delta(x) is not the derivative of f
#help-10
civic zealot
civic zealot
yes
civic zealot
use the limit defintion of the derivative.
Then take the left and right limits.
late roost
ok
civic zealot
at $x = 0$, $f'(0) = \lim_{h\to 0} = \frac{|0+h| - |0|}{h} = \lim_{h\to 0} \frac{|h|}{h}$\
When $h>0$, you have $|h| = h$ and when $h<0$ you have $|h| = -h$
warm shaleBOT
Zybikron
civic zealot
So $\lim_{h\to 0^-} \frac{|h|}{h}= \lim_{h\to 0^-} \frac{-h}{h} = \lim_{h\to 0^-} -1 = -1$\
$\lim_{h\to 0^+} \frac{|h|}{h} = \lim_{h\to 0^+} \frac{h}{h} = \lim_{h\to 0^+} 1 = 1$
warm shaleBOT
Zybikron
civic zealot
one sided limit. it's values to the left of 0, so they're negative (h < 0)
late roost
one sided limit. it's values to the left of 0, so they're negative (h < 0)
im really sorry can you expand on this part
late roost
**Zybikron**
this makes sense, im just missing on why its negitive from the left and possitive from the right
civic zealot
h -> 0- means you're only considering values of h < 0 as you approach 0.
late roost
ok
civic zealot
when h < 0, you have |h| = -h
civic zealot
yep]
late roost
Ok that makes sense
Is there a list of checks for what makes a function differenciable or is it legit just something you can tell by taking the limit or looking at the graph
nvm it would do that wil h'lopitals
civic zealot
you can check a graph, if it is smooth and continuous then it's differentiable.
you can check the derivative limit, if it's defined everywhere then it's differentiable.
late roost
you can check a graph, if it is smooth and continuous then it's differentiable. ...
ok perfect
thank you
civic zealot
The replacing it with 1 is just because h/h = 1
late roost
anything else to look out for or is that it
civic zealot
'smooth and continuous' should get you pretty far.
obtuse pebbleBOT
obtuse pebbleBOT
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barren cedar
obtuse pebbleBOT
barren cedar
please someone help š
smoky cairn
what have you tried
barren cedar
ohh
well
so of course i graphed the problem
and identified which would be the outer and inner radius
i made x^3-(-4) the outer radius
and 1-(-4) the inner
and set up the integral
pi integral from 0 to 2 (x^3+4)^2 - 25) dx
and then i solved the integral
^which gave me 226pi/7
deft violet
Attempting to solve this problem but the program is saying my solution is incorrect. Where am I going wrong?
obtuse pebbleBOT
Attempting to solve this problem but the program is saying my solution is incorr...
hardy widget
Bounds are wrong
deft violet
fuck, why are they wrong lmao
if the bound provided is x=5 then why is it not 0 to 2
hardy widget
$5=y^2+1 \implies y=\pm 2$
warm shaleBOT
Civil Service Pigeon
deft violet
oh it wants the fucking solid below the x axis too
hardy widget
Yeah you only drew half
finite jetty
can i do this?
$$\lim_{\epsilon\to 0}e^{-4x^2/\epsilon}=\lim_{\epsilon\to 0}e^{-x^2/\epsilon}$$
obtuse pebbleBOT
can i do this?
$$\lim_{\epsilon\to 0}e^{-4x^2/\epsilon}=\lim_{\epsilon\to 0}e^{...
warm shaleBOT
arizona
tame python
can i do this?
$$\lim_{\epsilon\to 0}e^{-4x^2/\epsilon}=\lim_{\epsilon\to 0}e^{...
yes, because of limit composition law\ $\lim_{\epsilon\to0}e^{-4x^2/\epsilon}=\lim_{\epsilon\to0}e^{-x^2/(\epsilon/4)}=\lim_{\epsilon/4\to0}e^{-x^2/(\epsilon/4)}=\lim_{\varepsilon\to0}e^{-x^2/(\varepsilon)}$
warm shaleBOT
mtt
hardy widget
You forgot to multiply this term by x
$\frac{x \left(-\sin x \ln x-\frac{\cos x}{x} \right)}{x (\ln x)^2}$
warm shaleBOT
Civil Service Pigeon
obtuse pebbleBOT
obtuse pebbleBOT
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eternal pawn
If a cat on a jetpack could theoretically go at 60 meters/second, but it plummeting downward will multiply your speed by 1.5x, how long will it take for you to die from 400 meters? Your acceleration speed is an average of 5m/s. We also assume that the speed and height will kill the cat from the height, and the gravitational constant will stay the same. The cat is also an average house cat
obtuse pebbleBOT
If a cat on a jetpack could theoretically go at 60 meters/second, but it plummet...
cursive pumice
Can someone explain this to me fully.
eternal pawn
If a cat on a jetpack could theoretically go at 60 meters/second, but it plummet...
<@&286206848099549185> can I get help pleaseš
timid silo
Can someone explain this to me fully.
This help channel is already occupied. Please enter on a different one.
obtuse pebbleBOT
@eternal pawn Has your question been resolved?
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
One
If a cat on a jetpack could theoretically go at 60 meters/second, but it plummeting downward will multiply your speed by 1.5x, how long will it take for you to die from 400 meters? Your acceleration speed is an average of 5m/s. We also assume that the speed and height will kill the cat from the height, and the gravitational constant will stay the same. The cat is also an average house cat
placid matrix
Iām a bit confused, you use the term you and cat, are we assuming when you say āyouā it refers to the cat?
