This makes it easier, because now you can just treat it as a normal problem and multiply by negative 1 at the end
#help-28
upbeat comet
torn jolt
no
empty grotto
all g dw bro
upbeat comet
Yes, makes it easier
torn jolt
can u explain how to do this without calc
instead of me just doing inverse of cos
on calc
upbeat comet
$\sec t &= \sqrt{2} \
\sec t &= \frac{1}{\cos x}$
glossy valveBOT
Kappa Mikey
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
glossy valveBOT
Kappa Mikey
upbeat comet
Now what if we did something sneaky
Because we don't know how to do this
What if we just
$(\frac{1}{\cos x})^{-1} = (\sqrt{2})^{-1}$
glossy valveBOT
Kappa Mikey
upbeat comet
Because that will give us
on the left side, cos(x), which we know how to handle
And on the right side
$\frac{1}{\sqrt{2}}$
glossy valveBOT
Kappa Mikey
glossy valveBOT
Kappa Mikey
upbeat comet
Then $\cos t = \frac{1}{\sqrt{2}}$
glossy valveBOT
Kappa Mikey
upbeat comet
Because $\sec t = (\cos t)^{-1}$
glossy valveBOT
Kappa Mikey
upbeat comet
$x^{-1} = \frac{1}{x}$
glossy valveBOT
Kappa Mikey
upbeat comet
**Kappa Mikey**
This works because we did it to both sides of the equals sign
upbeat comet
np anytime
warped hazel
can someone help me with this please? (quadratic inequalities)
so far i've factored denominator to (3x - 4)(x + 1) but i'm not really sure what to do next (such as with the numerator)
stiff musk
can someone help me with this please? (quadratic inequalities)
so far i've fact...
what can you say about the numerator? can it ever be negative?
warped hazel
what can you say about the numerator? can it ever be negative?
nope, as the answer must be >= 0
stiff musk
nope, as the answer must be >= 0
what answer?
warped hazel
what answer?
values of x
stiff musk
what can you say about the numerator? can it ever be negative?
^
if the num and denom were both negative, the result would be positive
i'm asking if the num itself can ever be negative
warped hazel
yes
warped hazel
oh yeah didnt think about it that way
since i factored my denom. to a product of binomials can i make a chart/table of negatives, positives, zeros
stiff musk
yep
warped hazel
for diff values of x
stiff musk
the product of two factors is positive if both factors are positive or both are negative
that should be useful here
warped hazel
right
thank you i'm gonna work on the table, i'll ping you if i get stuck or something lol
stiff musk
sure, sounds good
warped hazel
@stiff musk is this okay? am i missing any values of x to show?
stiff musk
<@761155030513352705> is this okay? am i missing any values of x to show?
well, if either factor is zero then the denominator is zero so the fraction is undefined
warped hazel
huh
stiff musk
the fraction itself can't equal zero because the numerator is never zero
warped hazel
oh i just wrote 0 because
stiff musk
so the fraction is >= 0 if and only if the denominator is strictly positive
so i'd just focus on + and -
warped hazel
mm i get what you mean
wait so is the answer (in interval notation)
$x \in (-\infty, -1] \cup [\frac{4}{3}, \infty)$
glossy valveBOT
Orange782
stiff musk
yep that looks right
vagrant hill
Either find an example of a holomorphic function f: C -> C that satisfies f'(z) = Re(z) or prove that no such example exists
vagrant hill
Not really sure where to start with this besides writing Re(z) as
$\frac{z+\bar{z}}{2}$
glossy valveBOT
zapyourtumor
vagrant hill
I am also trying to find a way to use the Cauchy Riemann equations
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vagrant hill
<@&286206848099549185>
vagrant hill
if anyone says something ping me please
well i somehow missed that part of the how to get help channel
.close
tribal musk
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tribal musk
Hello I got stuck on b and c, but I already solved a
jade radish
For b, can u identify what line segment's length it's essentially asking for?
