ruby shore
would my thing be right too..?
#help-36
frigid hawk
technically ur right, but ur answer is too vague
they were probably looking for something like the p-value is greater than the alpha level
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stark apex
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stark apex
how do i solve this after factoring out the x on tpo
onyx peak
how do i solve this after factoring out the x on tpo
Try plugging in x = 2
vital surge
always ask urself if the limit is an indeterminate form
stark apex
I checekd
onyx peak
and what did you get?
onyx peak
if its not 0 / 0 or infinity/infinity, then its just the value you get when you plug in
stark apex
ohh
onyx peak
(assuming its continous which most functions you'll deal with are)
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rapid helm
Can you distribute powers on complex numbers?
final saddleBOT
Can you distribute powers on complex numbers?
rapid helm
For eg is (ω²)^7= (ω)^14?
pure lodge
For eg is (ω²)^7= (ω)^14?
ig it fine if it is an integer
rapid helm
ig it fine if it is an integer
And if it is not?
soft zealotBOT
77²
pure lodge
is it equal to $(i^{4})^{\frac{1}{4}}$?
rapid helm
No
soft zealotBOT
77²
barren hound
in general no, powers don't work like that in complex numbers, but powers are usually multi valued anyway
final saddleBOT
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faint fern
$$ (e^{i \theta + 2\pi n})^a $$
soft zealotBOT
StrangeQuarkAL
faint fern
$$ e^{i a \theta + 2\pi n a} $$
soft zealotBOT
StrangeQuarkAL
haughty quiver
could someone please help me out with this question? i've understood up to pi x 6 x l
final saddleBOT
could someone please help me out with this question? i've understood up to pi x ...
drifting raptor
could someone please help me out with this question? i've understood up to pi x ...
what grade ur in btw?
drifting raptor
curved surface area = slant height x Perimeter of circle
haughty quiver
nah that's crazy 😭
drifting raptor
curved surface area = slant height x Perimeter of circle
try to do it here
haughty quiver
alr
drifting raptor
u know how to count perimeter on circle right?
haughty quiver
yessire
past timber
can someone explain this to me? im so dumb TwT
drifting raptor
350 cm = slant x 37.7
past timber
can someone explain this to me? im so dumb TwT
(√√16)² = ...
drifting raptor
can someone explain this to me? im so dumb TwT
bruh open new question
drifting raptor
can someone explain this to me? im so dumb TwT
past timber
sorry im new
past timber
thank you!
drifting raptor
350 cm = slant x 37.7
here
haughty quiver
350 cm = slant x 37.7
oh did i do the perimeter wrong
drifting raptor
,calc 350 / 37.7
soft zealotBOT
Result:
9.2838196286472
,calc 12 * 3.14
soft zealotBOT
Result:
37.68
ohh
drifting raptor
Result:
```
9.2838196286472
```
here is the slant
the heigh u can use phytagoras
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stiff tendon
hi
stiff tendon
Can anyone send notes for trigonometry jee?
shell mauve
cloud raft
Can anyone send notes for trigonometry jee?
there should be jee servers on discord
ask this question on that
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autumn geode
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@verbal owl Has your question been resolved?
jagged flare
let $a,b,c\in\mathbb{R}^+_{*}$
$$abc(a+b+c)=100$$
find the minimum value of $(a+b)(b+c)$
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let $a,b,c\in\mathbb{R}^+_{*}$
$$abc(a+b+c)=100$$
find the minimum value of $(a+...
soft zealotBOT
Skill_Issue
jagged flare
ac(ab+b^2+bc)=100
(a+b)(b+c)=k=ab+b^2+bc+ac
ac(k+ac)=100
k=100/ac-ac
it would be very nice if i csn just am-gm this but its -ac so :(
scarlet sequoia
well it's not too bad to analyse the function f(x) = x + 100/x
paper oxide
isnt it k - ac in line 3?
tranquil pine
the 3rd line is wrong
jagged flare
isnt it k - ac in line 3?
oh omg
scarlet sequoia
and yeah it's -ac
tranquil pine
should be ac(k-ac)
vital surge
it is 20 yes
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vital surge
🎉
paper oxide
oh yeah btw make sure to prove ac = 100/ac is possible
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jagged flare
how is this A
final saddleBOT
how is this A
jagged flare
is it not 1+12+23+34+45+56+67+78+89+100=505?
vital surge
yeah those answer choices are way too big
jagged flare
wtf so is the question wrong
tranquil pine
there is one answer that is none of the above so
vital surge
wtf so is the question wrong
are there multiple versions of the test? you could try looking at another and seeing if it's written differently
jagged flare
there is one answer that is *none of the above* so
but the answer was A
jagged flare
are there multiple versions of the test? you could try looking at another and se...