What does it mean your acceleration speed? Does it just mean acceleration, if thatās the case I believe the unit should be m/(s^2).
Alright, I think I know how to approach the problem, Iām curious what your first thoughts are though. Can you tell me what your first thoughts of s possibly vague approach might be
placid matrix
Tag me if you still need this question answered, Iām going to be working on some other things until then, and wonāt check discord for a while.
obtuse pebbleBOT
@eternal pawn Has your question been resolved?
eternal pawn
Iām a bit confused, you use the term you and cat, are we assuming when you say ā...
Yes- you does refer to the cat
placid matrix
Alright rad, do you have any initial thoughts?
eternal pawn
What does it mean your acceleration speed? Does it just mean acceleration, if th...
I mean that you speed up at a rate of 5m/s
placid matrix
If every second your speed increases by 5m/s then the units would be 5m/(s^2) but yeah I absolutely get what you mean
eternal pawn
I would to try to calculate how long it would take to hit the ground at 60meters per second
placid matrix
If we know itās speed will change immediately, and it has an acceleration then I feel like we might want to try to work out an equation to model the situation
eternal pawn
Yes
placid matrix
How do you want to do this, if you have any ideas
eternal pawn
I would to try to calculate how long it would take to hit the ground at 60meters...
Try this without any change of speed to see how long it will take to hit the ground
placid matrix
Since our speed coming towards the ground is changing I donāt believe that will do us much good unfortunately. But if you do have an idea of how to utilize that please talk me through your idea
eternal pawn
Okay
What Iām meaning is trying to get how long it will take to use that as a base time then add the acceleration to see if our answer is close to our base time
placid matrix
Do you have a method in mind to do that?
eternal pawn
No that is was I need help with
placid matrix
Cause acceleration will strictly make things end quicker, but the affect of acceleration isnāt linear, if we start fast enough it will make a negligible difference, but if we started at a stand still it would make a huge difference. So there isnāt really a set change acceleration would make if we were trying to do that
eternal pawn
Alr
placid matrix
Try modeling a position over time model where position measures our position in the y, or vertical, direction
obtuse pebbleBOT
@eternal pawn Has your question been resolved?
dark orchid
im confused, is y^2 - 4 right for the first stestep in solving the problem?
past tendon
Sounds about right.
gloomy mason
obtuse pebbleBOT
gloomy mason
How do I solve this
timid silo
whenever it says (f+g)(x) , it simply means ( f(x) + g(x) )
its just a shorthand
so
add both functions together
combine them
gloomy mason
Ye but the thing is it doesn't allow me to put a square root symbol
timid silo
the square root can be rewritten as an exponent
timid silo
you got it?
gloomy mason
Ye
timid silo
roots in exponent form are ___
(for clarification purposes)
(fill in the blank š )
gloomy mason
It's whatever the answer to the square root is
timid silo
.-.
gloomy mason
Like
timid silo
i was expecting "fraction"
timid silo
4th root is base to the power of (1/4)
square root is 1/2 power
roots are fractions š
see if that works
*fractional exponent
obtuse pebbleBOT
@gloomy mason Has your question been resolved?
gloomy mason
What is the domain of sqrt2x +7x-5
ionic parcel
What is the domain of sqrt2x +7x-5
[0,inf)
ionic parcel
Do u know how to find it
ionic parcel
Do u know the basics of finding the domain
gloomy mason
I forgot
gloomy mason
2
ionic parcel
No it is not
Itās all numbers
Because there are no restrictions
There isnāt an absolute or a root
gloomy mason
It just has to not equal zero right?
ionic parcel
Not really
Like
X can be any number
It can be 1000 can be 1
What ever
Because there are no restrictions
But if
Like
What about the second one
Whatās the domain of that
gloomy mason
X>_ 0
gloomy mason
X>0
ionic parcel
Because that number is inside a square root
The numbers inside of a sqrt
Cannot be negative right???
gloomy mason
Yes
gloomy mason
Yes
ionic parcel
So that would mean 2x+5 cannot be less than 0
What would this sentence be in equation form
gloomy mason
Y=2x+5
ionic parcel
Whatās Y
gloomy mason
The range?
gloomy mason
Ok
ionic parcel
So that would mean 2x+5 cannot be less than 0
Inequality
How to write this with inequality
gloomy mason
I forgot
gloomy mason
Ah ok
ionic parcel
Have x?
gloomy mason
-5/2?
ionic parcel
What is the domain of sqrt2x +7x-5
Then back to your question
gloomy mason
[X! X>_0
ionic parcel
What is [X!
ionic parcel
I don't think you can solve for x with that equation
You can solve for domain
gloomy mason
Ye
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
spring bloom
obtuse pebbleBOT
obtuse pebbleBOT
@spring bloom Has your question been resolved?
obtuse pebbleBOT
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peak jetty
obtuse pebbleBOT
peak jetty
been going at this problem for the past 30 minutes
plugged it into a calculator and my whole process was wrong
azure wraith
would be great
azure wraith
u can cancel the u
warm shaleBOT
Average Calc Student
azure wraith
use this magic
azure wraith
yes
peak jetty
then i plugged sqrt x back into the equation
azure wraith
,w integral from x=1 to x=4 (3)/(\sqrt{x}(\sqrt{x}+3))dx
warm shaleBOT
warm shaleBOT
peak jetty
ok nice
peak jetty
now i just need to integrate right
azure wraith
yes, evaluate, if u may
azure wraith
it's every calc student's bane of existence
peak jetty
thats good to hear
once i get to this part i usually do x^n+1 / n+ 1 can i do that here?
or would i need to use another integration method
obtuse pebbleBOT
Available help channel!
plain nebula
full mica
how do i do part b)
You would need to resolve the initial velocity into its horizontal and vertical components. The vertical component would be your u, s would be 1.2m and a would be -9.81 ms^-2 then you can use the suvat equation of v^2 = u^2 + 2as.