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tribal musk
<@&286206848099549185>
tribal musk
so nothing for b...?
no im not sure where to start for b
tribal musk
u said u already solved a
yes i got 1581 yards
jade radish
okay so at the point E
land is at P
the line segment there would be PE
or EP
same thing
tribal musk
oh ok
jade radish
but notive that now we got a big right triangle
with an angle, hypotheneus, and the distance we want (EP or PE)
so draw that out and then lmk what u got from there
u should be able to just solve it as soon as u write it tbh
@ me when ur back, afk for a sec
untold marlin
can someone explain this to me pls
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can someone explain this to me pls
@untold marlin Has your question been resolved?
untold marlin
can someone help me find the nth sequence of 11,20,35,56,83
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can someone help me find the nth sequence of 11,20,35,56,83
heavy lichen
116
nova wing
can someone help me find the nth sequence of 11,20,35,56,83
What have you tried?
heavy lichen
look at the differences @untold marlin
untold marlin
the thing is it keeps changing
heavy lichen
yeah but how
untold marlin
=6
heavy lichen
?
untold marlin
+6
heavy lichen
the differences themselves form a sequence
and you get the nth term by adding the n-1th term in the difference sequence to the actual sequence
the difference sequence has a pretty straightforward structure if you write it down
untold marlin
wait so is it 9n+6
heavy lichen
nah then it would be 6, 15, 24...
untold marlin
wait so how do i find the sequence
heavy lichen
wait mb
heavy lichen
you can also see it as 3.(2n+1) n>=1
each term of the sequence
9, 15, 21
then Tn = a + dn = 11 + 3(2n+1)
untold marlin
but thats not the sequence tho
untold marlin
the sequence is 11,20,35,,56,83
heavy lichen
idk formatting but its 11 + summation(3(2n+1))
= 11 + 3n(n+1) + 3n
= 11 + 3n(n+2)
untold marlin
huh?
heavy lichen
so basically to get the first term you add 11 and 0
to get the second you add 11 to the 1st difference
to get the third you add 11 to the 1st and 2nd differences
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rocky saddle
help how do I prove this
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help how do I prove this
thorny horizon
maybe call c = log_b(a)
write this as an exponent
and ig take log_a of both sides
severe basin
Else, you do change of base rule.
torn jolt
Yes silver is on the right track
rocky saddle
wait one sec
torn jolt
Consider
[
\log_{b}a = x \
\text{and using the definition of a log:} \
a = b^x
]
glossy valveBOT
torn jolt
Try to proceed from here
rocky saddle
Try to proceed from here
torn jolt
Hint 2: Try to solve for $b$ in $\ds a = b^x$
glossy valveBOT
torn jolt
Using exponents laws
rocky saddle
Using exponents laws
am I correct or close now？
torn jolt
err
rocky saddle
oh wait
torn jolt
yeah you are right in that [
a^{\f 1x} = b
]
glossy valveBOT
torn jolt
try and give this a think and proceed from that, keep in mind what we are trying to prove too
untold marlin
how can i find the turning point of y=x cubed-6x squared+16
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how can i find the turning point of y=x cubed-6x squared+16
devout valley
$y = x^{3} - 6x^{2} + 16$
glossy valveBOT
chartbit
torn jolt
"turning point" can have several implications
do you mean inflection points?
by any chance?
untold marlin
not really
torn jolt
well hm
torn jolt
you can take the derivative and set that equal to 0
untold marlin
**chartbit**
oh so =0
untold marlin
whats the devirative in this equation
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torn jolt
whats the devirative in this equation
Derivative is an operator
@untold marlin can u do limits ?
sharp flame
actually there should be a non-calculus way to find cubic extrema
Factorize it into a quadratic and a linear?
sharp flame
Good question
torn jolt
I can't think of much right now, the easy way out is to find $\map {f'} x = 0$
@untold marlin
glossy valveBOT
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marble bloom
So I was looking to calculate the limit of x * cos(a/x) as x -> 0+ (a is a negative number.)*
I figured it's probably 0 but I forgot how to calculate it, any help would be appreciated
marble bloom
Yeah but, I don't really know that
This is a question from an exam, I can't graph it on the fly
onyx glen
you do not know that cos is even...?
marble bloom
Pardon?
onyx glen
cos(t)=cos(-t) for all t
marble bloom
Oh, sure
Haven't thought about it I guess
the expression is a little longer so the fact that a is negative does hold some weight in uh...
