Not really a general rule
#help-36
low egret
Again both of the approaches are correct
There's nothing wrong with how you were doing it
And like I said, it's essentially the same process
I just didn't feel like it "deserved" me expand each of the functions in terms of sine and cosine
But yeah if you feel that it makes it simpler you can work with that as a "rule"
fluid gale
tranquil pine
dv = cos(5x)dx is not v = sen(5x)?
final saddleBOT
dv = cos(5x)dx is not v = sen(5x)?
void valley
dv = cos(5x)dx is not v = sen(5x)?
no because if you differentiated sen(5x) you would get 5cos(5x)
this is why you need to divide by 5 (or multiply by 1/5)
glossy phoenix
final saddleBOT
glossy phoenix
not sure how to start this question
would I have to define my own closed interval to see if it's continuous?
.close
final saddleBOT
soft zealotBOT
Yousuf
fossil geyser
Yeah, it's a constant function
robust mulch
Yes
fossil geyser
It gives 2 for any x
mint elbow
How to find the derivative of y=x^2(3x+4)^2 using chain rule/product rule/quotient rule
final saddleBOT
How to find the derivative of y=x^2(3x+4)^2 using chain rule/product rule/quotie...
tranquil pine
Do you have to use those? Or find the derivative by any means?
mint elbow
It just says find the derivative using a combination of product chain rule and stuff
mint elbow
X^2 and (3x+4)^2?
mint elbow
Ye
tranquil pine
Basically, all you have to do is use it here
mint elbow
U’v +uv’
mint elbow
To differentiate the (3x+4)^2 I have to use chain rule right
tranquil pine
Correct
tranquil pine
Yeah you can do that and then rearrange the terms
Are you sure you did the math correct?
mint elbow
Nice it was the correct answer
tranquil pine
How did you get 8x²?
mint elbow
It was 24x^2
tranquil pine
Yes
waxen egret
how is the new area dx?
final saddleBOT
how is the new area dx?
waxen egret
.close
waxen egret
what have i done wrong here?
waxen egret
<@&286206848099549185>
waxen egret
ok i know that d(cos(θ)) is negative because it decreases after increasing dθ but my answer is positive sinθ
<@&286206848099549185>
uncut mulch
Notice that your constructed (small) triangle is a right triangle, so θ < 90 meaning cos(θ) > 0. So to demonstrate the small change in cos(θ) you need the negative value of the bottom of your small triangle: -d(cos(θ)).
waxen egret
Notice that your constructed (small) triangle is a right triangle, so θ < 90 mea...
why -d(cos(θ))? that makes it positive
multiplying negative with a negative difference would give you a positive difference
uncut mulch
You have denoted that d(cos(θ)) is the bottom side of your small right triangle, so your visualization is built on the fact that d(cos(θ)) > 0 (on your triangle). You do know that d(cos(θ)), the change in cos(θ), has to be negative, so you need the negative value of the bottom of your triangle.
uncut mulch
The problem mostly stems from trying to vizualise a negative change by something that you have restricted to only be positive. Using this visualization with sin(θ) would work better, since the change here would be positive.
waxen egret
The problem mostly stems from trying to vizualise a negative change by something...
yep ive done that but the video suggested to try cos(theta) with the same visualization
waxen egret
You have denoted that d(cos(θ)) is the bottom side of your small right triangle,...
im have trouble to understand this
uncut mulch
I don't really know if I can explain any further than that. Haven't really worked with visualization of derivatives before. Only worked with proving them from first principles
waxen egret
I don't really know if I can explain any further than that. Haven't really worke...
hmm let me ask you this
do you agree on this?
where df is the change in area
uncut mulch
df is the change in height, on that picture
waxen egret
df is the change in height, on that picture
do you agree that f the initially area of rectangle?
uncut mulch
It is not
waxen egret
ok let df be the change in area
uncut mulch
f is the hyperbole you see as the blue line
uncut mulch
ok let df be the change in area
Sure, but you do realize that means f(x) ≠ 1/x?
