means x is approaching 1 from either side but NEVER equal to 1
lone mauve
when you take limit x -> 1, that means x is approaching 1 from either side but N...
Yes I know
sour token
So, you can't have 0/0
vagrant marsh
yeah
lone mauve
But then I also get a different answer if I use difference of two squares
vagrant marsh
so when you do some algebra, it will show you the coordinates of the hole
lone mauve
try this: lim x-> 4 (x^2-16)/(x-4)
8 is the answer?
lone mauve
8 is the answer?
That means there is still a hole at x=4
vagrant marsh
dividing by 0 is weird like that
lone mauve
Does it indicate the y coordinate for the hole?
vagrant marsh
That means there is still a hole at x=4
yes, but if you were looking at the function, the hole is incredibly small, that we can use limits to assume its position
vagrant marsh
Does it indicate the y coordinate for the hole?
yup
lone mauve
How would I find the y coordinate for the hole at x=4?
vagrant marsh
the limit
lone mauve
8?
vagrant marsh
yes
vagrant marsh
yup
vagrant marsh
in your original problem, the hole is at (1,2)
lone mauve
in your original problem, the hole is at (1,2)
It is?
vagrant marsh
yes
lone mauve
How did you get(1,2)?
vagrant marsh
lim x->1 (function)=2
vagrant marsh
yes, its a sign you have to do more work
lone mauve
Interesting! Thank you!
vagrant marsh
youre welcome 
lone mauve
@vagrant marsh Have you ever had a problem where the final answer is 0/0?
Just curious
Or it always means you can do more work to solve it
<@&286206848099549185>
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glass basin
how do you solve this
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how do you solve this
solid kilnBOT
monikanicity
dense breach
,w ln(71088884/6)
solid kilnBOT
glass basin
is that the answer? lol
@dense breach its still wrong
also how do you do the one under that>
dense breach
the one under it you just plug in 2 to find p(2) and then plug in p(2) to get f(p(2))
glass basin
okay
arctic fjord
How do u do q4?
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How do u do q4?
vagrant marsh
Draw a trinagle
whole coral
Remember what sec is defined as, then as they said, double angle formula
arctic fjord
Remember what sec is defined as, then as they said, double angle formula
Sec is 1/cos
So 1/cos2x
1/cos²-sin²
1/(cos²-sin²)
Then do i use a calculator?
whole coral
Remember there are three versions of the double angle formula for cos(2x)
arctic fjord
Ohh yea
whole coral
...and we are given sin(x)
whole coral
...well technically you could, but there's no need
arctic fjord
Oh
solid kilnBOT
chartbit
whole coral
...and we are given sin(x)
...
arctic fjord
I am not sure
whole coral
So right now we basically have said that $\sec(2x) = \frac{1}{1 - 2({\color{green} \sin(x)})^{2}}$, and we have that ${\color{green} \sin(x)} = \frac{3}{5}$, right?
whole coral
**chartbit**
Note the careful way I wrote it...
whole coral
...If I said to work out something like 3y^2 - 4 when y = 5, could you do that for me?
solid kilnBOT
chartbit
whole coral
Was my bad for not doing it in the first place, sorry about that!
whole coral
You don't need to find x here
arctic fjord
What are we trying to find
whole coral
**chartbit**
sec(2x), given that sin(x) = 3/5
wraith hinge
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kindred pier
Have you learned law of cosines yet?
vagrant marsh
pythagorean theorem?
wraith hinge
Yes both
kindred pier
you can use either
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frank axle
Hello I need help with a projectile motion question
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Hello I need help with a projectile motion question
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lone mauve
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lone mauve
Are these lines both equal?
zinc ginkgo
the first one is abuse of notation
lone mauve
The first is how Professor Leonard teaches it
random citrus
Are these lines both equal?
By coincidence yes
wraith hinge
There must be some context to it
dry ginkgo
i do
dry ginkgo
oh u just gotta type?
slay
https://screenrec.com/share/zvw2WAICu9 Anyways thats my assignment and I wanna check its right pls
Its trig
and
radians
9someone help pls
stoic iron
maybe you should submit and then you'll find out
dry ginkgo
maybe you should submit and then you'll find out
😭 i cant afford to lose points im already failing
zinc ginkgo
just screenshot and upload
whole coral
😭 i cant afford to lose points im already failing
Are you saying that this is a graded assessment?
dry ginkgo
Are you saying that this is a graded assessment?