It's technically
e^a/x + e + what I wrote
So a being negative and not positive holds grounds here
nevermind though, how do I calculate this limit?
torn jolt
intuitively, why do you think its 0?
marble bloom
In my head x dominates over cos in some way
Probably some notion I got from previous exercises*
torn jolt
because cos is bounded yeah?
marble bloom
I suppose, yeah
Well, not necessarily. But this probably helps
You helped with with uniformly continuous functions yesterday, we saw that even a bound function can have an "infinitely strong" derivative, so the fact that its bound doesn't necessarily imply dominance in my head, but rather its more probable that x is stronger
Pardon the inaccurate (blatantly wrong?) phrasing, this is my intuitive explanation
Naturally it doesn't make much sense ^^;
I think the actual proof for this would help me most though, and not the intuition behind it
torn jolt
hmm dont overthink it too much, we dont have to deal with derivatives or anything. We have a function that is bounded, and now we multiply it by x which goes to 0. It doesnt matter what exactly cos is doing, as long as we know its bounded the whole thing becomes 0
ok so for the proof
can you explicitely give some bounds for cos(a/x)?
marble bloom
hmm dont overthink it too much, we dont have to deal with derivatives or anythin...
Right, I'm just thinking what would've happened if I had to prove something of the sort in my exam, which emphasizes proper proofs
marble bloom
can you explicitely give some bounds for cos(a/x)?
Yeah sure, 1 and -1
torn jolt
so
-1 ≤ cos(a/x) ≤ 1
marble bloom
Right
torn jolt
can you think of some theorem with limits and inequalities?
marble bloom
Uh... the little sandwich rule
torn jolt
good
marble bloom
good
so
-x ≤ x * cos(a/x) ≤ x
if x-> 0+:
lim(-x) = 0
lim(x) = 0
So sandwich and tada?
torn jolt
correct
marble bloom
Christ
You're a really good teacher you know that?
My exam is next week and you've been extremely helpful*
Tysm! And to Ann as well if they read this
Cheerio~
.close
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long jackal
How can I multiply a vector by quaternion
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How can I multiply a vector by quaternion
long jackal
I know all the rules
Knowing that the quaternarnion isn’t pure, so it’s scalar component is not equal to 0, the result should be a quaternion right?
naive spear
how
naive spear
I know as all absolute values must be >=0 so f(0) = 0 and idk how to continue
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naive spear
<@&286206848099549185>
wonder how do I apply the left and right derivative
or do I even need to do that
torn jolt
i'm not sure at all
First it's continuous because when x goes to 0 x² goes to 0
Then using the definition of differentiable you look at if (f(x)-f(0)) /x has a limit at 0
If it does it's f'(0) so it exists so f is differentiable at 0
lim(f(0+))=limf(0-) so it's continuous at 0 i guess that's what you call left and right derivative?
naive spear
yes
torn jolt
anyway look at the limit of (f(x)-f(0)) /x when x goes to 0 using what you know of the function which is not much
it you find the value that's f'(0)
velvet marlin
This question is sus
torn jolt
well we have to use the only information they gave us on f(x)
vast fossil
Note that -x <= f(x)/x <= x
naive spear
Note that -x <= f(x)/x <= x
because of left and right limit?
torn jolt
wdym
vast fossil
No it's coming from the inequality |f(x)| <= x^2
naive spear
I need some time to digest all of these information
this is just too hard
torn jolt
it's about showing f is continuous at 0 and show f'(0) exists using the definition of f'(0)
vast fossil
$$\abs{f(x)} \le x^2$$
$$-x^2 \le f(x) \le x^2$$
$$-x \le \frac{f(x)}{x} \le x$$
$$\lim_{x\to 0}(-x) \le \lim_{x\to 0}\frac{f(x)}{x} \le \lim_{x\to 0}x$$
$$f^{\prime}(0) = \lim_{x\to 0}\frac{f(x)}{x} = 0$$
naive spear
sandwich rule?
glossy valveBOT
A Lonely Bean
vast fossil
Yes
naive spear
then how do we show that it is differentiable
wait if f'(0) exists that means its differentiable at 0
how did I forget that
then I'm done
.close
rose epoch
full forumBOT
rose epoch
Why are we not accounting for the fact that the value of [sinx] is 1 at x=pi/2 while integrating?
torn jolt
Assuming that you’re looking at someones solution
Its terrible working
Look at a different solution to the question
They make a simple question look very complicated
rose epoch
Could you share it?
rose epoch
My question has to do with the step prior to the integration.
torn jolt
Why are we not accounting for the fact that the value of [sinx] is 1 at x=pi/2 w...