Okay
Go on then
waxen egret
Sure, but you do realize that means f(x) ≠ 1/x?
no actually, what do you mean?
oh wait yes ok i see what you mean
do you agree on this?
actually forget about this
i still dont see why the bottom of the small triangle should be -d(cos(θ))
like this?
wait that doesnt make sense
d(cos(θ)) is a negative number
uncut mulch
Hmm, let's try it in a different way then. From your small triangle, you do agree that sin(θ)dθ = d(cos(θ)), right?
waxen egret
yes
uncut mulch
But sin(θ)dθ is clearly positive, since it's a right triangle
waxen egret
yes
uncut mulch
And you want the change in cos(θ) do be negative
waxen egret
yes
uncut mulch
So you take the negative of that and get -sin(θ)dθ = d(cos(θ))
waxen egret
oh that seems true
uncut mulch
Dividing by dθ you get d(cos(θ))/dθ = -sin(θ)
waxen egret
Hmm, let's try it in a different way then. From your small triangle, you do agre...
wait then sin(θ)dθ ≠ d(cos(θ))?
uncut mulch
I think something important is to notice the difference in the d(cos(θ)) that is the change in your cosine function, which is negative, and the d(cos(θ)) you use in your small triangle to vizualise the numerical magnitute of your change
waxen egret
oo so the d(cos(θ)) in my triangle will be positive
uncut mulch
Yeah
waxen egret
but in graph d(cos(θ)) would be negative
uncut mulch
And you can use this triangle to express the magnitute of d(cos(θ)) in terms of sin(θ) and dθ, but you need to take into account that you need the negative version of this magnitute
uncut mulch
but in graph d(cos(θ)) would be negative
Yeah
waxen egret
And you can use this triangle to express the magnitute of d(cos(θ)) in terms of ...
oh okay i see, this explains alot
wait a minute then how is df in this visualization the new area?
is it because f is the initial area and then thus the change in area would be df? in this visualization
uncut mulch
Because the nature of the x² function makes it possible to visualize it as a square. The actual function doesn't look like that, and you can't use area of that one to visualize the derivative like you also tried on f(x) = 1/x
waxen egret
true
waxen egret
Because the nature of the x² function makes it possible to visualize it as a squ...
then what should the new area be called for f(x) = 1/x if its not df?
uncut mulch
The old area (blue and red) was x ∙ 1/x, the new area (blue and green) will be (x + dx) ∙ (1/x + df) where df is negative
waxen egret
old area (blue and red) - new area (blue and green) = 0?
ill post the image agian for convenience
uncut mulch
No, old area - new area would be red area - green area
uncut mulch
No
waxen egret
let dA be the difference in area
uncut mulch
df is the change in the function's value
waxen egret
take dA/dx would give you the rate of change in area
that gives you the derivative
which is also df/dx
why cant the new area be called df?
uncut mulch
dA/dx will give you the function f itself
waxen egret
wait a minute, how?
waxen egret
id say i know 30% of it
uncut mulch
ill post the image agian for convenience
Well, actually no, in this instance dA/dx doesn't really mean much
I was thinking about the area under the function but above the box as included
uncut mulch
No, I was thinking about a different area
waxen egret
oh
uncut mulch
The area on the picture doesn't really have much meaning, unless maybe to express df in terms of x, dx and 1/x
Note that for your function up there df = d(1/x)
waxen egret
yep
the difference in y value after increasing dx
but for area visualization df would be the new area right?
uncut mulch
What, no?
df is defiently not the new area
df is the change in y as you say, that's it.
The area visualization you used earlier on x² can not be used in the same way here
waxen egret
df is the change in y as you say, that's it.
but thats in graph visualization
uncut mulch
If you want a visualization of the area of f like you had with x², you need some object whose area is calculated as 1/x
It could be a rectangle with length 1 and width 1/x
waxen egret
oo
uncut mulch
I'm sorry, but I have to go. If you still need help you can type in here that you need help or open a new channel
waxen egret
I'm sorry, but I have to go. If you still need help you can type in here that yo...
oh ok
waxen egret
I'm sorry, but I have to go. If you still need help you can type in here that yo...
thanks for the help for the sinx one
final saddleBOT
@waxen egret Has your question been resolved?
final saddleBOT
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Available help channel!
warped flame
Hello
warped flame
It’s the question 2) a)
I don’t understand why we have the binomial coefficient in factor in the exercice
final saddleBOT
@warped flame Has your question been resolved?
tranquil bone
final saddleBOT
wraith crater
Do this by contradiction
tranquil bone
I’m not sure how
grizzled tusk
use that gcd(x, x+1) = 1, same for y
tranquil bone
Still not seeing it
wraith crater
Hint p^2n must divide x or x+1. In either case can you come up with an inequality in x and p
Then the expression can be rewritten as (2x+1)^2 -1 = p^2n(2y+1)^2 - p^2n
hearty zephyr
.... why does p have to divide both?
wraith crater
I meant to say or
hearty zephyr
ah
tranquil bone
So p^2n <= x+1?
wraith crater
Yeah
wraith crater
Then the expression can be rewritten as (2x+1)^2 -1 = p^2n(2y+1)^2 - p^2n
Use this fact and find a cintradiction
tranquil bone
I’m not sure how
final saddleBOT
@tranquil bone Has your question been resolved?
final saddleBOT
@tranquil bone Has your question been resolved?
fallen reef
How would I find the five key points of a sine function if it has no phase shift?
final saddleBOT
How would I find the five key points of a sine function if it has no phase shift...
fallen reef
My textbook recommends I find the x intercepts, max and min points
And recommends I find it like this
But how would step 2 and 3 work if there’s no phase shift?
final saddleBOT
@fallen reef Has your question been resolved?
fallen reef
Without phase shift is the easy situation
How would you find your other points tho?