Kinda but not really
i get teacher points if i get this right
not like in my actual grade
is that allowed?
whole coral
not like in my actual grade
Oh alright, fair enough, think that should be fine then, carry on!
As long as it's not on your grade then you should be fine I think 
whole coral
what does deg mean
Read the question carefully
dry ginkgo
oh mb
whole coral
Same here
whole coral
is it like 12 something?
Yep, the number you gave is correct, but it should be in terms of a multiple of pi [which you have given it just now!]
whole coral
How are you getting this one?
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@dry ginkgo Has your question been resolved?
dry ginkgo
Yep, the *number* you gave is correct, but it should be in terms of a *multiple*...
OOOH OKIE
whole coral
Seeing we have the channel back, wanna tell me how you got this?
dry ginkgo
Seeing we have the channel back, wanna tell me how you got this?
lemme look for my workk
oh mb
its 24
dry ginkgo
Seeing we have the channel back, wanna tell me how you got this?
is that still wrong?
whole coral
Right for this one you may need to help me a bit, not used to the terminology
[I think the rest have been catReacted to already 
]
What do they mean by "coterminal angles"?
inland orbit
coterminal angles are angles that differ by an integer multiple of a full turn
i.e. their terminal rays are the same
dry ginkgo
This here <:catYes:830588319472812044>
yay
whole coral
coterminal angles are angles that differ by an integer multiple of a full turn
Ah, thank you for that 
in that case...
whole coral
to this one then?
dry ginkgo
yay
dry ginkgo
also can u explain how i could fix this? dont give out the solution but rather what i did wrong?
whole coral
also can u explain how i could fix this? dont give out the solution but rather w...
Again, read the question, what they ask for, and check your calculator
You're technically correct, but you didn't answer the question they asked
tl;dr ||you had your calculator set to radians but the question asks for degrees||
dry ginkgo
tl;dr ||you had your calculator set to radians but the question asks for degrees...
ahh
whole coral
ahh
hence my 
and spelling out deg[rees] as reacts
But other than that, I think you have everything there, right?
dry ginkgo
hence my <:catNo:618077846283485203> and spelling out deg[rees] as reacts
gotcha
dry ginkgo
But other than that, I think you have everything there, right?
yess I have another quizz too tho
whole coral
Cool cool, well feel free to do it and then send the questions here, you'll be alright! 
dry ginkgo
Cool cool, well feel free to do it and then send the questions here, you'll be a...
thank youu
dry ginkgo
ahh
whole coral
[can be written as 12pi, hence my reacts there too!]
dry ginkgo
but thats my answer 37.68
whole coral
Don't worry, if you're around long enough, you'll get used to me!
whole coral
but thats my answer 37.68
Read the question!
dry ginkgo
im sorry bro i'm stupid 😭
whole coral
whole coral
im sorry bro i'm stupid 😭
You aren't just make sure you take things slowly and make sure you check what they ask of you!
You're alright for the most part, most of the ones you didn't get here are because you didn't check the question, not because you didn't know how to do it!
whole coral
See this one was correct but in the wrong units...
whole coral
...this one was correct but not in the form asked, and...
whole coral
...this one was assumedly a small error you made in your working out!
whole coral
``$12\pi \text{ in}$" is fine to write
solid kilnBOT
chartbit
dry ginkgo
okieokie
dry ginkgo
also how do i fix this
again, really sorry for bugging you
oh mb
you told me
degrees
whole coral
There ya go, you have that one
dry ginkgo
this is the other quiz- for the second one idk what 4 is
i hate this kinda division, my other answers wre- and another one
whole coral
this is the other quiz- for the second one idk what 4 is
Domain restrictions is a
whole coral
i hate this kinda division, my other answers wre- and another one
incomplete simplification
dry ginkgo
what does track mean
dry ginkgo
incomplete simplification
both of them?
whole coral
what does track mean
You have the right idea [you're "on the right track" to the answer] but [in this case] you need to keep going
dry ginkgo
i hate this kinda division, my other answers wre- and another one
also for this 2x_2/3x+5?
whole coral
also for this 2x_2/3x+5?