There is no point
You integrate then focus on the limits
rose epoch
Its a greatest integer function?
I mean we wouldn't do that even if it was a modulus.
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@rose epoch Has your question been resolved?
marsh surge
Which is -1
so the solution above is wrong?
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@rose epoch Has your question been resolved?
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@rose epoch Has your question been resolved?
shell pulsar
I'm guessing that [] is the floor function here
wise wyvern
That's right.
You aren't adding [sin(x))] while integrating, you're adding [sin(x)]dx, even if sin(x) value is 1 at some one point, it doesn't matter since it'd be left with mere dx.
While integrating, that's about what you neglect for the integral to work.
shell pulsar
The previous answer is also wrong - it is -pi
wise wyvern
Didn't they write -pi?
shell pulsar
Which is -1
this guy didn't
wise wyvern
Oh, I didn't read anything they wrote. They didn't know it was floor function.
shell pulsar
Yeah that seems likely
wise wyvern
@rose epoch
shell pulsar
If you really want to convince yourself here just do the integral everywhere apart from an epsilon-interval around pi/2 and take it to zero
don't write it ofc just think about it
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slate crypt
Need help
slate crypt
quaint prawn
, rotate
glossy valveBOT
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Available help channel!
lilac cobalt
I get (9x^3-7y^2)^2 but don't know which is A or B in y as the question asks can someone explain it please?
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@lilac cobalt Has your question been resolved?
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@lilac cobalt Has your question been resolved?
thorny horizon
,calc 297
glossy valveBOT
Result:
126
@lilac cobalt Has your question been resolved?
velvet marlin
I get (9x^3-7y^2)^2 but don't know which is A or B in y as the question asks can...
I mean, you got your answer. A = (9x^3 - 7y^2), B = (9x^3 - 7y^2). The only way they distinguished A and B was by saying that the coefficient of y in A was greater than or equal to the coefficient of y in B
rose epoch
You aren't adding [sin(x))] while integrating, you're adding [sin(x)]dx, even if...
What does "left with mere dx" imply? Integration of dx will still yield us x unlike the values from [0,pi/2) which would've yielded us a zero. I was asleep so I apologise for the late reply.. the channel has been closed now so I reckon I need to open a new one?
(My query has been answered below, Thank you for your time and assistance.)
frank grove
,calc 195
glossy valveBOT
Result:
195
,calc 297
glossy valveBOT
Result:
297
,calc 14^3
glossy valveBOT
Result:
2744
,calc 14x + 5 = 30
glossy valveBOT
The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 9)
frank grove
,calc 14x+15 =
glossy valveBOT
The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 8)
frank grove
,calc 14x+15
glossy valveBOT
The following error occured while calculating:
Error: Undefined symbol x
frank grove
,calc 14x+15x
glossy valveBOT
The following error occured while calculating:
Error: Undefined symbol x
frank grove
bro
velvet marlin
Can you not?
velvet marlin
surely there's a bot channel you can do it in
velvet marlin
What does "left with mere dx" imply? Integration of dx will still yield us x unl...
They're basically saying that although your answer is correct, what you've failed to mention in your solution was the integral [sinx] dx from 0 to pi/2 and pi/2 to pi since sinx attains a value of 1 in that situation. Ofc, you might already know why it's 0, but it is better to check and make sure the concepts are clear
rose epoch
They're basically saying that although your answer is correct, what you've faile...
"Ofc, you might already know why it's 0" That was my question.
velvet marlin
"Ofc, you might already know why it's 0" That was my question.
Woops I missed that
velvet marlin
What does "left with mere dx" imply? Integration of dx will still yield us x unl...
Ok so, integration of dx is indeed = x, but consider this:
Let's say I have an integral from 1 to 1.1 of dx. That would be equal to x, which when calculated is 1.1 - 1
Now let's say it's 1 to 1.01. Then it integrates to x, which we then evaluate as 1.01 - 1.