Like I get youd start at zero, but how would you find your max and min?
livid ice
So basically
You know the max, min, and midline points occur at these angles:
0, pi/2, pi, 3pi/2, 2pi repeat
Set the inside of the trig functions equal to those angles
final saddleBOT
@fallen reef Has your question been resolved?
leaden latch
been staring at this one and i’m just not sure where to start
final saddleBOT
been staring at this one and i’m just not sure where to start
vital crag
been staring at this one and i’m just not sure where to start
Use Pythagorean theorem
tranquil pine
Trig identities
leaden latch
do i use cos^2x+sin^2x=1?
leaden latch
awesome thank yuo
hollow flare
Somebody help
final saddleBOT
Somebody help
rare cradle
Let epsilon > 0
Bound |f/g| above
Then find something x should be bigger than so the bound is < epsilon
rare cradle
Bound |f/g| above
You would do this using the limits for f and g which you're given
fossil geyser
Let epsilon > 0
For a second I thought this was your entire hint and that was hilarious
rare cradle
Lol
hollow flare
What does that eplison sign mean right there?
rare cradle
Then find something x should be bigger than so the bound is < epsilon
less than epsilon
hollow flare
I mean what kind of prove is that?
rare cradle
Also this more of an epsilon-N proof than an epsilon-delta proof
rare cradle
You would do this using the limits for f and g which you're given
And you would add the condition x is bigger than some number
Then at the end say that x should be bigger than all the N's you've used
hollow flare
Then at the end say that x should be bigger than all the N's you've used
Ahh I still didn't get what you said
vital crag
Ahh I still didn't get what you said
hollow flare
https://www.milefoot.com/math/calculus/limits/DeltaEpsilonProofs03.htm
Thanks
sweet cloud
final saddleBOT
tranquil pine
Is ur last name totally not patel tho? Just making sure
tranquil pine
Probability is way out of my league
tranquil pine
They will help if they want to
final saddleBOT
final saddleBOT
Available help channel!
unique yoke
Hi i am trying to find x by finding the circumference, but cannot find the crucial angle CAB, can anyone help pls?
final saddleBOT
Hi i am trying to find x by finding the circumference, but cannot find the cruci...
unique yoke
or my approach could be wrong
final saddleBOT
@unique yoke Has your question been resolved?
unique yoke
<@&286206848099549185>
final saddleBOT
@unique yoke Has your question been resolved?
final saddleBOT
@unique yoke Has your question been resolved?
unique yoke
.close
tranquil pine
Odd question, but why does this occur? It is kind of interesting and I'm interested to know the reason for it
final saddleBOT
Odd question, but why does this occur? It is kind of interesting and I'm interes...
tranquil pine
thorn grotto
for the squares: notice that it's like difference of squares (n+1)^2 - n^2 = (2n + 1)
tranquil pine
Oh interesting
thorn grotto
and I guess you could prove cubes with induction
maybe difference of cubes also helps
tranquil pine
(n+1)^3-n^3 = (2n+1)((n+1)^2+n^2-n(n+1)) = (2n+1)((n+1)^2-1)=n(2n+1)(n-2)
then something to do with arithmetic progressions
Interestinggg
thorn grotto
so
I have proven it
it's kinda ugly though
$s=\sum_{n=a}^{b}2n+1=\left(b-a\right)+2\sum_{n=a}^{b}n=\left(b-a+1\right)+2\cdot\frac{1}{2}\cdot\left(a+b\right)\cdot\left(b-a+1\right)=\left(b-a+1\right)\left(b+a+1\right)$
soft zealotBOT
Jelle
thorn grotto
this is the sum of odd numbers from 2a + 1 to 2b + 1
soft zealotBOT
Jelle
thorn grotto
these are the values of a and b we want, where x is just a natural number
thorn grotto
$=\left(x+2\right)^{3}$
soft zealotBOT
Jelle
thorn grotto
which is the sum we want
maybe the values of a and b are wrong actually
maybe b = a + x
oh well
tranquil pine
buoyant lynx
please help
final saddleBOT
please help
final saddleBOT
@buoyant lynx Has your question been resolved?