ill try to dig trough the internet
vital surge
aight
tranquil pine
@jagged flare
your teacher added an extra "0" after the answer ig
i got 505
which is quite "similar" to 5,050
tranquil pine
which is quite "similar" to 5,050
or perhaps its 505 (sum) x 10 (number of rows/columns） = 5,050
jagged flare
https://seamo.com.br/Paper_E_2020.pdf
unless if you guys can open this somehow, the link is broken for me
vital surge
https://seamo.com.br/Paper_E_2020.pdf
unless if you guys can open this somehow,...
yeah i can open it but it's the same issue
tranquil pine
i can open and see a TCIMO
vital surge
looks like they just wrote it wrong
jagged flare
yeah i can open it but it's the same issue
wtf its stuck on downloading for me >:(
vital surge
your teacher added an extra "0" after the answer ig
this is not for a class
jagged flare
or perhaps its 505 (sum) x 10 (number of rows/columns） = 5,050
but the example wont hold then
vital surge
also they alrd know the answer is 505 (cuz they calculated it on their own)
tranquil pine
this is not for a class
oh
vital surge
they were just making sure the test was wrong
jagged flare
this is not for a class
i mean they had no way of knowing :p
tranquil pine
they were just making sure the test was wrong
ah
jagged flare
<:hmmcat:831508801646755850>
jagged flare
wtf i didnt even see that lmao
vital surge
ket
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tranquil pine
<:hmmcat:831508801646755850>
my eyes are broken
vital surge
fair enough 😭 happens
tranquil pine
true
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foggy warren
Hi, how can i find the domain of sqrt of x -6 (the minus 6 is not in the squar root theres a space between them)
final saddleBOT
Hi, how can i find the domain of sqrt of x -6 (the minus 6 is not in the squar r...
formal trail
,, \sqrt{x} - 6
soft zealotBOT
cloud
jagged flare
do you know the domain of sqrt(x)
pulsar venture
im sorry lol
if udk what that means
plot the graph of root x
and see what x values it can take
domain means
x values
foggy warren
ok
foggy warren
ur gonna kill me but im still not understanding what you mean by defined
foggy warren
im associating it with like vocabulary definitions like a dictionary
pulsar venture
inside the root
foggy warren
no
foggy warren
no negative numbers under a root
foggy warren
correct
pulsar venture
now domain means
ur asking urself
what x values can the function take
so negative nos. are gone
can i put x = 0
inside a root
foggy warren
yea
pulsar venture
and can i put positive nos.
foggy warren
yea
foggy warren
any number thats positive
foggy warren
yup
pulsar venture
thats the domain
pulsar venture
no that doesnt affect the x values
foggy warren
so if my hw is asking "Domain where F
is one-to-one and increasing"
would i put [0, infinity)?
pulsar venture
this function is always increasing
lol
do u know how to check that
in fact it is one one as well
i mean increasing implies it is one one but yeah
foggy warren
ngl im lost again, what sorta answer as an example would i put
is it asking for a notations?
pulsar venture
and increasing?
foggy warren
idk but increasing means its always getting bigger
foggy warren
idk but if i had to guess it would be by checking the function, for example its root x MINUS 6 so in this case it would be decreasing?
idkkkk im so sorry thats just a guess
im being dumb imma let you explain
pulsar venture
idk but if i had to guess it would be by checking the function, for example its ...
no
u differentiate the function
and check if that is positive or not
if that is positive always
then it is increasing
in this case the derivative is 1/2(rootx)
which is always positive
so it is increasing
and if it is increasing it is one one
so the domain doesnt change
if only a part of the function behaved this way
u would have to chop off the domain
by some bit where it doesnt obey what the question says
foggy warren
im trying my hardest to wrap by head around what all that means but its gibberish to me and i hate that
im not good at math at all im sorry
literally the only part im good at is finding the f inverse
pulsar venture
lol its okay
foggy warren
this whole domain thing is difficult for me
foggy warren
ik i said this already but basically i dont touch the 6 at all?
cuz were looking at root x which shows that all positive numbers including 0 can be graphed
but dont i like move the start of the graph to a specific area either left or right by 6 units?
pulsar venture
nope
pulsar venture
.close
foggy warren
.close
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cloud raft
but if n = 2, we get 0.01 which has many numbers lesser than it
final saddleBOT
but if n = 2, we get 0.01 which has many numbers lesser than it
static fractal
it's for all n
onyx peak
read it like this:
there is no positive number that is (less than 1/10^n for all n)
cloud raft
read it like this:
there is no positive number that is (less than 1/10^n for all...
what is meant by "all n"
it means any value of n right?
onyx peak
It means that there is no positive number that is less than 1/10 and less than 1/10^2 and less than 1/10^3 and less than 1/10^4 ....
onyx peak
it means any value of n right?
