Idk if this breaks the rules
#help-19
final grove
waxen talon
alr i see
where do you start?
also you need the condition to start off
it's when the denominators are different from 0
final grove
it's when the denominators are different from 0
Is it correct?
final grove
Okay, I haven't learned that, yet
waxen talon
well
so to get the domain restriction
you need some kind of conditions that the denominator that are different from 0
in this case $x^2 - 4$ and $x^2 - 2x$
clever fjordBOT
1 divided by 0 equals Infinity
waxen talon
both of them needs to be different from 0
also i think you are wrong right from the first step?
because $x^2 - 2x \neq (x + 1)(x + 2)$
clever fjordBOT
1 divided by 0 equals Infinity
final grove
also i think you are wrong right from the first step?
I am on like the 8th grade
waxen talon
you should check the second fraction on your first step
the denominator is wrong
you should fix it
final grove
Okie
waxen talon
ping me when you have your updated answer
final grove
ping me when you have your updated answer
To tell you the truth: I didn't understand anything you said. I have been anxious, trying get to atleast the perfect answer. I thought I got it right until asked yall and used a calculator. My mind is exhausted. I should just do the other paper
waxen talon
To tell you the truth: I didn't understand anything you said. I have been anxiou...
wdym?
you don't need to focus on what i said yet
because you haven't learned it right?
final grove
Most likely...
waxen talon
but i know that your first step is wrong
because $x^2 - 2x$ is not equal to $(x + 1)(x + 2)$
clever fjordBOT
1 divided by 0 equals Infinity
final grove
because $x^2 - 2x$ is not equal to $(x + 1)(x + 2)$
Iirc, I was factoring
Although I think you know that. Right?
clever fjordBOT
1 divided by 0 equals Infinity
clever fjordBOT
1 divided by 0 equals Infinity
final grove
Thanks for helping but I might just ask my teacher. Its possible that I don't need to get the perfect answer. Just that I tried my best with my understanding. End of the thread.
sturdy cape
To tell you the truth: I didn't understand anything you said. I have been anxiou...
This isn't a calculator issue - you just haven't factorised x^2 -2x correctly
broken snow
I need help answering number 1 using mathematical induction, i became stuck on n = k + 1 due to not knowing what to do
graceful viper
try for n=k+1 and plug in your induction hypothesis
can u write down a general expression for what happens when n=k+1?
broken snow
Not sure but I'll try
crystal charm
generally you want to also try to get the expression equal to when you substitute k + 1 into the expression from n = k
broken snow
Yeah that's what I've been doing but keep getting stuck after, I'll update once I get stuck rq
I got stuck here rn, idk what to do here (srry for bad handwriting)
broken snow
Do i like, turn (2(k+1)-1)² to
(2k+1)²
(2k+1)(2k+1)
4k² +4k +1?
broken snow
then just take common
Common?
solemn zenith
lcm
solemn zenith
yea?
broken snow
Not in my math knowledge knows about that, but I'm willing to discover
broken snow
Yeah, and when the denominator is the same which is 3, it prioritizes the numerator
solemn zenith
yes
broken snow
Continuing with the left side, do i simplify
k(2k-1)(2k+1) to get
(2k²-k)(2k+1)
And then do foil?
There's something I've done wrong there i feel it
solemn zenith
Continuing with the left side, do i simplify
k(2k-1)(2k+1) to get
(2k²-k)(2k+1)
...
yes
solemn zenith
There's something I've done wrong there i feel it
ig not
broken snow
ig not
Literally, i feel like something i did there is wrong like do i substitute k to both like:
k(2k-1)(2k+1)
k(2k²-k)(2k²+k)
solemn zenith
Literally, i feel like something i did there is wrong like do i substitute k to ...
no
i mean
if u have any doubts
then just simplify the brackets and multiply lastly by k
broken snow
then just simplify the brackets and multiply lastly by k
How do i do that?
solemn zenith
Literally, i feel like something i did there is wrong like do i substitute k to ...
what
simplify the brackets?
broken snow
Yeah
solemn zenith
(2k x 2k + 2k x 1 -1 x 2k -1 x 1)k
broken snow
I got to here
broken snow
Ah, wait wait lemme solve it rq
broken snow
Wait I'm not done rq
solemn zenith
alr
broken snow
Now what's next
broken snow
u forgot to multiply (4b^2 + 4b +1) by 3
💀 can't believe that joke from school told me i write k like the number 6 or b but, nope
I didn't multiply it to 3
solemn zenith
lmao
broken snow
u forgot to multiply (4b^2 + 4b +1) by 3
All terms multiplied to 3?