thorn grotto
how would you find the prime factor decomposition of 252?
final saddleBOT
Available help channel!
smoky mason
final saddleBOT
tranquil pine
no
amber holly
Yeah, x + a doesn't approach x for nonzero a
Generally if two functions approach infinity, it doesn't mean that they approach each other
sinful fiber
if you track y = x and y = x + a they don't approach each other
sinful fiber
Generally if two functions approach infinity, it doesn't mean that they approach...
although from thinking about it they never approach wouldn't rewriting it as x(1 + a/x) mean you would get lim x, what is the flaw in that thinking
smoky mason
Generally if two functions approach infinity, it doesn't mean that they approach...
oh
smoky mason
if you track y = x and y = x + a they don't approach each other
Their difference at infinity is small though
amber holly
What I mean is that they aren't asymptotes of one another
It'd imply that the distance between them approaches 0
But (x + a) - x doesn't approaches 0
(For nonzero a)
rare cradle
Right idea but not rigorous
rare cradle
But (x + a) - x doesn't approaches 0
Yea but (x+a)/x approaches 1
amber holly
Ik
rare cradle
So in the limit x+a is approx. x
sinful fiber
@smoky mason the typical way of doing it is just dividing by x so that you get a / x and you say that goes to 0 that definitely works, idk if your way is right or not lol
clearly there is some discourse 🤣
smoky mason
Ive solved it correctly with another method and got $-\frac{a}{2}$. This is a question some companion asked me and I didn't know how to invalidate his method.
soft zealotBOT
𝙹o
sinful fiber
@dire dune what are your thoughts
final saddleBOT
@smoky mason Has your question been resolved?
final saddleBOT
@smoky mason Has your question been resolved?
still fox
could u answer part A via the geometric distribution?
final saddleBOT
@still fox Has your question been resolved?
charred pebble
final saddleBOT
charred pebble
how is my answer wrong here
charred pebble
charred pebble
might be that its too imprecise
still incorrect 😦
heres the full question
i just guessed the bottom 2
charred pebble
yeah unlimited tries
solemn sage
replace t with P?
charred pebble
replace t with P?
that worked jeez thanks a bunch
solemn sage
charred pebble
.close
bright birch
final saddleBOT
final saddleBOT
final saddleBOT
Available help channel!
dim cedar
Heya!
I have a task where I need to determine if something is injective, surjective or bijective
Im just confused with part of the task what
∅ -> [-1,1] , x-> sin(x)
is
final saddleBOT
Heya!
I have a task where I need to determine if something is injective, surject...
dim cedar
since ∅ has no element so its injective I guess?
surjective makes no sense bc it doesnt hit R at all
bijective doesnt work too bc it isnt surjective?
ocean lintel
Its image is the empty set, which is not R. So surjectivity is still handled the same way
jagged quest
I think yes, but your example is weird
ocean lintel
since ∅ has no element so its injective I guess?
It's a property about the elements of the empty set, therefore it is true.
dim cedar
I think yes, but your example is weird
ah, I gave the wrong question ops
Its
∅ -> [-1,1], x -> sin(x)
ocean lintel
Same thing
dim cedar
Same thing
hm so
∅ -> anything is always injective?