The order in which you read it is important
This (there is no positive number that is less than 1/10^n) for all n
is different from this there is no positive number that is (less than 1/10^n for all n)
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@cloud raft Has your question been resolved?
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bitter pike
Can someone help me with some of these?
final saddleBOT
Can someone help me with some of these?
bitter pike
I have some idea but need help
craggy plank
Which one?
bitter pike
all, ill run down my answers
craggy plank
Alr
craggy plank
Correct
craggy plank
Correct
bitter pike
alright, jotting down one sec
ok, as x approaches 3, its at the origin
so the limit is 0?
craggy plank
Correct
bitter pike
got it, jotting down
so at f(3), its at origin but there is a black dot, so -1?
ill get stuff wrong later, just wait
craggy plank
so at f(3), its at origin but there is a black dot, so -1?
Yep
bitter pike
ok, as x approaches -1, it goes infinite, and infinity cant be a limit
so DNE?
or -1?
bitter pike
You look familiar with it
im a struggling calc student
i did very bad on a test and my grade is very very poor
and my parents dont like it at all
so im trying my best
just a couple more, thanks for sticking with me
bitter pike
You look familiar with it
so as x approaches 0 from the left its at a closed circle, so DNE? or is it 1 since theres an open circle below it
craggy plank
Notice that limit is a concept of "approaching something"
craggy plank
Check where would it approach when from the left side
bitter pike
it hits 2, but its a closed circle?
craggy plank
Yes, it’s just 2
bitter pike
but i thought closed circles were DNE?
craggy plank
The exact value has nothing to do with limit
craggy plank
but i thought closed circles were DNE?
Nah
craggy plank
Notice that limit is a concept of "approaching something"
👍
craggy plank
No, it’s not
bitter pike
is it 1
craggy plank
DNE only appears when left limit ≠ right limit
bitter pike
ok, so whats the reasoning for 1) being DNE?
craggy plank
yes
bitter pike
ok ran thru 11) in my head, it is true
craggy plank
Before that, lemme ask you a question rq to confirm you actually knows how it works
bitter pike
ok
craggy plank
What’s f(0)?
bitter pike
2
bitter pike
ok ran thru 11) in my head, it is true
11 is correct, at lim x approaches -4, it is -2, and f(-4) is also -2
craggy plank
Correct
bitter pike
and 12 is false, as at x->3, it is 0, and f(3) is -1
bitter pike
thank you so much, just talking about it helps, and you really wanted me to learn it
i really appreciate you!
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vital valve
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bleak granite
,w dist((-25,-25),(-10,15))
soft zealotBOT
bleak granite
vital valve
<:catthumbsup:614540188747563008>
so im right>
bleak granite
well unless wolframalpha is wrong, then yes
bleak granite
the points are barely visible, idk where K is 😅
vital valve
this shit got me tripping
vital valve
the points are barely visible, idk where K is 😅
it changed for some reason
are the cords on this not 2,2 and -1-1?
bleak granite
they are
final tangle
distance formula / pythagoras
soft zealotBOT
Result:
5.6568542494924
,calc 4 * sqrt(2) * 0.25
soft zealotBOT
Result:
1.4142135623731
@vital valve Has your question been resolved?
jade fable
Given P is the centroid of triangle ABC, there’s a line passes point P and intersects with line AB and lineAC at point Q and point R respectively. If vector AQ = a vector AB, and vector AR = 3a/2 AC, then a=?
final saddleBOT
Given P is the centroid of triangle ABC, there’s a line passes point P and inter...
jade fable
I can only find that Q lies upon the pink line and R is upon the yellow line
I try to put the circumstances into xy plane then I can analyze it using coordinates
I think I should use the property of P being the centroid
<@&286206848099549185>
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hard frost
I genuinely don'T get it
rare estuary
you got c correct
and imo, its the hardest one
a and b and easier, try
consider the first displacement as a vector A with magnitude ||A||=6 and the second displacement as a vector B with mag ||B||=8
hard frost
Yeah I tried using the formula "A * B = AB Cos" but i was horribly wrong at first
rare estuary
thats the dot product, i dont think it has anything to do here
hard frost
yeha I realized that after the first attempt
rare estuary
you want the magnitude of A+B
to be 14
what angle must be between A and B to have that?