The v that youāll get is for the vertical component so you need to use Pythagoras to get the final v.
obtuse pebbleBOT
@plain nebula Has your question been resolved?
median mica
can someone help me solve a quadratic equation using complex roots
obtuse pebbleBOT
can someone help me solve a quadratic equation using complex roots
median dome
!da2a
obtuse pebbleBOT
No need to ask āCan I askā¦?ā or āDoes anyone know aboutā¦?āāitās faster for everyone if you just ask your question! See https://dontasktoask.com/
@median mica Has your question been resolved?
grim ocean
grim ocean
<@&286206848099549185>
empty maple
This sequence includes every 102-x value for x values other than 1, 0 < x < 100 and x mod 2 = 1 for example If we say x = 39, 102-39 = 63 is in the sequence.
Lets first add 1..51 to the list, now we have 26 integers in our list and we are sure about none of sum of those 2 integers is 102 (we are sure about it because our biggest int in the list of 51 and it's pair is 51 which is istelf)
If we add any other number to our list we are sure about we will get 102, for example if we add 67 we already have 35 in our list and we get 102 as sum
grim ocean
This sequence includes every 102-x value for x values other than 1, 0 < x < 100 ...
so ur saying there's 26 pairs?
what does x mod 2 =1 mean?
empty maple
what does x mod 2 =1 mean?
Odd x values
grim ocean
so answer is C?
empty maple
26 + 1
grim ocean
sorry, where did the +1 come from
oh wait nvm
just realised
alright i got it tyvm
.close
obtuse pebbleBOT
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Available help channel!
gloomy vector
,rccw
warm shaleBOT
gloomy vector
how would you do this question? i know that the top left angle is an angle bisector and i want to find ?
rose scroll
angle sum is 180 on two triangles?
gloomy vector
wait is this even solvable lol?
rose scroll
theta + x + 45 = 2theta + ? +x
gloomy vector
theta + x + 45 = 2theta + ? +x
yea
rose scroll
so you get the angle in terms of theta. Which is kinda to be expected given the lack of information
rose scroll
yes. If you feel like whether the information is indeed insufficient, try and reconstruct the figure given only the stuff you know
gloomy vector
,rccw
warm shaleBOT
gloomy vector
i want to find BDE
obtuse pebbleBOT
@gloomy vector Has your question been resolved?
opaque dome
E mid of BC ?
gloomy vector
no
opaque dome
Ok
gloomy vector
AE angle bisector of BAC
low summit
i want to find BDE
Hint: ||You don't need trig, just pure addition and subtraction||
gloomy vector
how?
obtuse pebbleBOT
@gloomy vector Has your question been resolved?
obtuse pebbleBOT
@gloomy vector Has your question been resolved?
low summit
Do you know what the angles in a triangle add up to?
Do you know what the angles in a quadrilateral add up to?
Do you know what the angles on a line add up to?
Use that to slowly find every angle
obtuse pebbleBOT
Available help channel!
exotic shell
Let $E$ be a vector space, and let $E_1$ and $E_2$ be subspaces of $E$, such that both $E/E_1$ and $E/E_2$ are finite-dimensional. Then
[
E/E_1 \cap E_2 \text{ is finite-dimensional, and } \dim E/E_1 \cap E_2 \leq \dim E/E_1 + \dim E/E_2.
]
\begin{proof}
By the fundamental theorem of homomorphisms, the diagonal map $E \to E \oplus E$ induces an injection
[
E/E_1 \cap E_2 \to E/E_1 \oplus E/E_2.
]
(Referring to the Chinese remainder theorem.) Hence, the conclusion follows.
\end{proof}
obtuse pebbleBOT
Let $E$ be a vector space, and let $E_1$ and $E_2$ be subspaces of $E$, such tha...
warm shaleBOT
Sapientia
exotic shell
I just wonder why is this mapping
[
E/E_1 \cap E_2 \to E/E_1 \oplus E/E_2.
]injective.
warm shaleBOT
Sapientia
obtuse pebbleBOT
@exotic shell Has your question been resolved?
obtuse pebbleBOT
@exotic shell Has your question been resolved?
stable flame
obtuse pebbleBOT
stable flame
To clarify, I don't see how b != 0 violates any of the subspace conditions
stable flame
Yeah, that's right! thank you!
Quickly, is there a way to copy-paste latex directly into the chat box?