ocean lintel
Looking at this property's negation might make it clearer
jagged quest
normally the sinus function is bijective for -pi to pi if it's help you 😉
dim cedar
ok I dont get it
final saddleBOT
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dim cedar
.close
lavish aurora
I got a question
final saddleBOT
I got a question
lavish aurora
so if the avarage working hours were 38.5
sweet summit
I got an answer (maybe)
sweet summit
oh yeah okay
so to see the percentage increase, you do $\frac{\text{new - old}}{\text{old}} \times 100$
soft zealotBOT
MellowDramaLlama
sweet summit
so then it's $\frac{40 - 38.5}{38.5} \times 100 = \frac{2.5}{38.5} \times 100 = 0.06494 \times 100 \approx 6.49 %$
lavish aurora
so 38.5-40 decided through 40 times 100
soft zealotBOT
MellowDramaLlama
lavish aurora
lord have mercy
I gotta do this in excel😭
thank you very much !! I might be back (probably will)
sweet summit
oh for excel it's not too bad
have a column for new, old, then have another cell for new - old, then a final cell where you do that cell, divide it by the old cell then multiply by 100
so like if for example old = A1, new = B1, C1 = B1 - A1, D1 = (C1/B1) * 100
lavish aurora
Perfect thank you 😊
lavish aurora
.close
lyric sandal
If I is parallel to M, find the value of x and y
final saddleBOT
If I is parallel to M, find the value of x and y
tranquil pine
Since they are parallel their corresponding angles should be the same yes
lyric sandal
i try to solve for X
but its always wrong
this is how im doing it, im not sure what im doing wrong
tight crag
First solve for x
Well you can solve both of the variables in the short term
tight crag
this is how im doing it, im not sure what im doing wrong
Woah what
lyric sandal
idk wtf im doing
tight crag
-21-16
That’s like negative adding another negative
-37
31x-37=180
add 37 to both sides
31x=217
sweet summit
so what will help here is something like this. Notice the red i, ii, and iii. Since we have parallel lines, then i = ii = iii. So if we let iii = 8x - 21, then we know. that (8x - 21) + (23x - 16) = 180. So then you just solve for x
tight crag
X is 7
Btw
Both values are the same
After when the value of the variable is plug-in and has been solved
lyric sandal
okay thank you
tight crag
That’s an hint btw
For (8x-21) the value for x is 7
35, 145, y=24
sh
I think these are the answer
X=7, Y= 24
fast grotto
can someone explain why this step is possible
final saddleBOT
can someone explain why this step is possible
final tangle
x(1+y) + y+1 = x**(y+1)+ 1(y+1)**
sweet summit
$x(1 + y) + y + 1$ is the same thing as $x(y + 1) + 1(y + 1)$, now we have a factor of $(y + 1)$ to factor out, so we get $(y + 1)(x + 1)$
soft zealotBOT
MellowDramaLlama
final saddleBOT
Available help channel!
silver willow
HELPPPP
silver willow
i can't figure out how to do this two step equation
i will senddd
pleasee helppp
fathom walrus
Do u know what cross multiplication is
silver willow
yess
as in like
lemme get an example
also i have to use the two step method which I don't understand well
wait i have a better example that makes sense im gonna delete the old one
fathom walrus
Ok, tag me when ur rdy
silver willow
it is two stepp
so in
in the question i have to the opisite of the thing to get to the real answer
and you have to use bedmas back wards
il show you the video i used as refrence
so addition and subtraction would be first
so x + 2 i think would have to be x + 2 - 2 canceling out the 2 leaving you just with the x which is the desired out come
next the 5 6 are involed in division
so instead of dividing the oppisite of division is mulitplaction so 5 x 6 = 30. 30 = x
i dont know if i did the equation right but I know that is the right answer
fathom walrus
Unfortunately that is neither the right answer nor the right method.
silver willow
dangg
wait i think i know the problem
its still x + 2
so x would have to be 28
because 28 + 2 = 30
fathom walrus
Correct
silver willow
and 30 divided by 5 = 6
fathom walrus
x=28
silver willow
so how would i do two step equations which is the big part
fathom walrus
For the first problem u sent?
silver willow
yea
fathom walrus
Multiply the numerator of the first fraction by the denominator of the second fraction and set it equal to the product of the denominator of the first fraction and the numerator of the second fraction. This is cross multiplication
silver willow
okay i get it but how am i suppose to multiply
x + 3 * 5
im gonna use * to symbolize multiplactions cause x is a variable and multiplaction in this question
fathom walrus
so we have (x+3)*5
If we wanna distribute the 5, we can do something like this
a*(b+c) = ab + ac
silver willow
so
what does it mean when ab and ac are right beside eachother
Im guessing multiplaction?
silver willow
3(4+2) = 18 + 6
i dont think i did that right
that is very confusing to me right now
wait lemme try something
silver willow
isnt suppose to be
a = 3, c = 2, b = 4 and d = 5
so that would make
b + c = 4 + 2, = 6 * a = 6 * 3 = 18
silver willow
so
fathom walrus
x*(y+z) = xy + xz
silver willow
3 * 4 + 3 * 2 | 3 * 4 = 12 and 3 * 2 = 6 so 12 + 6 = 18
fathom walrus
Yes
So back to our problem
so we have (x+3)*5
Use that same method u just did
5*(x+3)
silver willow
3 * 5, x * 5 | 3 x 5 = 15, | x * 5 = unknown??
silver willow
20x?
fathom walrus
No, we can’t combine the two because one has an x and the other doesn’t
silver willow
so just 20?
fathom walrus
That’s the answer to 5*(x+3)
silver willow
ohh
fathom walrus
So we multiplied the numerator of fraction 1 to denominator of fraction 2
Now set that equal to multiplication of numerator of fraction 2 and denominator of fraction 1
fathom walrus
Yes
silver willow
so 2 x 4 = 8
meaning in the ful equation
okay this is confusing
so now i have these numbers
what do i with them
fathom walrus
Well we have to find x
silver willow
but i still have trouble understanding 5x + 15
so
5x + 15 = 8
can i structure it like that?