hard frost
isn't there a formula for that
rare estuary
notice 6+8=14
rare estuary
exactly xd
hard frost
since cos0 = 1
hard frost
LISTEN 😭
rare estuary
the two vectors will be alligned
and therefore the magnitude of their sum
will be simply 6 + 8 = 14
hard frost
Okayy yeah that makes a lot of sense
now, 6 + 8 = 2
i could've sworn there's like a formula for this
oh it's a tight angle
rare estuary
they chose 14, 10, and 2 in this exercise cuz they result in special angles
after you do this exercise, if you got time, try to generalize it :p
hard frost
I see,
rare estuary
okay, how about 2m
hard frost
it should be 8-6
but i can'T change can I
wait
180 deg?
since it's the opposite of
i have no idea wrtf I'm sayting
rare estuary
exactly, if you walk forward 8m then backward 6m
youll end up 2m forward
from where you started
think of these displacements as vectors
rare estuary
me horribe at explaining, but ty gl
hard frost
.close
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tranquil pine
Hi i need help graphing a parabola with only vertex and focus/directrix given
tranquil pine
i got this example but idk how to process
I need to know the step by step process🥹
rocky tusk
ask your teacher
vital crag
Or classmates
rocky tusk
the guy in the green hoodie ought to know
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ancient basalt
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ancient basalt
Dunno how to start
rare girder
Dunno how to start
looks like taylor series helps
evaluate derivatives of f at 0 and see what happens
ancient basalt
looks like taylor series helps
I haven't been taught this ;-;
ancient basalt
multinomial theorem maybe?
Probably but I don't know how to properly expand f(x) here
rare girder
that's what multinomial theorem does, it expands powers of polynomials by referencing multinomial coefficients
like how binomial theorem expands powers of binomials by referencing the n choose k's
ancient basalt
that's what multinomial theorem does, it expands powers of polynomials by refere...
Oh i see
ancient basalt
like how binomial theorem expands powers of binomials by referencing the n choos...
Yea
rare girder
I think my suggestion is naive, maybe there's something prettier out there but whatever lol
ancient basalt
So how would it apply here like what would we get after we apply it
ancient basalt
I think my suggestion is naive, maybe there's something prettier out there but w...
Oh ;-;
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muted prairie
Do you know how to find a_0 + a_1 + ... + a_n ?
There's a certain complex number that can be plugged in for x here that's very useful
muted prairie
Do you know how to find a_0 + a_1 + ... + a_n ?
And it turns the problem into a more difficult version of this
ancient basalt
Do you know how to find a_0 + a_1 + ... + a_n ?
Yea
ancient basalt
There's a certain complex number that can be plugged in for x here that's very u...
Which one?
muted prairie
That's for you to find out
What gives you a pattern of 1, -1/2, -1/2
as you take powers
muted prairie
how would you find a_0 + 2a_1 + 4a_2 + 8a_3 + ...
ancient basalt
I'd expand the polynomial upto a few terms and see if there's a pattern in the coefficients and solve
final saddleBOT
muted prairie
.reopen
final saddleBOT
✅
muted prairie
you're supposed to react to the bot message to keep the channel open
ancient basalt
Oh mb
muted prairie
what do you get when you plug in 1 to the polynomial
ancient basalt
4^1959
ancient basalt
Don't really know any techniques ;-;
muted prairie
Not really sure why you said you knew how to solve it then
ancient basalt
I thought you meant like finding the coefficients
ancient basalt
Ye mb
muted prairie
what do you get on the right side when you plug in x=1
ancient basalt
By putting x=2?
muted prairie
Right
Now what complex number has powers that look like 1, -1/2, -1/2, 1, -1/2, -1/2, 1, ...
not exactly like that but close enough
ancient basalt
Now what complex number has powers that look like 1, -1/2, -1/2, 1, -1/2, -1/2, ...
I haven't really learned many complex numbers , i only know the general form and stuff like z = a+ib
muted prairie
Ah
Idk where you're getting these problems from but this one is way too hard for you
ancient basalt
Idk where you're getting these problems from but this one is way too hard for yo...
Olympiad mock test ;-;
Most of them are hard af
muted prairie
Plug in x = -1/2 + isqrt(3)/2
take the real parts of both sides
the answer will magically emerge
muted prairie
yw
ancient basalt
.close
novel schooner
I need help with y=mx+b
final saddleBOT
I need help with y=mx+b
novel schooner
I need help find the “mx” part and creating an equation based on the slope
This is what i have now.
I can identify B, but i’m having trouble identifying mx
I’m unsure if “mx”, or just the “m”, is the refers to the slope.