So as Jeeves said, you can now take the limit as a -> 1 of integral 1 to a of dx and you'll find that = 0
In a similar fashion, sinx only attains the value 1 at pi/2 and nowhere else. So you're left with the integral pi/2 to pi/2 1 * dx, which is just 0
torn jolt
hi
tough marsh
brisk obsidian
If you have a math question, just ask your question.
torn jolt
hello I dont have one right now but I might if I do
😂
wht ru doin here
I might need help at some point
brisk obsidian
If you want to just chat, you should do that in #discussion
velvet marlin
#❓how-to-get-help my friend
velvet marlin
This isn't something you can just reserve
torn jolt
This isn't something you can just reserve
oh I did not realise
velvet marlin
Nop
brisk obsidian
No, you open a chat when you need help.
brisk obsidian
.close
slender orbit
tan *( 3x + pi) + 2sin (3x +pi) = 0 find all solutions
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tan *( 3x + pi) + 2sin (3x +pi) = 0 find all solutions
torpid sentinel
full forumBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
tulip raptor
@slender orbit
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@slender orbit Has your question been resolved?
paper lagoon
@tulip raptor Area of complete circle= $\pi\cdot r^{2}$
glossy valveBOT
rino
jade radish
yes
jade radish
okay
paper lagoon
64pie
jade radish
ok
tulip raptor
Correct
paper lagoon
so now what do I do
paper lagoon
its ok
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torn jolt
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sharp flame
$\cos (t) = \cos (-t)$
glossy valveBOT
NEONPerseus
sharp flame
Cosine is an even function
torn jolt
is cos the x value of the angle tho
sharp flame
Sorry didn't understand you
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slender onyx
is cos the x value of the angle tho
visually yes
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✅
torn jolt
if i have cos of 120 degrees
thats quadrant 2
and x is negative
so cos t = cos -t
sharp flame
-120 degrees is in the third quadrant
torn jolt
this would make x negative still
so im thinking this is how to understand it?
cos (positive angle) = -x
then cos (same angle but negative) = still -x
so makes even?
nvm sorry
.close
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sharp flame
Well uh the sign of cosine in what quadrant would depend on the sign of x
Since it's x/hyp
In the graph you showed us
So it's positive in the 1st and 4th quadrants
If that's what you're asking
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torn jolt
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torn jolt
do i memorize the identities
wise wyvern
It was meant to be a question for them, an exercise for them to do. Solution is about the right word. Although not minding English at this point. What is your doubt ed?
wise wyvern
do i memorize the identities
You do. But not all of them.
torn jolt
which one
sharp flame
There are three basic Pythagorean Identities
torn jolt
are these the three i need to memorize
wise wyvern
Ideally the first one is the one you should remember.
torn jolt
oh ok
wise wyvern
Yes, you do get tan in your work much often.
sharp flame
@wise wyvern have we met before
wise wyvern
We have.
wise wyvern
Let me check our dms if there's a conv.
You were doing some circles thingy.
Although that was long ago, it was when I was very active in this server.
sharp flame
Ah I see
wise wyvern
Anyways, I suppose wrong place to dicuss this.
sharp flame
Yup :P
wise wyvern
@torn jolt so anything else you'd like to ask?
wise wyvern
Great.
torn jolt
.close
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sick burrow
Need answer
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Need answer
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As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
sick burrow
nothing
jade radish
are you sure
sick burrow
i got 635
tulip marlin
,,\sqrt[2]{25}+25^2
glossy valveBOT
tulip marlin
did you get this?
sick burrow
yes
jade radish
yeah it is
torn jolt
what is the square root of 25
sick burrow
5 sry
jade radish
okay and what is 25^2
sick burrow
625
jade radish
okay now add them
sick burrow
630
jade radish
there u go
jade radish
u just got 630
jade radish
so u just did it right. if you want, send ur work for the wrong answer and I can point out the mistake
sick burrow
thanks
jade radish
,w sqrt(25)
viral jasper
I totally saw it
jade radish
thanks for reacting to it
viral jasper
jade radish
I was like "wait a minute"
sick burrow
.close
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viral jasper
I had a whole dissertation ready
sick burrow
@jade radish thanks again
viral jasper
tbf, in complex analysis, $x^{1/2}$ is a set of solutions
glossy valveBOT
SWR
jade radish
yuh
safe trench
Pretend we never
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dense edge
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dense edge
At this point I get stuck on what to do next.. nothing else can be done?