💀 one of those things i can't properly read
solemn zenith
bru
solemn zenith
💀 one of those things i can't properly read
lemme re do
solemn zenith
All terms multiplied to 3?
$\frac{k(2k-1)(2k+1)}{3} + \frac{3(2k+1)^2}{3} = \frac{(2k+1)[k(2k-1) + 3(2k+1)]}{3}$
clever fjordBOT
dexa.cld
solemn zenith
$\frac{(2k+1)(k+1)(2k+3)}{3}$
clever fjordBOT
dexa.cld
broken snow
**dexa.cld**
My first question is where did 3(2k+1) come from
solemn zenith
My first question is where did 3(2k+1) come from
ahhh
u know
3/3 =1
to make denominator same we multiply the needed number in both numerator and denominator
we make denominator same so we can add numerators
broken snow
**dexa.cld**
This is the right side but mine is (k+1)(2k+1)(2k+3)
3(2k+1)²
(6k+6)²
(36k²+36)?
solemn zenith
what grade are u
broken snow
what grade are u
11th
broken snow
I'm way too confused 😭
solemn zenith
I'm way too confused 😭
ok
simply
we know
$\frac{a}{b} + c = $\frac{(a+bc)}{b}$
bruuuu
aaaaaaaah
clever fjordBOT
dexa.cld
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
solemn zenith
this is everything
solemn zenith
This is the right side but mine is (k+1)(2k+1)(2k+3)
3(2k+1)²
(6k+6)²
(36k²+36)...
remember BODMAS
broken snow
remember BODMAS
Sure, I'll try and use it
broken snow
**dexa.cld**
Compile Error! Click the <:errors:504266556054962196> reaction for ...
I'll save this and try to figure out
But thx!
clever fjordBOT
solemn zenith
i am kinda in a halfconscious state so
i am sorry if i wasnt able to help
if needed help
Ping
broken snow
It's fine but, you still helped nonetheless, you can close this ticket now and i may return if i need assistance for another time, thx
broken snow
.close
odd edgeBOT
odd edgeBOT
Available help channel!
tired pecan
@exotic bobcat
odd edgeBOT
<@683806305730953258>
crystal charm
!nopings
odd edgeBOT
Please do not ping individual helpers unprompted.
odd edgeBOT
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.
@tired pecan Has your question been resolved?
lone elbow
odd edgeBOT
lone elbow
can someone help me prove the right direction
modern sundial
I'm not sure what part of the right direction is confusing you if you could already do the left
lone elbow
I havent done the left
I was starting out with the right, because I wanted to try that first
is left direction easier?
modern sundial
Well, start by taking an element in the right and breaking down what each symbol means for that element
lone elbow
Well, start by taking an element in the right and breaking down what each symbol...
does this convince you ? @modern sundial
modern sundial
What is that contradicting
lone elbow
What is that contradicting
we are assuming that x1 is in AnB
so x1 is in A and is in B
if x is not in (AxC)n(BxC) then x1 is notg in A and x1 is not in B
modern sundial
Yeah that seems fine
modern sundial
I had a moment there, I shouldn't have needed you to repeat
lone elbow
yeah, my proof is not clear enough I think\
glossy basin
"and x2 does not belong to C" is wrong.
if x1 does not belong to A and x2 belong to C, still we can say x does not belong to (AxC)n(BxC)
modern sundial
I mean, you could clean it up by specifying what you mean by x1 and x2. You are forcing the reader to read between the lines and fill in the fact that x = (x1,x2), since you are now simultaneously assuming that x is in one set and x is in another set, the readability goes down. But the main idea is fine.
lone elbow
if x1 does not belong to A and x2 belong to C, still we can say x does not belon...
wdym
modern sundial
if x1 does not belong to A and x2 belong to C, still we can say x does not belon...
I missed that, but mostly because I think a contradiction is a round about way of doing it rather than a direct proof. You do need to address this.
It is probably easier if you make a simple example, like look at AxC where A = {1} and C = {2}. The element (1,2) is an element of AxC, but the element (1,3) is not an element of AxC.
lone elbow
I mean, you could clean it up by specifying what you mean by x1 and x2. You are ...
$(A \cap B) \cross C \subseteq (A \cross C) \cap (B \cross C)\\$ Assume, $x_1 \in (A \cap B)$ and $x_2 \in C$, $\$then $x_1 \in A$ , $x_1 \in B$ and $x_2 \in C\$ Now, suppose $(x_1, x_2) \notin (A \cross C) \cap (B \cross C)\$ then $x_1 \notin A, x_2 \notin C$ and $x_1 \notin B, x_2 \notin C\$ Thus, we get a contradiction of our assumption that $\x_1 \in (A \cap B)$ and $x_2 \in C$
lone elbow
I missed that, but mostly because I think a contradiction is a round about way o...
wdym?
clever fjordBOT
Renato
lone elbow
It is probably easier if you make a simple example, like look at AxC where A = {...
what about it?