.close
obtuse pebbleBOT
glossy yacht
What do you mean?
stable flame
.reopen
obtuse pebbleBOT
ā
stable flame
If there is a way to typeset maths directly into the chatbox, instead of doing screen shots like I did
glossy yacht
$x^2=i$
warm shaleBOT
Xetrov
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
last kestrel
whats the easiest way to multiply big numbers with no calc
for example 13x22
last kestrel
<@&286206848099549185>
severe valley
hmm
last kestrel
also how do u solve 2/3(24) +1/5(35)
bold axle
whats the easiest way to multiply big numbers with no calc
for example 13x22
Practice
marble bronze
also how do u solve 2/3(24) +1/5(35)
2/3(24) = 16
1/5(35) = 7
16+7=23
obtuse pebbleBOT
@last kestrel Has your question been resolved?
last kestrel
2/3(24) = 16
1/5(35) = 7
16+7=23
how do u solve it without using a calc
marble bronze
how do u solve it without using a calc
for 2/3(24), lets say its 2 units over 3 units. 3 units = 24, 1 unit = 24/3 = 8 (mental sums). 2 units = 8 x 2 = 16
for 1/5(35), its 1 unit of 5 units, 5 units = 35, 1 unit = 7 (mental sums), 1 unit = 7
16 + 7 = 23
last kestrel
huh
marble bronze
2 / 3 is a fraction, but not the actual number. ill use oranges. 2/3 x (24 oranges), there isnt 2 or 3 oranges in total, but 24, correct?
so 2/3 of 24 oranges = a fraction (aka a part of) that 24 oranges
last kestrel
nvm i figured out but tysm
bold axle
thank u for not anwering i guess
np i guess
obtuse pebbleBOT
@last kestrel Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
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calm haven
I know that when we do the hessian matrix the way to interpret it for 3 variables is:
D1 > 0, D2>0, D3>0 means local minimum
And
D1 < 0, D2 > 0, D3 < 0 is local maximum
Is it the same for 2 variables? Just without the D3?
obtuse pebbleBOT
I know that when we do the hessian matrix the way to interpret it for 3 variable...
obtuse pebbleBOT
@calm haven Has your question been resolved?
wide brook
Was wondering if anyone could help with question c. All I've got so far is (x-a)Ā² + (y-b)Ā² = 1 and I don't even know where to go next
obtuse pebbleBOT
Was wondering if anyone could help with question c. All I've got so far is (x-a)...
unreal musk
Think about the fact that the circle rolling about the [positive] x axis means that the x axis is a tangent to the circle, and being "stopped" by the line y = x means that said line is a tangent to the circle...
wide brook
Do I do something with the fact that the radius is perpendicular to the tangent?
So the gradient of the radius is -1? Idk if I actually need this I'm just trying to gather information I know to show I'm tryingš
unreal musk
I mean, using the fact they're perpendicular, and the "radius" equation (for the point where it meets y = x) will have gradient -1
Pictures might help a bit, to be fair, if you draw it out a bit 
wide brook
I've got this. Obvs not accurate cos just a sketch
Do I need to find the point where the radius and tangent meets coordinates then somehow get the centre from that?
unreal musk
That could help, also, as the x axis is a tangent too, you know that there's also a radius which is perendicular to it where they meet, so it's of the form x = [something]
wide brook
You mean the equation of the radius perpendicular to the tangent is x = something?
The tangent being the x axis
unreal musk
Yep, cause of course, the x axis is y = 0 
Also, if you draw it in too, it may appeal to more circle theorems as well
wide brook
Something about the tangents being equal in length from the point they meet the circle to where they meet each other (which would be the origin)?
unreal musk
Yep, that one should also give you a bit more information
(also, the fact that the circle has radius 1 should instantly tell you the y coordinate of the circle's centre, at least, given what we have 
)
wide brook
So the y coordinate is definitely 1 because the circle meets the x axis, meaning the radius straight upwards would be 0+1
unreal musk
Yep, that's it
wide brook
I'm confused I think I just did something wrong
I was trying to work out the equation of the radius perpendicular to the x axis but I got like 1=Mx+0
That might not even be relevant
unreal musk
Well, for now, we only know that it's of the form x = [something]
(because it's perpendicular to the x axis, which has gradient 0, the whole "1/m" thing doesn't really count here, but we know it's gonna be something like that)
Anyways, let's think about the point where y = x and the circle meet, they're tangents there - let me call the point (d, d) or something (both coordinates are the same because they lie on the line y = x)
wide brook
That makes sense
unreal musk
From that, what's the distance from the origin to that point (d, d), in terms of d?
)
wide brook
I don't think so
But I might've. We got equations at GCSE bcos of covid
So might know how to use it just not what it is
unreal musk
You may have seen it, it's the one saying the distance between the points $(x_1, y_1)$ and $(x_2, y_2)$ is $\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$
warm shaleBOT
@unreal musk
wide brook
I've never seen that before but I think I might be able to use it
unreal musk
Awww 
do give it a go! we want the distance between (0, 0), and (d, d), in terms of d
(I do notice they say you may need to do some research, after all, so there's that 
)
wide brook
Is that right up to that point? Also if it is can I sqrt each sepertarly or do I have to make it 2dĀ² before I sqrt it
Oh wait
I messed it up I think
unreal musk
Is that right up to that point? Also if it is can I sqrt each sepertarly or do I...
Yep, that's good!
You can't square root each part separately, you have to change it to 2d^2
unreal musk
I messed it up I think
(you didn't 
)
unreal musk
So I just leave it as ā2 d?
Yep, perfect we'll come back to this in a second 
wide brook
Okay
unreal musk
So the gradient of the radius is -1? Idk if I actually need this I'm just trying...
But, anyways, before, you said the gradient of the "radius" line was -1, so could you find it's equation, in terms of d, given that it has gradient -1 and passes through (d, d)?
unreal musk
Not quite 
I'm sure you've also seen that if you have a line with gradient $m$ and that passes through the point $(x_0, y_0)$, that it has equation $y - y_0 = m(x - x_0)$, which you can then rearrange to get it in the standard $y = mx + c$ form
warm shaleBOT
@unreal musk
wide brook
Is x_0 the origin or is it just a way to represent the coordinate?
unreal musk
It's just to represent the coordinate, each of those can be whatever you want, in this case both x0 and y0 are d, cause the point is (d, d)
wide brook
And I'm supposed to rearrange this for y=Mx+c?
unreal musk
And I'm supposed to rearrange this for y=Mx+c?