fathom walrus
What r u not understanding about 5x + 15?
fathom walrus
5x + 15 = 8
Yes
silver willow
okay wait then i got something
okay so i got close
but im guessing i have to multiplie 5 with something negative to get -12 because -12 + 8 = 15
silver willow
5 * x
fathom walrus
No
U want to isolate the term with the x
Meaning get that term alone on one side
silver willow
so would i just
5+ - 5
wait i got someone else to help who i can speak audio with thank your for helping me like this though
fathom walrus
Np
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honest crescent
What do I do with a and b when I derive the function in this problem?
honest crescent
A function with parameters a and b is given. Describe the critical points and possible points of inflection of f in terms of a and b. Assume a, b > 0. f(x) = a/(x^2+b^2)
shell mountain
a and b are just constants
honest crescent
So I don't touch them and just derive the x?
shell mountain
You wouldn't touch them anymore than you'd touch the 2s in 2/(x² + 2)
final saddleBOT
@honest crescent Has your question been resolved?
uncut totem
2lnx (1/x) = 2lnx/x?
final saddleBOT
2lnx (1/x) = 2lnx/x?
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astral prawn
How do I determine where the intervals are increasing and decreasing along with maximums and minimums?
final saddleBOT
How do I determine where the intervals are increasing and decreasing along with ...
dry light
Do you know what increasing means
astral prawn
Well I understand its increasing from(-3,-1)
Just not sure about where that break is at 2
dry light
Where or what
astral prawn
Like that jump at 2
slender citrus
help
slender citrus
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dire oar
hey there, need help with the derivative of this function, the simplification is where i stuck
final saddleBOT
hey there, need help with the derivative of this function, the simplification is...
dire oar
oh yea?
fossil geyser
It actually looks like e^sqrt(x) is the derivative, and you're meant to find the original function
tranquil pine
Integration time
dire oar
i did find the derivative of all options and none of them matched 
tranquil pine
You are meant to find the primitive function
So you have to integrate and find the anti derivative
tranquil pine
I guess in this case, take the derivative of each of the options and see if they get you the original derivative
So do process of elimination
tranquil pine
It is one of them in fact
dire oar
is it?
dire oar
I integrated and found it
good for u
dire oar
Do the derivative again
tranquil pine
Product rule
dire oar
makes a diff?
tranquil pine
Of course it does
tranquil pine
I believe you did it correctly for this one
dire oar
no doubts
tranquil pine
Okay this isn't it, move on to part b
dire oar
ok
tranquil pine
Derive that
dire oar
Derive that
tranquil pine
Your derivative is incorrect, but I don't believe this is it anyways
Oh nvm u got it right, just got confused by the order
tranquil pine
Ah but u missed an x
dire oar
where
tranquil pine
The x?
dire oar
tranquil pine
Also it should be $2e^{\sqrt{x}}\sqrt{x}-2e^{\sqrt{x}}$ based on the integral, but I'm trying to see some sort of simplification with your choices
soft zealotBOT
♡LexQa♡
tranquil pine
I will admit, I did think it was Part a at the beginning, but I confused the derivatives. It looks like none of them match the integral
Which is weird
Are you sure about your choices ?
dire oar
one may do but
dire oar
Are you sure about your choices ?
yes
tranquil pine
Eh I guess there is some sort of simplification I'm not seeing
dire oar
Eh I guess there is some sort of simplification I'm not seeing
thats it
tranquil pine
**♡LexQa♡**
That's the antiderivative though, so it needs to be something of that form
Let me recheck what you have done
dire oar
wait, what if i calculate f’(5) for example, test all options and see which one matches e^sqrtx
maybe that works?
i mean then i get decimals
tranquil pine
Oh yeah sure
dire oar
now e^sqrt5 is 9.356
dire oar
My mind is still on part A though
and i thought it maybe b at first
tranquil pine
That's why integration is God sent 🥴
dire oar
i see
tranquil pine
Although the integral of e^(sqrt(x)) might be a problem for most beginners
dire oar
no doubt it is
dire oar
according to this, f’(5)=12.6 and didnt match e^sqrt 5 which is 9.356
dire oar
f’(5)=0.25
tranquil pine
according to this, f’(5)=12.6 and didnt match e^sqrt 5 which is 9.356
Although this was the closest as I expected. Maybe they made a typo?
dire oar
Although this was the closest as I expected. Maybe they made a typo?
i have no idea
tranquil pine
hey there, need help with the derivative of this function, the simplification is...