, with the way you've written it, not quite
dry ginkgo
also this one is -2/3x+1 isnt it
is this right?
@whole coral u thereee
sorry if im annoyyinggg
whole coral
<@788085606483361802> u thereee
Hey hey, sorry, tiny bit multitasking!
dry ginkgo
Hey hey, sorry, tiny bit multitasking!
nonono dw bout it im so grateful for your help sis
whole coral
[I'm also going though your questions in the "easiest to hardest" way too lol]
dry ginkgo
[I'm also going though your questions in the "easiest to hardest" way too lol]
hahaha totally understandable
I was just asking cause I need to submit it sooon
my teacher's waiting for me haha
whole coral
Try to substitute the solutions you found back into the original equation, and see how that turns out 
dry ginkgo
you right it's 2 and 1 as extraneous?
whole coral
you right it's 2 and 1 as extraneous?
Yep, dividing by zero, very illegal 👮♀️
Anyways other than one I think I've answered them all for you?
dry ginkgo
Yep, dividing by zero, very illegal 👮♀️
dry ginkgo
what does telephoen cat mean
whole coral
oh wait this one too, give me a sec
whole coral
what does telephoen cat mean
It's just a placeholder to remind myself I've done that for you
dry ginkgo
also this one is -2/3x+1 isnt it
also is it -2/3x+1
dry ginkgo
It's just a placeholder to remind myself I've done that for you
oo okie
dry ginkgo
It's just a placeholder to remind myself I've done that for you
was it right tho
whole coral
,w (x+1)/x + (x^2 + 5x)/(x^2 + 4x - 5)
whole coral
was it right tho
dry ginkgo
Only one is this one here, for which, I'm confused lol
i think x is the number of loaves because that seems like the only thing variable here
whole coral
Actually this isn't total cost but average cost
dry ginkgo
oo u right
whole coral
You want the total cost
dry ginkgo
4+(x-1)?
whole coral
4+(x-1)?
Matter of fact that seems fine to me I think!
[n.b. I cannot be held liable if I've made stupid mistakes or anything lol]
dry ginkgo
also what was the answer to this
dry ginkgo
[n.b. I cannot be held liable if I've made stupid mistakes or anything lol]
never ily
whole coral
also what was the answer to this
Try it out again, I shall say to you
You have the same denoms do just add the numerators
whole coral
i think it was -2/3x+1
it is!
whole coral
also this one is -2/3x+1 isnt it
oh lol you said that here, I'm blind 
Sorry for that 
dry ginkgo
ahh i got this wrong its the 4th option
whole coral
ahh i got this wrong its the 4th option
Yea actually you say that, they're really sneaky for that
I literally wrote down the fourth but didn't notice yours was different, sorry!
I got $\frac{3x+4}{2(x-1)}$ on my paper here
solid kilnBOT
chartbit
whole coral
you're amazing
Awww thank you
dry ginkgo
Yea actually you say that, they're really sneaky for that
ikrrrr
dry ginkgo
I literally wrote down the fourth but didn't notice yours was different, sorry!
dwwwww
atleast i submitted it thank youuu
whole coral
No worries, hope you have a good one! Best of luck with everything!
dry ginkgo
No worries, hope you have a good one! Best of luck with everything! <:catlove:92...
Thank youuu have a wonderful nighttt
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winter bluff
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hushed stirrup
u must integrate
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wraith hinge
Which graph is better
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Which graph is better
night zodiac
,rotate
wraith hinge
How should I do this
solid kilnBOT
wraith hinge
How do I take the area of this
I goofed the second graph
Fixed it
But how can I take the area
Whilst accounting for the y=1 bound
Should I take with respect to x or y
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wraith hinge
<@&286206848099549185>
lone flax
i have no clue how to do this
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i have no clue how to do this
vagrant marsh
is this a test?