Yep, you can
(You could even leave it like that, if you really really wanted to, but may as well rearrange it!)
wide brook
So y=-x+2d?
unreal musk
So I just leave it as ā2 d?
Yep 
now, let's go back to here
unreal musk
Something about the tangents being equal in length from the point they meet the ...
Remember how there was this theorem here?
wide brook
Yes
unreal musk
That tells us that, in terms of d, the equation of the radius for the x axis is sqrt{2} * d, right?
wide brook
Yeah that's the bit we did earlier right?
unreal musk
Yep, but now we know what the "something" is
So, do you know what the centre of the circle is, in terms of d?
wide brook
One second I got a bit muddled up
wide brook
So y=-x+2d?
Is this bit the equation of the radius perpendicular to y=x?
unreal musk
Is this bit the equation of the radius perpendicular to y=x?
Yea, that's the y = x one
unreal musk
That tells us that, in terms of d, the equation of the radius for the x axis is ...
this one is the x axis one
wide brook
But I thought that was the distance
Oh wait
The distance is the same on the x axis too become of the circle theorem
But how does that get the equation of the radius being ā2 d
unreal musk
Because the distance from the origin to that point where they meet is sqrt{2} * d, which gets you the x coordinate being sqrt{2} * d too
unreal musk
Yep, there we go now, one final thing
wide brook
Okay
unreal musk
So y=-x+2d?
We have that in terms of d, but we also know that this radius here also passes through that point, right?
wide brook
So I replace y and x with the centre coordinates?
Idk how to add -ā2 d to 2d
I feel like I'm being stupid and this is easy
unreal musk
Well, you can factor out the common factor of d, when you add them together
So you can have it as $-\sqrt{2}d + 2d = d(2 - \sqrt{2})$, like that
warm shaleBOT
@unreal musk
wide brook
So d= 1/(2-ā2)?
unreal musk
Yep you can rationalise that as well too
unreal musk
So the centre point is (ā2 d, 1) in terms of d
But anyways, now we have d, we can put that back in for that d * sqrt{2} that we have, so we have the exact x coordinate
unreal musk
So the X coordinate is ā2/2-ā2?
Yep of course, you could rationalise that to make it look neater, but at least you have its value, you know the centre now 
obtuse pebbleBOT
obtuse pebbleBOT
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lament stone
Can I just get some help with a few of these until I get the hang of it?
quaint wing
its ok
the main idea with a lim x->c of f(x)
is you're saying
what is the value of f(x) as x gets really close to c
but it never actually reaches c
so you dont care about the value at the actual point
so what is it approaching for lim x-> 0- f(x)
(the limit coming from numbers less than 0 and going to 0)
what value does the function approach
lament stone
Thatās whatās confusing me tho like am I supposed to use the graph for that š
The only guess I have is 1
Idk where Iām supposed to be looking
quaint wing
near x = 0
well technically it would be the left side
cuz its 0-
so around here
what does the y value approach as x goes to 0 from the left side
lament stone
Is it 3? š
quaint wing
Is it 3? š
yeah
lament stone
Ok ok
quaint wing
a lot of the times for these problems its just the obvious answer
lament stone
But what about positive 0 then Iām approaching it from the right side
quaint wing
But what about positive 0 then Iām approaching it from the right side
yes
thats right
lament stone
Would it still be 3
quaint wing
it means from either side
quaint wing
Still 3? š
yeah
quaint wing
in general when you have lim x->c f(x)
it only exists when lim x->c+ f(x) and lim x->c- f(x) are both the same
lament stone
Oh yea I remember my teacher saying that
And if theyāre not the same then u just say no limit exists or whatever
lament stone
I think Iām good for the most part now but how would I do f(0) is that also just 3 š
quaint wing
for f(0) you have to look at the black point
lament stone
I completely missed that
quaint wing
It would be 2 right
yeah
quaint wing
I completely missed that
yeah thats the hardest part about these problems
quaint wing
you have to remember the limit is different from the actual value
lament stone
Yea I think I got it now but ima still type my answers here and when Iām done Iāll ping you and u can quickly check if u want but ty
quaint wing
Yea I think I got it now but ima still type my answers here and when Iām done Iā...
np
lament stone
np
v) 1
vi) 0?
vii) doesnāt exist?
viii) 3
ix) 1
x) 1
xi) 1
xii) 1
Idk the ones at the end are weird cuz thereās no point
And for vi) the line ends so thereās no way to come at it from the right side which is how I got zero but I also dk if thatās right
@quaint wing
quaint wing
v) 1
vi) 0?
vii) doesnāt exist?
viii) 3
ix) 1
x) 1
xi) 1
xii) 1
yeah thats all right
quaint wing
yep
lament stone
Thanks bro ig this really isnāt that hard š
Alright Iāll close this now
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
gloomy mason
obtuse pebbleBOT
haughty stump
How do I find the local maximum
where is the graph at its highest point that is on the graph shown
||there are 2 and they are labeled with a dot each respecitively||
gloomy mason
where is the graph at its highest point that is on the graph shown
(-2,4) and (6,4)
How do I do the local maxima
haughty stump
How do I do the local maxima
those are the local maxima
its asking you for the x values
gloomy mason
So the local maxima and local maximum is the same thing
haughty stump
So the local maxima and local maximum is the same thing
maxima = plural version of maximum
maximums can also be used, but math teachers like to be fancy for no reason
gloomy mason
haughty stump
gonna be honest i have no idea what "what are" is trying to ask
maybe its asking for the y value?