if I plug in 0 I will get undefined
devout valley
Wait, what's the function you're dealing with?
dense edge
devout valley
You forgor the other 3
dense edge
damn you're right
jade radish
he forgor 💀
weren't actually needed 
dense edge
for the first function you mean? f(x+h)
it's not needed because no sign out front
second f(x) is needed with brackets
because - in front of that one
devout valley
Should be either:
$$
\frac{\sqrt{9 + h} + 3 - (\sqrt{9} + 3)}{h}
$$
or
$$
\frac{\sqrt{9 + h} + 3 - \sqrt{9} - 3}{h}
$$
glossy valveBOT
chartbit
devout valley
Cool, then that expands to the bottom one
safe trench
This is what happens when you run too much and do math
devout valley
what is the reason for even doing this first way?
As in the first principles way? They're just being mean a bit 
safe trench
For learning
devout valley
But really, it's just to give you a flavour of how to do these things, and e.g. the power rule comes from first principles to begin with
dense edge
pointless fills up space
if it's not even used
dense edge
But really, it's just to give you a flavour of how to do these things, and e.g. ...
If I want flavour I will go to the ice cream shop
devout valley
Like a lot of the time you don't need to do things from first principles anyway because you prove a general result with them that saves you time
dense edge
https://tenor.com/view/ice-cream-ice-cream-cone-lick-gif-26189762
How I feel after every day with math
dense edge
Like a lot of the time you don't need to do things from first principles anyway ...
remind me again, is it pascal's triangle that provides the shortcut method?
i know it helps with binomial expansion. say (a+b)^3, according to pascal's triangle it's 1331 so I expand accordingly
but for derivatives I can't remember why the power becomes a constant and the exponent subtracts by 1
devout valley
Erm, you can use the binomial expansion to prove that the derivative of $x^{n}$ is $n x^{n-1}$ for positive integer $n$
glossy valveBOT
chartbit
hot herald
derivative rules come from first principles
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thorn fjord
How do I graph the following polar curves?
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How do I graph the following polar curves?
thorn fjord
Examples on yt have more basic equations and dont use fractions :\
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@thorn fjord Has your question been resolved?
thorn fjord
torn jolt
How do I graph the following polar curves?
just like normal functions just that you use angle and radius
if you’re not sure id suggest to play around with desmos, it helps you understand better
in desmos you use r(θ) =
thorn fjord
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rugged harbor
👋 Hi! I'm having a hard time solving this:
x¹⁰ - x⁸ + 8x⁶ - 24x⁴ + 32x² - 48 = 0
I was trying to use ruffini's rule to factorize, but I can't find any zeros
Feel free to suggest any other method
vast fossil
Rational root theorem?
I have to go
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grave elm
Rational root theorem?
Sadly it doesn't have rational roots.
grave elm
You could at least simplify it by substituting u instead of x^2
vast fossil
Cya
grave elm
Bye
atomic blade
👋 Hi! I'm having a hard time solving this:
x¹⁰ - x⁸ + 8x⁶ - 24x⁴ + 32x² - 48 =...
Graph
vast fossil
Yeah x^5 - x^4 + 8x^3 - 24x^2 + 32x - 48 does have a rational root
vast fossil
I don't think a human sees the factorisation immediately
vast fossil
,w divide x^10 - x^8 + 8x^6 - 24x^4 + 32x^2 - 48 by x - 2
glossy valveBOT
sharp flame
,w divide x^10 - x^8 + 8x^6 - 24x^4 + 32x^2 - 48 by x^2 - 2
vast fossil
Ah mb
glossy valveBOT
NEONPerseus
sharp flame
ugly ass constant term fucks everything up
vast fossil
How would we prove x^4 + x^3 + x^2 - 4x + 24 has no real solutions
sharp flame
How would we prove x^4 + x^3 + x^2 - 4x + 24 has no real solutions
derivatives? :/
vast fossil
I expected inequalities but sure
sharp flame
,w graph x^8 + x^6 + x^4 - 4x^2 + 24
glossy valveBOT
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atomic blade
Find minimum and IVT :kek:
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Find minimum and IVT :kek:
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sharp flame
.coose
atomic blade
I hate you
vast fossil
The bot?
vast fossil
Ah
worthy tree
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torn jolt
Hey
torn jolt
This is correct right?