Because the thing is, for this the e^sqrtx and the sqrtx need to be in opposite order
If they were
It would be correct
For part a
dire oar
what do u mean by sqrtx needs to be in opposite order
tranquil pine
actually eh it still would be 4 which is wrong
Don't worry about it
Anyways maybe your teacher did a mistake or we did. You should definitely check either way 😄
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tranquil pine
kind of studying more about vectors, but i am kind of confused about vector projection
final saddleBOT
kind of studying more about vectors, but i am kind of confused about vector proj...
tranquil pine
if the dot product tells us how much of magnitude u is in the direction of say v, which is just the magnitude of u in the direction of v, how exactly does that differ from the projection u has onto v?
desert mantle
well the dot product is a number
the projection is a vector
but you calculate the projection with the dot product so they are of course very related
tranquil pine
huh, so is the projection just the dot product multiplied with the unit vector of err
dry light
Projection basically minimizes the distance beteeeen the tips when you manipulate the vectors by a scalar
It's how I make right triangles lol
tranquil pine
hmmm
dry light
Like if you project a onto b, you're changing the magnitude of b such that the distance between the tips of a an b are minimized
tranquil pine
but shouldn't the direction of that projection be the exact same as the vector being projected onto it anyways?
huh
so i guess i am understanding more of the formula now
oh i gues the magnitude of u would give u the length and the direction would be of the unit vector of v
makes sense makes sense
tranquil pine
yeee
dry light
You see, if A and B have an acute angle between them the projection will go in the same direction as A or B
But if it's obtuse, it'll go the complete opposite direction
tranquil pine
yep
dry light
That's because of the A • B
It's all derived from the Pythagorean theorem
There's a derivation online
tranquil pine
oh so the dot product would just be the magnitude of that projection
if i am getting this right
and the direction is just the unit vector of v
well no
not the dot product
so it is just going to be the x component of the vector a, so **|a|**cosx
uncut mulch
so i guess i am understanding more of the formula now
You could say you are connecting the dots
tranquil pine
so shouldnt the formula just be (acosx)b/b
uncut mulch
🧍♂️
fathom iris
i dont get what im doing wrong
final saddleBOT
i dont get what im doing wrong
fathom iris
to find angle B
I do sin(37)/45 = sin(B)/46
and then get arcsin(46(sin(37)/45)) = 37.96 and then I round that up to 38 and that also is wrong
final saddleBOT
@fathom iris Has your question been resolved?
elfin ravine
Hey guys so i have a question about derivatives
final saddleBOT
Hey guys so i have a question about derivatives
elfin ravine
so this is the particular question that im trying to solve
and the professor provided working out in pink
but i dont get where Delta x^2 goes
cuz i get how a^2 cancels out
but the delta x^2 just disappears no? unless im misunderstanding something
it just jumps to (2a * delta x )/delta x
sorry if my explaining is really weird idk how to use symbols on discord
so basically idk where to go from here
apaprently the answer is 2a
but i get
where am i going wrong?
do the limits do something so that the delta x cancels out by itself?
<@&286206848099549185>
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@elfin ravine Has your question been resolved?
elfin ravine
<@&286206848099549185>
tranquil pine
do the limits do something so that the delta x cancels out by itself?
So $\lim_{Δx \to 0}\frac{Δx(Δx+2a)}{Δx} = \lim_{Δx \to 0} Δx+2a = 2a+0 =2a$
soft zealotBOT
Gilgamesh
tranquil pine
@elfin ravine
tranquil pine
Bro you must to use limits if you want to do the derivatives
tranquil pine
close to 0 but not actually 0
Yes
elfin ravine
but why not just sub in 0 at the very beginning fot he equation
is there a specific place where i can sub in limtis?
tranquil pine
Because you divide by 0???
elfin ravine
ohhh so as soon as i get rid of the denominator i can just sub in 0 right?
tranquil pine
Nah, you can use it at the end if you remember that you cancel out nothing
final saddleBOT
tranquil pine
ohhhh okay okay thank you very much
You are welcome
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tranquil pine
hello
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tough dagger
How do i solve this
final saddleBOT
How do i solve this
rare cradle
How do i solve this
u = e^2x
vital crag
sinc
tough dagger
solemn sage
is this not integration by parts?
vital crag
<@261933205387477002> why dont u help me 😦
i asked you multiple times to stop pinging me
tranquil pine
Why do you feel like it's obligated for someone to help you
crystal lotus
Why do you feel like it's obligated for someone to help you
oh lol i remember you
tough dagger
so uhm back to the integral
tranquil pine
is this not integration by parts?