so try 4,4 or something
wait
gloomy mason
I feel like it trying have me explain it
haughty stump
I feel like it trying have me explain it
seems kinda weird for a thing that seems like itll auto check
obtuse pebbleBOT
@gloomy mason Has your question been resolved?
gloomy mason
It is asking for y values. What are the y values for local minimums?
gloomy mason
seems kinda weird for a thing that seems like itll auto check
My teacher said this
haughty stump
My teacher said this
ĀÆ_(ć)_/ĀÆ
pallid holly
I'm doing piecewise Functions and I'm stuck on how to start
obtuse pebbleBOT
I'm doing piecewise Functions and I'm stuck on how to start
pallid holly
i dont know how to start
plain stag
you don't know how to construct the equation of a line using the graph?
pallid holly
no i dont
plain stag
can you identify two points on that line segment?
pallid holly
(-4,-5) & (0,-1)
plain stag
cool
you can use those two points to determine the slope and intercept of the line segment
pallid holly
can i use rise over run method?
plain stag
not only can you, but you should
plain stag
seems fine
now because this is a line segment and not just a line, you need to specify the domain
pallid holly
-4 < or equal to x < or equal to -1
plain stag
<= can be used instead of "or equal to"
i don't like part of that. Why is x forced to be <= -1?
timid silo
can you identify two points on that line segment?
There's a point at y=2 you also need to consider
plain stag
no there isn't
even after the edit, that point has nothing to do with the line segment
timid silo
pallid holly
i don't like part of that. Why is x forced to be <= -1?
wdum?
plain stag
i'm aware of the point, it has nothing to do with what i'm currently trying to do. Please leave
pallid holly
or is it 0?
plain stag
so then the line segment's domain is?
pallid holly
F(x) = x-1 For -4 <= x <1
plain stag
<1?
pallid holly
so the domain is just -4 <= x < 1
plain stag
it is not
plain stag
what does a hollow dot mean?
i'm gonna ask for a more precise answer this time. What does the hollow dot at x=0 mean?
plain stag
that's better
pallid holly
ill try the other segment on my own but what do i do about that dot on x=0 y=2
plain stag
it's no different
what is the value of the function, and what is the relevant domain?
pallid holly
2 For x=0?
plain stag
sounds good
pallid holly
for the second one will i get a fraction
plain stag
fraction for what?
pallid holly
plain stag
i'm still not sure what you mean
pallid holly
for my r/r
plain stag
you might
pallid holly
-1/2
plain stag
seems right
plain stag
you seem to have forgotten the intercept
pallid holly
-4?
plain stag
better
plain stag
plain stag
yeah i'll drink to that
pallid holly
WOOOOOOOOOOOOOOO
better than my real teacher
PRIs LORD STEAK
Thanks bro
appriciate it a lot
plain stag
np
pallid holly
do you mind if i screen shot these with your tag in a folder on my pc
plain stag
sure
pallid holly
is there a way to have you as a permanent mentor
@plain stag can i get help with another if ydm?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
strange wraith
How do I do C on calculator?
obtuse pebbleBOT
How do I do C on calculator?
native inlet
you have a graphing calculator right? a Ti-84?
strange wraith
you have a graphing calculator right? a Ti-84?
Yes
native inlet
you can put both the function as an equation and y=3 then find intersection points in the Ti-84, it's built in
obtuse pebbleBOT
@strange wraith Has your question been resolved?
strange wraith
you can put both the function as an equation and y=3 then find intersection poin...
Wdym both functions
native inlet
y=polynomial and y=3
knotty portal
i feel so stupid asking but i just cannot comprehend word problemsšš can someone either explain it better for me or tell me how to set it upš
obtuse pebbleBOT
i feel so stupid asking but i just cannot comprehend word problemsšš can someo...
open token
Use eqn of motion
hollow dove
knotty portal
THANK YOU
hollow dove
(you have u=2.6, a=1.9, and v=19.1, and you're looking for s)
obtuse pebbleBOT
@knotty portal Has your question been resolved?
calm patrol
How can I solve sine 135? I don't know where to start
obtuse pebbleBOT
How can I solve sine 135? I don't know where to start
tardy epoch
How can I solve sine 135? I don't know where to start
,tex .unit circle
warm shaleBOT
riemann
calm patrol
All I know is that sine is y and cos is x
calm patrol
,tex \.unit circle
What are the fractions and square roots supposed to mean?
frigid prawn
How do they correspond to the radians and degrees?
the angle is between the point (cos angle, sin angle), the origin, and the point (1,0)
calm patrol
Is there an equation to convert sine 135 to radians or something?
frigid prawn
degree * pi/180
calm patrol
no I mean the -square root of 2 over 2, square root of 2 over 2.
frigid prawn
that is the point (cos angle, sin angle)
calm patrol
Hmm.
frigid prawn
Is there an equation to convert sine 135 to radians or something?
sine is a unitless length
degrees are for angles
they're not interchangable
calm patrol
I thought sine corresponded to cosecant, not cosine.
frigid prawn
it's related to both
as you said, sine is y, cosine is x
a unit circle, as its name implies, is a circle with radius 1
due to circle formula
x^2 + y^2 = 1
sub for sine and cosine
cosine(angle)^2 + sine(angle)^2 = 1
so they're related that way
sine(angle) = 1/cosecant(angle)
sine is related to both, actually like all of the basic trig stuff is related
calm patrol
What would be the difference between sine 135 and cosecant 135?
obtuse pebbleBOT
@calm patrol Has your question been resolved?
obtuse pebbleBOT
@calm patrol Has your question been resolved?
calm patrol
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
jolly radish
for C and D
obtuse pebbleBOT
for C and D
jolly radish
for C, I'll just factor and find the solutions right?
so for item 1 that's 3(z^2-9) - > 3(z-3)(z+3)
tawdry lark
for C, I'll just factor and find the solutions right?