You cant divide 1 by 0 though right ?
Im confused why its especially equal to infinite
torn jolt
x approaches 0
But if it approaches it, why is the solution = infinite ?
torn jolt
What about this then, in this video it shows infinite for the part with 1/x
For x-> 0
clear lily
1/x does not approach infinity as x goes to 0
1/x approaches infinity as x goes to 0+
torn jolt
1/x approaches infinity as x goes to 0+
Are you saying the video has a mistake basically?
clear lily
yes
its sloppy
they should say 0+
but since there's an ln in the limit its kind of implied
they should still say 0+ though
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rustic briar
How to make a pyramid (2d or 3d) with 135 boxes and none left over? I tried 4 types, none worked
dim compass
How to make a pyramid (2d or 3d) with 135 boxes and none left over? I tried 4 ty...
What kind of pyramid, there are many types: sq pyramid, triangular pyramid, etc
dim compass
Then your surface of pyramid is square, cool
Just wanted to ask that, thank you..I hope help will arrive you soon!
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rustic briar
How to make a pyramid (2d or 3d) with 135 boxes and none left over? I tried 4 types, none worked
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strong prism
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strong prism
i dont get how they got 4+a = 7 and 4+2a+b=6
i mean one thing i saw that was common which was b = b and c = c
but i was wondering if you could do that
atomic blade
You can
glacial pasture
they just factorised the x terms and constants
strong prism
so say
glacial pasture
-collecting like terms
strong prism
if it was like ax^2 + rest of the equation = 7x^2 +rest of the equation
to find the a
i make a= a?
so x = 7?
atomic blade
You could
strong prism
oh.
atomic blade
Assuming that "the rest" of the equation has no other x^2 terms
glacial pasture
it will work with any degree polynomial that are equal to eachother
doesnt matter if the degree is the same for each one
vague yew
How to I change the index of recursive relation like this to be in terms of its previous terms?aka from n + 1 to n -1?
vague yew
Do I just put n in place of n + 1 and n - 1 in place of n?
glacial pasture
wdym by that do you want 3a(n)-4a(n-1)=0?
vague yew
Yes
vague yew
Do I just put n in place of n + 1 and n - 1 in place of n?
I just wanted make sure of this
glacial pasture
yeah that works fine just be consistent
fallow obsidian
how to solve
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how to solve
fallow obsidian
i know derivative of a = v(t)
native flicker
Integrate acceleration function to get velocity function , integrate velocity function to get distance function
quaint prawn
prey
native flicker
- acceleration is given as a=v+1, so we integrate both sides wrt time .
- it is given that the particle is at rest initially , so v = 0, t=0. Sub these values into the velocity equation found in 1)
- we know that s=0 when t = 0, so sub those values into the distance eqn , where u will find the distance function
- To find the distance travelled in the first 5 seconds, we need to evaluate this equation at t = 5. Since no value for the acceleration is given , we can't find a numerical answer, but you can give an expression instead
barren iris
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barren iris
Anyone see where I'm going wrong?
oh
already found it
I wrote the problem down wrong
9 is under the root!
oof
misty birch
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misty birch
have an idea
but i need a second opinion or solution
because mine feels incorrect
this is a proof and i do know i can square and get x-3 = 1
but
any ideas or solutions
would be welcome
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misty birch
There's definitely one value that doesn't work
of course
2-3 = -1
4-3 = 1
so 4 is the only one that works
brisk trench
Isnt it every R except 4? Its a wild guess
misty birch
but for the actual "why" part im lost
brisk trench
I mean 2 and 4 are the only real solutions to thr first equation and 2 isnt a solution to the second
misty birch
yeah i got that too
atomic blade
4 makes it true
misty birch
hence the rest are false?
brisk trench
Uft?
atomic blade
Logically yeah. Idk how vigorous it needs to be
tough bolt
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tough bolt
how they get 2y here
hot herald
antiderivative of 2
limber berry
Hello I would like to make sure I set this question up correctly.