quartz yoke
sounds like they want you to differentiate
lone flax
sounds like they want you to differentiate
how would i go about doing tht
haughty oasis
use the fact that the vertex of a parabola is a local min/max
and the derivative at a local min/max is zero (Fermat’s theorem)
lone flax
how do i find the derivative of tanx using product rule
lone flax
.close
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ionic jasper
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inner cradle
Hi, i need help on that Limit
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Hi, i need help on that Limit
inner cradle
I dont know what to do with the factorial x tbh
the exp() way probably doesnt lead to anywhere, but i dont see anything i can do with the lim
sour token
for first divide everywhere by x^x
notice that x! = o(x^x) ie x!/x^x -> as x -> infinity
sour token
yes, just use what I mentioned
inner cradle
yes, but i dont understand what you mentioned
sour token
$\lim_{x \to \infty} \frac{x!}{x^x} = 0$
solid kilnBOT
numbpy
sour token
Seems like this limit diverges
inner cradle
yes, its infinity
sour token
but i would have to prove that to use it
That's not hard, use sterling approximation
or take log both sides then use sterling approximation
rugged latch
how can calculate alpha and beta if i know that the sum = 47 degrees. 4 lb is a force vector, as well as 19 lb, and 21.924 is the resultant, 19 lb vector is on the x-axis
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wraith hinge
Hi
wraith hinge
So its confusing me where cotangens tangens sin and cos have to be
Translation Exercises 1) Draw the 4 trigonometric numbers in one trigonometric circle for an angle E II
main sigil
You are confused why the tangent and cotangent are on the place where they are?
wraith hinge
Ye but i mainly asking where they should be idk if i noted it correct on my papers
wraith hinge
No look each seperate line is named
main sigil
Is this thing tan?
wraith hinge
There is tan cos and sin but also cos B sin B Tan B and Costg B that should be put on each line
wraith hinge
Is this thing tan?
Idk its wrong i think but thats Tan B its either bottom or above the circle where it should be
main sigil
I don't really get how did you conclude that length of that segment is tan but it seems wrong
wraith hinge
It all also depends on this number always give its either 1 2 3 or 4 its where u should make a line
wraith hinge
U see what i circled u see above t thats stand for tangens just a shortening for me
I already said there is tan cos sin and sin B tang B Cos B and Cotangens B
wraith hinge
Between the 2 yellow lines is 1 tang B and where i drew an arrow pointed at t is tan
main sigil
what does tan even mean?
Tan is a function
it's possible to show tan(B) but how do you show tan on the picture
Drawing tan is the same as drawing ². You can graph x² but not just ²
As well as you can graph/visualize tan(B) but not just tan
main sigil
this is tan(B)
I already posted a pic for quadrant I. the length is tan because of the right triangle. Tan(a)=opposite/adjacent=orange/1=orange
This thing you posted is perfect. It shows everything
wraith hinge
I already saw these pic online thats why i came on this server those pics dont show what i need
main sigil
And what do you need?
wraith hinge
B is just a name i can be A or C
main sigil
okay and what do you need to do?
wraith hinge
Between the 2 yellow lines is 1 tang B and where i drew an arrow pointed at t is...
This
wraith hinge
No look each seperate line is named
Knowing where tan B cos B cot B Is
main sigil
what between the 2 yellow lines is 1 tang B
main sigil
wraith hinge
? Ye there are 2 line one of them is NOT IMPORTANT AND WRONG the other is Tan B
B is just a name its can be named Tan Hh
main sigil
? Ye there are 2 line one of them is NOT IMPORTANT AND WRONG the other is Tan B
just reposted the question for helpers
wraith hinge
Oh ok
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short spruce
"Analytically determine" in this question means to calculate this by hand right?
random citrus
Yes
short spruce
.close
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stoic iron
"Thanks Giannis!"
random citrus
"Thanks Giannis!"