Factor, find solutions, then find the sum and products of the solutions
jolly radish
so it's - 9 + 3 and - 9*3?
exotic marsh
a shortcut for this: if you get it into standard form (e.g. ax^2+bx+c), you can just use -b/a for the sum of roots, c/a for the product of roots
tawdry lark
so for item 1 that's 3(z^2-9) - > 3(z-3)(z+3)
Z^2-9 = (z+3)(z-3)
jolly radish
oh right sorry
exotic marsh
however you can also not have to memorize that and just do it by hand which is sometimes easier
jolly radish
I prefer doing it by hand
so ik what's actually going on
so now I have 3 and - 3
how do I know if it's - 3 + 3 or 3 + (-3)
ik it doesn't matter since it's both three cuz u get the same answer but sometimes they're not the same
tawdry lark
Man is losing itšš„
jolly radish
-1000 aura unfortunately
I'll try answering them and I'll ask for questions later if I have any, thank you!!
exotic marsh
damn bros already thinkin bout arithmetics with non-commutative addition š
coral bluff
I prefer doing it by hand
wth
obtuse pebbleBOT
@jolly radish Has your question been resolved?
tawdry lark
Wait why did you separate-5z
Nvm that works
Im dumb
So basically now you have two terms with the same coefficient (z+1)
So you can write it as (z+1)(3z-8)
Then solve
jolly radish
So you can write it as (z+1)(3z-8)
are my roots - 1 and 8?
tawdry lark
How 8
jolly radish
idk either
tawdry lark
3(8)-8 = 0?
jolly radish
I just want my roots
tawdry lark
Right, so solve 3z-8 for 0
jolly radish
is it z-(8/3)
tawdry lark
z=8/3 yes
tawdry lark
Ye
obtuse pebbleBOT
@jolly radish Has your question been resolved?
obtuse pebbleBOT
@jolly radish Has your question been resolved?
jolly radish
<@&286206848099549185>
minor quiver
That equation should have been this 6z^2 -6z-1 = 0
cinder kestrel
for C, I'll just factor and find the solutions right?
$(x-p)(x-q) = 0$ expands to $x^2 - (p+q)x + pq = 0$ so you can read off sum and product directly from the coefficients
warm shaleBOT
CyclicTree
cinder kestrel
obtuse pebbleBOT
@jolly radish Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
near saddle
I know that you normally want to multiple by highest power of x in the denominator but i am confused
obtuse pebbleBOT
I know that you normally want to multiple by highest power of x in the denominat...
warm shaleBOT
Average Calc Student
near saddle
ok i got it now, i had tried simplifying but it was just confusion
So I did got sqrt5/ 7
azure wraith
Yeah
azure wraith
Yes
frosty patrol
Can someone help me out? Iām doing vectors and scalars and I know the answer is 2.28 but I need it to be in a fraction for cm so I can draw out the line on my ruler and Iām not sure how to do that
obtuse pebbleBOT
Can someone help me out? Iām doing vectors and scalars and I know the answer is ...
frosty patrol
Hereās one my teacher did for us and it was 2.625 and then she got it to 2 5/8 but I donāt remember how she did it
Idk if I did this right but at least for this one the answer was 6.3 so I did 3/10
<@&286206848099549185>
neon gazelle
well 6 3/10 is 6.3
terse tree
!original
obtuse pebbleBOT
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.
frosty patrol
frosty patrol
well 6 3/10 is 6.3
Yeah Iām just confused on how to get problems like 2.125 to translate to cm/in on the ruler
neon gazelle
uhh
terse tree
Are you confused on how to get 2.125?
Oh wait, I see
Youāre looking for the fraction form
Right?
terse tree
Well what do you think would be the first step?
frosty patrol
125/1000?
terse tree
Sure, letās start with that
Whatās a really easy common factor between 125 and 1000?
frosty patrol
5?
terse tree
Yep, so if we divided both by 5 what do we have now?
obtuse pebbleBOT
@frosty patrol Has your question been resolved?
frosty patrol
25/200?
misty magnet
I need help writing proofs. This is my second time attempting this discrete math course, and I have always been a little lacking with my proof writing skills. I understand how to do it conceptually, and I understand the correct answers when they're posted, but I can't seem to do it myself.
obtuse pebbleBOT
I need help writing proofs. This is my second time attempting this discrete math...
tardy epoch
Show the question and your attempt and someone can review it
obtuse pebbleBOT
@misty magnet Has your question been resolved?
misty magnet
Show the question and your attempt and someone can review it
yeah absolutely
here are the problems for context
My attempt at some of these
4 is supposed to be 5
Let me correct it
Actually 4
obtuse pebbleBOT
@misty magnet Has your question been resolved?
obtuse pebbleBOT
@misty magnet Has your question been resolved?
obtuse pebbleBOT
@misty magnet Has your question been resolved?