But what do i do when i do find the slope? Do i leave it as a fraction, or is there another step after that?
short swift
I’m unsure if “mx”, or just the “m”, is the refers to the slope.
its only the m
do u know the formula to find the slope?
short swift
Rise over run is what i hear alot
what about if ure given coordinates?
are u familiar with this? the second one i mean
novel schooner
Yes i have seen this before
short swift
yeah use this one to find the slope, m
just take any 2 points from the graph then plug it in this equation
novel schooner
Ok i’ll give it a try
So for the Y, i did 5 - 9 = -4
And for X, i did 45 - 39 = 6
But it feels like i did something wrong
short swift
are those the points from the table?
novel schooner
I got these numbers from the table above the graph
short swift
yeah but, u should take the points from the graph get it?
novel schooner
The points from the table are the points that are on the graph. So i assumed that both would give the same answer
But many of the points don’t fall directly on the line, so i wasn’t to confident trying to eyeball the graph
short swift
hm but what i observed is that the points from the table were scattered points, and the graph is like the best fit line, am i corrrect?
short swift
But many of the points don’t fall directly on the line, so i wasn’t to confident...
yeah that's it
the graph u constructed is a best fit line
novel schooner
Yes. The line is a line of the best fit.
Ohh i think i might have said the wrong then
I want to find the equation for the line of best fit
short swift
yep thats why we need to take a point (any point) from the line, not the table
bcs, if we want an equation for the line, then we need the gradient of the line, therefore we need to take 2 points from the line
do u get my point?, the values from the table and from the line is not the same
novel schooner
i think i get what you mean. So i’m taking an x and y point from the best fit line?
short swift
yeppp
novel schooner
Oh. That makes much more sense. I’ve been focusing on the wrong thing the whole time
short swift
mhm but its okay
novel schooner
So the gradient of this line would be 14/22.5? With 14 as the Y and 22.5 as the x.
Can rounding be used with coordinates? Or should i try and be as accurate as i can?
short swift
So the gradient of this line would be 14/22.5? With 14 as the Y and 22.5 as the ...
okay how do u get 14 and 22.5?
short swift
Can rounding be used with coordinates? Or should i try and be as accurate as i c...
sure ig, but mostly ppl jus leave it in a fraction form
based on my observation, i assume u took the points (14, 30) and (22.5, 15)?
novel schooner
Yeah
short swift
are u familiar with this? the second one i mean
again we need to use this
novel schooner
What do you by the -8.5?
short swift
14 - 22.5
sour socket
.
novel schooner
Ohh i see. I see what you mean
Yeah and that would be the y point of the gradient needed for the equation. So the x point would be 15 (30 - 15)?
So i think it would be -8.5/15 ?
short swift
u got it but its the other way around now😭
u reed the coordinates x first, then y right?
novel schooner
Yeah i was about that doesn’t the x come first in the coordinates?
Since 14 and 22.5 are the first coordinate in the parenthesis
short swift
well um thats bcs 14 and 22.5 are the x points
novel schooner
So what do you mean them? Not sure i understand
Oh wait nevermind. I think i see it now
Called 15 the x coordinate. I mean that 15 should be the Y coordinate and -8.5 should be the X coordinate
short swift
Called 15 the x coordinate. I mean that 15 should be the Y coordinate and -8.5 s...
yeah u got it haha
novel schooner
So now that i have y=-8.5/15(x)+55
What would the x be?
short swift
it should be 15/-8.5
short swift
So now that i have y=-8.5/15(x)+55
What would the x be?
x and y are variables, we dont need to find them
short swift
Called 15 the x coordinate. I mean that 15 should be the Y coordinate and -8.5 s...
we need to take the Y first, then the X, m = Y/X
short swift
are u familiar with this? the second one i mean
hre
novel schooner
So as a recap, in the equation y=mx+b the -8.5/15 is the “m” part of the equation correct? And the 55 would be the “b” part of the equation. And the “x” part of the equation is a variable i leave blank?
Just to make sure i fully understand it
short swift
yeahh
short swift
it should be 15/-8.5
but then again😭
novel schooner
Oop
short swift
Called 15 the x coordinate. I mean that 15 should be the Y coordinate and -8.5 s...
Y first then X
novel schooner
Gotcha. And is that the same with all problems that use the coordinate plane?
All throughout middle school, i’ve always done the x coordinate first and haven’t been corrected on it being incorrect.
short swift
it's like this, dont get confused
to READ a coordinate, we read the x first, then y
but to find gradient, we put y first, then x, as in m = (y2 -y1) / (x2 - x1)
got it?
novel schooner
Ah ok. I think i understand
short swift
good
novel schooner
So my last question would be, how would i find a point that isn’t on the graph. I’m assuming that is what the x variable is used for?
short swift
exactly
so if u have a y point and u want an x point just plug the y point into the equation then solve it
or vice versa
novel schooner
So if i wanted to find the x point for 40 minutes, i would have to construct this equation to find it? Y=15/-8.5(40)+55?
short swift
u want to find the x point or the y point?
novel schooner
I’m assuming it would find the Y point .