_money
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pale lynx
Hello, I would like to know how I can get some sort of "slight" version of a direction vector. Say an object is moving in a direction, i want it to move in that direction, but not directly, kinda like slightly towards it.
scarlet escarp
that doesn't quite make sense
are you saying an object is moving in a direction A, and you want it to slightly deviate to direction B?
pale lynx
No no
the object is moving forward constantly
like, wherever it's facing
but it is supposed to slowly turn in the direction of another object
pale lynx
oh
scarlet escarp
then slowly deviate to the other
pale lynx
i guess
scarlet escarp
there's many different ways to achieve this. can you give more context to what you're looking for?
pale lynx
i have the direction vector of that other object, however i dont known how i can make it not "directly" go to that direction
hard to explain
okay
ill give u an illustration
scarlet escarp
you want it to accelerate in the direction of the other object i imagine
not just change velocity to it's direction
take the current velocity vector and add to it the vector pointing at the second object from the first object
scarlet escarp
this has too many variables i thnk
like the same algorithm could give you both, it just depends on the strength of the acceleration
and the starting velocity of the object
wraith hinge
f:R->R^3 is a curve
scarlet escarp
it seems that what you want is:
given objects A and B, where A is moving with some velocity v
take the directional vector AB, scale it by some factor, and add it to v
wraith hinge
if you want a path its f:[0, 1] -> R^3
pale lynx
sounds about right
pale lynx
if you want a path its f:[0, 1] -> R^3
this uses time, no?
wraith hinge
what time?
scarlet escarp
if you want a path its f:[0, 1] -> R^3
i think this is beyond what they're talking about
deity is this for some kind of computer program
pale lynx
yes, i am trying to achieve this, in 3d space
scarlet escarp
it seems that what you want is:
given objects A and B, where A is moving with so...
then im 99% sure what i said here is what you want
scarlet escarp
just know that it's very much dependent on your starting positions, velocities, and how you scale the acceleration
you might also want to look at some kind of distance-based acceleration
where the scaling factor depends inversely to the distance, or something similar
pale lynx
Theoretically the object is constantly moving forward, slowly tilting it's direction towards the other object
that is what i want to achieve
scarlet escarp
yes, and what i shared should give you that effect. it just depends very heavily on the starting parameters and acceleration scaling
pale lynx
ok
rough linden
Greetings, what did I do wrong?
rough linden
<@&286206848099549185>
final coyote
if you do not say what was asked, how should someone know what is wrong? You are caclulating the height in a triangle. and there are triangles with this height.
rough linden
if you do not say what was asked, how should someone know what is wrong? You are...
Calculate the total surface area of a regular quadrangular pyramid with a base edge of length 18 cm and a side edge of 15 cm. Give your result in square centimeters.
final coyote
4x12x9 instead of 4x12
rough linden
Why x9?
final coyote
what is the area of the triangle?
final coyote
you are asked to calculate the surface of the pyramid.
the surface is the base-quadrat + 4 times the triangle
the base-quadrat you have calculated with 324
rough linden
Let’s skip that
final coyote
now you need the area of the triangle.
rough linden
I have difficulty with this
The figure shows one of the lateral scans of a regular hexagonal pyramid. Calculate the lateral surface area of this solid.
@final coyote
final coyote
I have difficulty with this
you do not know how to calculate the area of a triangle?
then look at this:
final coyote
you have the baseline (18) you have calculated the height (12), so it should be possible to calculate the area of one triangle.
dire charm
Don't ping random users for help.
wraith hinge
is 18*40/2 really 320?
rough linden
1920
final coyote
(remember: hexagonal pyramid)
what are you talking about?
wraith hinge
"The figure shows one of the lateral scans of a regular hexagonal pyramid. Calculate the lateral surface area of this solid."
final coyote
Calculate the total surface area of a regular quadrangular pyramid with a base...
@wraith hinge this.
wraith hinge
Of how many triangles of area 360 does the lateral surface of the hexagonal pyramid consist?
final coyote
Of how many triangles of area 360 does the lateral surface of the hexagonal pyra...
the task was calculating the surface of a quadrangular pyramid. I dont know why youre talking about hexagonal pramid.
wraith hinge
sounds good
final coyote
if 2160 is correct you posted the wrong example. Just waste of my time.
wraith hinge
2160 is indeed the answer to the question posted in #help-38 message
rough linden
360 cm^2 whole triangle area and it’s hexagonal pyramid 6 * 360 cm^2
final coyote
its a very bad style to change the example in a discussion. the original example was #help-38 message
tacit sedge