obtuse pebbleBOT
@misty magnet Has your question been resolved?
obtuse pebbleBOT
@misty magnet Has your question been resolved?
shadow dagger
My attempt at some of these
looks mostly ok-ish?
idk what problem 1 is so i won't comment on that
shadow dagger
Actually 4
i don't understand what u've done here though
some of the problems here are like 'trivial' so it's a bit hard to understand what exactly they want
shadow dagger
My attempt at some of these
i think u've written the question in front for your own sake, but i wouldn't do thta if u were presenting ur final proof
shadow dagger
My attempt at some of these
ignoring the bit in front, i think you could rewrite it as i.e. for q2,
Let $x \in \mathbb{R}$, then let $y = 4 - x \in \mathbb{R}$. Then $x+y = 4 \geq 4$ so $\forall x \in \mathbb{R}, \exists y \in \mathbb{R}$ s.t. $x+y \geq 4$
warm shaleBOT
LY
misty magnet
some of the problems here are like 'trivial' so it's a bit hard to understand wh...
They want a standard direct proof
But I feel very clumsy at writing a standard direct proof
So I restate the facts I know and the definitions I have
shadow dagger
But I feel very clumsy at writing a standard direct proof
don't think too hard abt the first few ones cus it is just trivial & obvious and not very helpful in practising writing proofs
shadow dagger
So I restate the facts I know and the definitions I have
you mentioned this came from a discrete maths course, so i don't think u'll have done like the axioms for the reals, but if you do know the axioms for real numbers, probs apply those to prove the first few results essentially
shadow dagger
Actually 4
ur p4 seems...dubious
try writing up a proof for 6 cus that's actually more interesting than just "R is a field so we have closure"
misty magnet
you mentioned this came from a discrete maths course, so i don't think u'll have...
We havenāt done axioms for reals no but maybe looking at axioms will make it easier for me?
Iām going to attempt 6 and post it here
shadow dagger
We havenāt done axioms for reals no but maybe looking at axioms will make it eas...
if you haven't done the axioms then i think p1-5 are bit bad for writing proofs
cus ultimately 4 just says (x+y)/2 is a real number which follows trivially cus R is a field
misty magnet
Hereās my attempt at 6
I tried. Itās shitty but I tried
I donāt think Iāve tied it together with my last statement yet
@shadow dagger
shadow dagger
i mean like
shadow dagger
how would you solve x^5 >= 3x^4 + 5x^2 + 2333?
misty magnet
how would you solve x^5 >= 3x^4 + 5x^2 + 2333?
Well I need to prove x^5 is greater than the entire right hand statement
I could make an argument about the powers
But Iām not sure
I feel like I hit a wall in the middle of it
shadow dagger
right so we're comparing x^5 vs smaller powers of x
misty magnet
Yeah
shadow dagger
so x >= 10 so we can say i.e. x^5 >= 10x^4
misty magnet
But isnāt that assuming something too soon
shadow dagger
?
misty magnet
Okay so youāre saying to state it as x ^5 greater than or equal to 10 multiplied by x^4?
I wanna make sure Iām understanding
shadow dagger
Okay so youāre saying to state it as x ^5 greater than or equal to 10 multiplied...
i mean i was talking about how to solve the problem
as in there are many ways of doing this
my approach was to spot that
misty magnet
How did you get 10 times x^4
Like what were you able to manipulate
I think thatās the other thing that confuses me here
shadow dagger
x^5 >= 10x^4 = 3x^4 + 7x^4 >= 3x^4 + 700x^2 = 3x^4 + 5x^2 + 695x^2 >= 3x^4 + 5x^2 + 2333
shadow dagger
How did you get 10 times x^4
cus x >= 10?
misty magnet
Yeah but
Arent we saying for anything greater than or equal to 10? I guess in my mind it feels like a violation of the universal quantifier because Iām unsure if we are allowed to state anything about xās value
shadow dagger
Arent we saying for anything greater than or equal to 10? I guess in my mind it ...
yeah?
sorry i'm super confused by ur question
if x is a number bigger than 10
then x >= 10
so x^2 >= 10x
so x^3 >= 10x^2
etc.
misty magnet
Yeah okay thatās what I thought
But
Okay let me see if I can properly explain my thought process
okay so in our original statement we know that x is greater than or equal to 10
so that means 3 is going to be multiplied by (x >= 10) ^ 4
and 5 is going to be multiplied by it's respective values
shadow dagger
so that means 3 is going to be multiplied by (x >= 10) ^ 4
i also don't understand ur notation
misty magnet
i'm just stating the original question and trying to write out the logic
if the equation is x >= 10 -> x^5 >= 3(x)^4 + 5(x)^2 +2333
then we have 3(x>=10)^4 + 5(x>=10)^2 + 2333 for the second half
like 3 multiplied by whatever that x number is that is greater than or equal to 10
misty magnet
so x^3 >= 10x^2
i get what you're saying with this
but i'm wondering how i'm supposed to manipulate the problem to show this
because if i am not allowed to state anything concrete about the value of x
then i'm not sure how i should manipulate the problem with 3(x>=10)
but this could be me totally misunderstanding what is needed in this problem
shadow dagger
then we have 3(x>=10)^4 + 5(x>=10)^2 + 2333 for the second half
that doesn't make sense as notation
shadow dagger
then i'm not sure how i should manipulate the problem with 3(x>=10)
why are you still trying to manipulate 3(x>=10)???
misty magnet
because it's the only bit of information i have about x