Since the number of students was 0 after 32 minutes, how many students would there be after 40 minutes.
short swift
I’m assuming it would find the Y point .
ure right
logically still 0
but mathematically
negative something
but ofc we need to use logic
novel schooner
Gotcha. So does that mean that an x coordinate can found this way also?
short swift
yeps
novel schooner
So if i wanted to find an X coordinate, would i place my Y coordinate that i’m using to find the X coordinate, in that same variable?
If that makes sense
novel schooner
The X variable. I replaced it with an X coordinate to find a Y coordinate
short swift
oh yeah that is correct
novel schooner
So i would replace the X variable with a Y coordinate to find a X coordinate?
short swift
well technically its not replacing but substituting
okay let me give u an exmple
say we have a coordinate (x,10) and we want to find x, usng the same equation, Y=15/-8.5X+55, we substitute the 10 value to the Y term, then, solve the equation to find X
novel schooner
Not too sure i’m understanding.
Would the 15 become 10? Or is the actual Y letter of the equation being substituted?
short swift
Not too sure i’m understanding.
Would the 15 become 10? Or is the actual Y lett...
oh 10 is just an example
short swift
Not too sure i’m understanding.
Would the 15 become 10? Or is the actual Y lett...
yeah the actual y letter is being subsituted
short swift
well its a pleasure to help, u can reach me if u need any more help
novel schooner
Will do. Thanks alot for talking me through. It was very very helpful. Have a great rest of your night or morning.
.close
final saddleBOT
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orchid coral
is is ((sec(c))^2 always greater than ((tan(c))^2
final saddleBOT
is is ((sec(c))^2 always greater than ((tan(c))^2
orchid coral
becaues i have proved this:
root(1-sin^2) = cos^2
cos^2 * sec^2 = 1
root(sec^2 - tan^2) = 1
sec^2 = tan^2 + 1
tranquil pine
becaues i have proved this:
root(1-sin^2) = cos^2
cos^2 * sec^2 = 1
root(sec^2 ...
Yes
That's correct
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haughty rampart
Hey im trying to solve: Prove by induction that for all positive integers n, k=0 to n Σ k(k!) is equal to (n+1)! -1
ive gotten my base but when i try to plug in n=m+1 I cant find the right way to the answer
final saddleBOT
Hey im trying to solve: Prove by induction that for all positive integers n, k=...
rocky tusk
$\sum_{k=0}^n k(k!) = (n+1)! - 1$
soft zealotBOT
knief
rocky tusk
and you did the base case to get 0 = 0
rocky tusk
then you assumed that for n=m it is true
and you’re verifying that it works for n=m+1
haughty rampart
yeah
haughty rampart
m?
soft zealotBOT
knief
rocky tusk
yea sorry i’m used to assuming n=k
rocky tusk
the k(k!) under the summation though yes
haughty rampart
yeah
rocky tusk
so you can rewrite that
because you assumed $\sum_{k=0}^m k(k!) = (m+1)! - 1$
or n
m
not not n+1
m+1
soft zealotBOT
knief
rocky tusk
so then you have $(m+1)! -1 + (m+1)(m+1)!$
soft zealotBOT
knief
rocky tusk
do you know how to rewrite that
haughty rampart
yeah or well thats where im confused
rocky tusk
well if you had $x - 1 + (m+1)x$
soft zealotBOT
knief
rocky tusk
how could you rewrite that
haughty rampart
yeah i know that i can factor it out but i dont get like shouldnt (m+1)(m+1)! be on the other side
rocky tusk
so you’d have $(m+2)(m+1)! - 1 = (m+2)! -1$
soft zealotBOT
knief
rocky tusk
which is precisely what you wanted to show
haughty rampart
i mean like like sum... k(k!) + (m+1)(m+1)! = (m+1)! -1
rocky tusk
because $1(m+1)! + (m+1)(m+1)!$ is $(1+(m+1))(m+1)!$
soft zealotBOT
knief
rocky tusk
which is $(m+2)(m+1)!$
soft zealotBOT
knief
haughty rampart
Yeah but im confused with sum... k(k!) + (m+1)(m+1)! = (m+1)! -1, so when you move (m+1)(m+1)! shouldnt it be negative?
haughty rampart
cause when you are here $\sum_{k=0}^n k(k!) = (n+1)! - 1$
soft zealotBOT
daveslave
haughty rampart
and then $\sum_{k=0}^{m+1} (k)(k)!$
soft zealotBOT
daveslave
haughty rampart
making it $\sum_{k=0}^{m} (k)(k)! + (m+1)(m+1)!$ no?