I believe the integral sinu/u isn't gonna get you much with ibp
It is a special integral
tough dagger
Interesting
tranquil pine
You have to use some wild stuff like Feynman I believe
But that's out of my league
solemn sage
i tried ibp, it works if you do it twice
tough dagger
Ibp?
solemn sage
ah wait this isnt sin(x) e^(2x), nvm
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mighty tapir
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mighty tapir
14
dawn elk
make two cases one where a=1 and another where a!=1
and then u should hav some limits to solve to get a
@mighty tapir
mighty tapir
ok
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next pagoda
I have the equation (x-h)^2 / a^2 - (y-k)^2 / b^2 = 1 in mind for this.
next pagoda
So I know I need to find the equation for this using what is given
I also know it is not centered at 0
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@next pagoda Has your question been resolved?
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@next pagoda Has your question been resolved?
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languid arrow
It's a broad question so idk if this applies
Any rescources to pass calc 1? Been eating dirt in it lately and feeling hopeless about it. I struggle with differebtiation the most though. The actual calculus isn't too bad. Thank you and sorry in advance if this question is inappropriate
final saddleBOT
It's a broad question so idk if this applies
Any rescources to pass calc 1? Been...
dusty harbor
the organic chemistry tutor
opaque stirrup
Hey can anyone help me with polynomial expression
final saddleBOT
Hey can anyone help me with polynomial expression
@opaque stirrup Has your question been resolved?
stuck owl
What is the name of this/how could I phrase this better? I think it has something to do with a linear combination.
I want to say that every integer can be expressed as the sum of a multiple of p and a multiple of n, where p is prime and n isn’t a multiple of p.
final saddleBOT
What is the name of this/how could I phrase this better? I think it has somethin...
stuck owl
Ignore that first “there exists” prime p. It has to work for every prime so make that “for all” prime p.
amber holly
"For all n there exists n"?
stuck owl
yes but thats not the goal of this. I need to prove the above
and i wanted to maybe state it differently
so that it becomes easier for me
trail mango
n not equal to kp before k is mentioned?
stuck owl
thanks will fix that.
amber holly
You could just write that p doesn't divide n tho
stuck owl
okay
Is this the same. Yes right
Nvm
Ill remove the k its redundant
Is it fine to write the A,B like that at the end
Or do I need to put it in front of the n=Ap+…
unique spoke
Or do I need to put it in front of the n=Ap+…
then $\exists A,B \in \mathbb{Z}$ such that $n = Ap + Bn$
soft zealotBOT
Kurt
unique spoke
is more readable
lyric ether
Whether the inequality is true for positive x and y. 8x^3 + y^3 + 1 > 6xy
final saddleBOT
@lyric ether Has your question been resolved?
scenic notch
How do I simplify the equation( 2/(log6(100))+(1/(log3(100)) down to a single logarithm. The 6 & 3 are the bases.
final saddleBOT
How do I simplify the equation( 2/(log6(100))+(1/(log3(100)) down to a single lo...
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@scenic notch Has your question been resolved?
scenic notch
I mean log base three of 100 and log base 6 of 100
sturdy cypress
yeah
scenic notch
So log base 3 of 100 is the same as log base 100 of 3
sturdy cypress
after being divided by, sure
ebon oar
How do you calculate the actual change in acidity when pH changes from 8.1 to 8.0
final saddleBOT
How do you calculate the actual change in acidity when pH changes from 8.1 to 8....
vital crag
change in function f from 8.0 to 8.1 = f(8.1) - f(8.0)
ebon oar
what function do i input it into?
vital crag
acidity
ebon oar
for example 10^(8.1) - 10^(8.0) ?
vital crag
is 10^x your acidity formula?
ebon oar
not sure what the acidity formula is
vital crag
then you'll have to look it up in your book/notes
ebon oar
.close
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unique fox
In a math exercise, each student from a group of 15 students had 8 correct answers each.
On each of the tasks, there were 6 students who had answered correctly.
final saddleBOT
In a math exercise, each student from a group of 15 students had 8 correct answe...
unique fox
How do I solve a problem like this?
(missed the lecture so havent been able to try anything, not sure how to start)
tranquil pine
Can someone help
supple copper
Can someone help
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@unique fox Has your question been resolved?
unique fox
<@&286206848099549185>
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@unique fox Has your question been resolved?
astral thunder
i think it has to do something with the formula used for calculating the distance between a point and a line but im not sure how
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@astral thunder Has your question been resolved?
astral thunder
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