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limber berry
<@&286206848099549185>
torn jolt
do u have an image of the graph
quaint prawn
I can tell you right now that your bounds are probably incorrect
you have your integral with respect to x
from 0 to 2
but the question wants from y=0 to y=2
so you can plug those into your formula for x to change your bounds to the proper numbers
limber berry
so bounds are sqrt(9) and sqrt(5) @quaint prawn
limber berry
do u have an image of the graph
No graphs are allowed to be used in assignment lecture
I am confused because it is dx but my notes say over y-axis should be dx
quaint prawn
if you are supposed to use this method yes
limber berry
so this would work if there is both y and dx ?
I think I should find y as a fucntion of x
then take the sqrt(1+f'(x)^2) that way?
@quaint prawn
<@&286206848099549185>
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barren iris
For questions like this, is this really all I need to do?
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For questions like this, is this really all I need to do?
barren iris
I can see I don't need to do direct substitution
And factoring either of them won't do anything.
From what I recall and what I've gathered from Paul's notes online, this looks like what I'm supposed to do
Mainly just think about the behavior.
limber berry
No plug in 7.9 then 7.99 then 7.999 on a calculor. Make a table
unless you know the more advanced rules Thats all you do.
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@barren iris Has your question been resolved?
barren iris
unless you know the more advanced rules Thats all you do.
I recall my professor doing that earlier.
He called it the table method
Problem though, we aren't allowed a calculator.
Is there anything else I can do?
limber berry
plug in 6 and 7
what number it SEEM to approach?
Since the numerator is positive and the denominator
x
2
−
64
approaches zero and is less than zero for
x
near
8
to the left, the function decreases without bound.
−
∞
so yeah you are right
but you have to show that as x approches 8 the value gets closer to -0
and 1/small neg number is -inf
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gentle smelt
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half inlet
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fast peak
what is the question?
onyx glen
"i want somebody to solve this for me and not have to do shit myself"
half inlet
what is the question?
I have to resolve the factorized equation, I've done most of the other ones but this one I have no idea how to do it 🤷♂️
half inlet
"i want somebody to solve this for me and not have to do shit myself"
bit rude just asking for some help
fast peak
you just put a picture and nothing more
onyx glen
apologies
fast peak
what exactly do you mean with resolve
half inlet
dw
onyx glen
force of habit, given that a lot of people just post questions here with no further commentary.
onyx glen
I have to resolve the factorized equation, I've done most of the other ones but ...
so you know the zero product property, yes?
half inlet
what exactly do you mean with resolve
I need to find the value of x
half inlet
so you know the zero product property, yes?
no
onyx glen
but you have solved equations by factorization before.
either you actually do know the zero product property or you are going through the motions with no understanding
half inlet
I would just factor out the common term for most
onyx glen
a * b = 0 if and only if (a = 0 or b = 0)
you know this, yes?
half inlet
yeah
onyx glen
thats the zero product property.
here you simply have more factors
$4x^2 (x+1)^2 (x-2) = 0 \iff [4x^2 = 0 \text{ or } (x+1)^2 = 0 \text{ or } x-2 = 0]$
glossy valveBOT
Ann
elder bobcat
And after that what we suppose to do ?
half inlet
so either 4x^2 is =0 or (x+1)^2*(X-2) is 0, right?
onyx glen
well if you want to adhere strictly to the 2-factor version then sure.
onyx glen
well, you insisted on saying "either 4x^2 is 0 or (x+1)^2 (x-2) is 0" instead of breaking it down all the way immediately.
half inlet
break it down by multiplying 4x2 by the parenthesis?
onyx glen
no...
half inlet
oooh the ^2?
OOOOH
okay so uh
I am not the brightest
but I got a quadratic equation for the first one and x=2 for the second one
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inland snow
why is the limit taking to infinity?
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why is the limit taking to infinity?
inland snow
originial document: https://research-repository.griffith.edu.au/bitstream/handle/10072/58722/88799_1.pdf?sequence=1 if you need some more context
stable plover
looks like a riemann sum-like process