soft zealotBOT
daveslave
haughty rampart
cause thats what i did for another proof
$\sum_{k=0}^{m} (k)(k)! + (m+1)(m+1)! = (m+1)! -1$
soft zealotBOT
daveslave
rocky tusk
$\sum_{k=0}^{m+1} (k)(k)! = \sum_{k=0}^m k(k!) + (m+1)(m+1)!$ but we know $\sum_{k=0}^m k(k!) = (m+1)! - 1$ from our first assumption during the induction step
soft zealotBOT
knief
rocky tusk
so we have $(m+1)! - 1 + (m+1)(m+1)!$
soft zealotBOT
knief
rocky tusk
you’re welcome
haughty rampart
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unique fable
final saddleBOT
unique fable
Can someone check my answer please
solemn bear
Can someone check my answer please
for the area you can also use heron's formula if yk what that is, other than that it seems to be correct
final saddleBOT
@unique fable Has your question been resolved?
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Available help channel!
tall crow
what i do wrong here
final saddleBOT
what i do wrong here
tall crow
languid yoke
I don't think the first limit evaluates to 0
rose hamlet
what i do wrong here
1-cosx/x^2 should evaluate to 1/2
and for sin use the basic stuff
tall crow
1-cosx/x^2 where u get this
tall crow
1-cosx/x^2 should evaluate to 1/2
?
rose hamlet
u gotta
make that
duh
remember this
and sinx/x when x tending to 0 is 1
now go ahed and do the algebraic manipulations to find the form and solve
or use lhopitals rule
tall crow
what is wrong with waht i did
rose hamlet
what is wrong with waht i did
1-cos4x/4x when tending to 0
makes 0/0
which is indeterminate
u know about indeterminate forms right?
tall crow
tall crow
u know about indeterminate forms right?
hello
final saddleBOT
@tall crow Has your question been resolved?
summer dragon
final saddleBOT
summer dragon
can someone explain the meaning of this here
i think im reading the line of reasoning wrong maybe
im thinking this is more of an abuse of notation
but still it doesnt make too much sense
from chatgpt: The left-hand side refers to the functional derivative, which describes how the loss changes when the function H is perturbed at x_i ...... The right-hand side focuses on how the loss changes with respect to the value of H(x_i) treating the prediction as a scalar quantity.
this makes sense but if someone smarter can verify/not
final saddleBOT
@summer dragon Has your question been resolved?
final saddleBOT
@summer dragon Has your question been resolved?
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Available help channel!
unreal knoll
final saddleBOT
flat saddle
product rule is $uv'+vu'$
soft zealotBOT
Carter
unreal knoll
Yeah thats what i did
My primes are just switched places is all
With the non prime
unreal knoll
Because for one i was told to do that by dumbass in the last help thing
flat saddle
lmao no you weren't
unreal knoll
you only implictly differentiate sin(y) on one
I figured to do dy to cosy too bc it had a y on it
unreal knoll
lmao no you weren't
I asked and bro said “yes”
flat saddle
get rid of the dy from the first term because you didn't implictly differentiate y there
unreal knoll
So i should remove dy from cosy then yes?
flat saddle
no whenever you differentiate sin(y) you need it
but when you differentiate just x
it should be $1 \cdot \sin(y)$
soft zealotBOT
Carter
unreal knoll
So no dy on the siny
flat saddle
yes
the whole point of implicitly differentiation is that you're basically doing the chain rule whenever you differentiate y
because $y$ in implicit differentiation is an implicitly defined, differentiable function of x
soft zealotBOT
Carter
unreal knoll
Okay
And i thought it didnt make sense i had dy on both cuz i need to move smth to the other side to get dy by itself
flat saddle
so what do you have now?
unreal knoll
flat saddle
good
unreal knoll
Now i can plug in my points?
flat saddle
so actually instead of dy write dy/dx because we are differentiating with respect to x
unreal knoll
Ik that i just shortcut it
Unless i have multiple respects
Like dy/dt then ill specify
flat saddle
the point is to find $dy/dx$
soft zealotBOT
Carter
flat saddle
so isolate it
unreal knoll
Thanks
Was just that dumb dy thing
Could you explain one more time why it was we didnt dy the siny in the formula
flat saddle
because you didn't differentiate y you differentiated x
in your mind whenever you see $y$ you should instead see $f(x)$
soft zealotBOT
Carter
flat saddle
because whenever you differentiate $sin(y)$ and get $cos(y)\frac{dy}{dx}$
soft zealotBOT
Carter
flat saddle
that's just like $\sin(f(x)) \implies \cos(f(x))\cdot f'(x)$
soft zealotBOT
Carter
flat saddle
it's just different notation that's all
unreal knoll
Chain rule
flat saddle
so your $f'(x)$ is your $\frac{dy}{dx}$
soft zealotBOT
Carter
flat saddle
yes chain rule
that's what it all is
the only reason we write $y$ is so it's easier to read
soft zealotBOT
Carter
flat saddle
but don't let that implicitly confuse you. it's very logical in terms of derivatives.
final saddleBOT
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cloud portal
How do i know with sequences if they start at 0 or 1
final saddleBOT
How do i know with sequences if they start at 0 or 1
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
stone wagon
How do i know with sequences if they start at 0 or 1
context?
stone wagon
"sequences" is a super broad term
sequences can start with anything
0, 1, 2, 10000, -3, x
or do you mean the indexing?
stone wagon
or do you mean the indexing?
like if the first term is $a_0$ or $a_1$
soft zealotBOT
artemetra
stone wagon
is that what you are asking?
cloud portal
Exactly
stone wagon
just a matter of style really
cloud portal
How do i know?
stone wagon
sometimes it's that, sometimes it's the other
stone wagon
How do i know?
context and what that author is using already
final saddleBOT
stone wagon
so really no one definitive answer
final saddleBOT
Available help channel!
sharp cliff
Question ten, I’m stuck I multiplied out the brackets but idk where to go from there cus I got like x^4 + x^-2 + x^-2 + 1 dunno if I add the two x^-2 ‘s together or not and like if I did would I get 2x^-2 or like what
final saddleBOT
Question ten, I’m stuck I multiplied out the brackets but idk where to go from t...
sharp cliff
Grinding at 2 am to get the homework done 😈
Also I used rule of indices or whatever yall wanna call it
To simplify
Powerssss
vivid walrus
which rule did you use?
vivid walrus
sharp cliff
When a^-m = 1/a^m
But I sorta assumed the -m would be 2
Idk if I’m right probably not 😞
vivid walrus
have you learned the chain rule?
sharp cliff
Nope
vivid walrus
,tex .diff rules
sharp cliff
Please do tell tho if it’s important
soft zealotBOT
vivid walrus
last two
vivid walrus
it means evaluate g at x, then evaluate f at the result g(x)
in another words, composition functions
sharp cliff
Oh composite functions
Okay okay
Question, how does this have anything to with what I’m doing like not in a mean way it’s just I’m really new to this stuff so idk
trail mango
kensukeken in help channel 
vivid walrus
hai
trail mango
vivid walrus
Question, how does this have anything to with what I’m doing like not in a mean ...
you should try watching a video or just look at the rule
are you familiar with f'(x)? like what does it mean
vivid walrus
I think first thing they tell you it is inverse of function but in calc it is the rate at which the function is changing at a given point
sharp cliff
I swear it’s got something to do with the steepness of the curve or wherever
whatever
Differentiation is crazy :(
sharp cliff
Okay so like I’m like a minute into the video and the man says that the derivative of 5x + 3 is 5 and I’m lost how’d he pull out a five where 😰😰
Maybe I should accept my fate and fail 😞
Only eight months till exam anyways
This only the beginning too 😞
shut gazelle
Okay so like I’m like a minute into the video and the man says that the derivati...
Do you know the shortcuts, ie power rule, quotient rule, etc or just limit definition?
sharp cliff
I do not have any knowledge on those words accept for the power rule
shut gazelle
What method have you been taught for taking derivatives?
sharp cliff
Uhm this but lowkey idk the difference between dy/dx and d/dx, my teacher just sorta told me to copy it down so I did 🤷♀️
I mean there’s more
But it’s basically like the same thing
Guys I might be doomed
Smart ppl pls help 🙏
dusty dock
Guys I might be doomed
How much of calc do you know?
sharp cliff
Uh
dusty dock
Because if we're looking at the same question, it's not possible via just power rule
proud parrot
yeah, to me it seems the problems that are being given don't match what you currently know ^
sharp cliff
🤷♀️
proud parrot
do you know the product or quotient rule?
sharp cliff
I think if I did I would be able to do the question 😞
dusty dock
I think if I did I would be able to do the question 😞
Are you doing a guided course?
Or is this independent
sharp cliff
It’s school stuff
dusty dock
??? What kind of shitty ass curriculum
proud parrot
are you working ahead perchance? lol
dusty dock
Are you sure your teacher didn't tell you to solve specific problems or maybe you missed a reading?
sharp cliff
No
proud parrot
yeah question 10 would use the chain rule which appears to have not been taught to you lol
you could also use the product rule by splitting it into 2 terms if im not mistaken
proud parrot
Wait
you gave me an idea by saying wait aswell
couldnt you foil it out?
and solve using the power rule?
dusty dock
Yeah
dusty dock
couldnt you foil it out?
FYI by foil we mean distribute