I dont understand :(
modern sundial
The point that Shubham already said is that it is not $x_1 \not\in A$ and $x_2 \not\in C$, it is $x1\not\in A$ or $x_2 \not\in C$, and similarly for the second part.
clever fjordBOT
JessicaK
modern sundial
It is probably easier if you make a simple example, like look at AxC where A = {...
.
lone elbow
wait a second
AxC = {(x,y) : x in A, y in C}
both need to happen, x in A and y in C
modern sundial
Yes, and if an element is not a member of AxC, then one of those statements, x in A or y in C is not true
lone elbow
ahh so if x is not in AxC then either x1 not in A or x2 not in C
lone elbow
Yes, and if an element is not a member of AxC, then one of those statements, x i...
yes, or both of them yeah
modern sundial
yeah
lone elbow
so I need to fix that, things will get harder then
$(A \cap B) \cross C \subseteq (A \cross C) \cap (B \cross C)\\$Take, $x_1 \in (A \cap B)$ and $x_2 \in C$, $\$then $x_1 \in A$ , $x_1 \in B$ and $x_2 \in C\$ Then, if $x_1 \in A$ and $x_2 \in C$ then $\(x_1, x_2) \in (A \cross C)$
modern sundial
It doesn't really get harder, but at no point do you ever really explain what the contradiction is.
You established that x1 must be a member of A and it must be a member of B, and that x2 must be a member of C. So now just show that an element that satisfies those three things must be a member of AxC and it must be a member of BxC.
lone elbow
You established that x1 must be a member of A and it must be a member of B, and...
so no proof by contradition then?
modern sundial
I personally find when people do things by contradiction that doesn't really need to be done this way, it is somewhat of a pain because you have to keep track of all these extra "nots" everywhere.
You can if you want, I am just restating that it is strategically not advantageous
lone elbow
You established that x1 must be a member of A and it must be a member of B, and...
is hard
modern sundial
Part of practice is going down both paths and seeing when one way is more cumbersome than the other.
lone elbow
Part of practice is going down both paths and seeing when one way is more cumber...
now that I think about it
if x in AxC then x1 in A and x2 in C
$(A \cap B) \cross C \subseteq (A \cross C) \cap (B \cross C)\\$Take, $x = (x_1, x_2) \in (A \cap B) \cross C\$ then it follows $x_1 \in (A \cap B)$, $x_2 \in C$, $\$then $x_1 \in A$ , $x_1 \in B$ and $x_2 \in C\$ If $x_1 \in A$ and $x_2 \in C$ then $\(x_1, x_2) \in (A \cross C)\$ Similarly, since $x_1 \in B$ and $x_2 \in C$, then $\ (x_1,x_2) \in (B \cross C)\$ We conclude $\(x_1, x_2) \in (A \cross C) \cap (B \cross C)$
modern sundial
You still have to write a line to show you understand that means (x1,x2) is in both of those sets but yeah
clever fjordBOT
Renato
lone elbow
You still have to write a line to show you understand that means (x1,x2) is in b...
this is good enough?
we showed an arbitrary element in (AnB)xC is in (AxC)n(BxC)
@glossy basin
lone elbow
let me try to prove the other direction
glossy basin
u can rewrite your previous proof as
Assume (x1, x2) in (AnB)xC, then x1 in A, x1 in B and x2 in C.
Now, suppose (x1, x2) not in (AxC)n(BxC), then either x1 not in A or x1 not in B or x2 not in C.
But we know x1 in A, x1 in B and x2 in C for all (x1, x2) in (AnB)xC.
Thus, there exists no (x1, x2) in (AnB)xC which is not in (AxC)n(BxC).
Hence (AnB)xC is subset of (AxC)n(BxC).
But with this, you might need to prove the other way around as well.
lone elbow
I appreciate it, but as jessica said, doing a proof by contradiction is overcomplicating things
lone elbow
$(A \cross C) \cap (B \cross C) \subseteq (A \cap B) \cross C \\$ Take, $x = (x_1, x_2) \in (A \cross C) \cap (B \cross C)\$ then $x_1 \in A, x_2 \in C, x_1 \in B, x_2 \in C\$ And so, $x_1 \in (A \cap B)$, $x_2 \in C\$ And thus, we conclude $(x_1, x_2) \in (A \cap B) \cross C$
clever fjordBOT
Renato
glossy basin
yes looks fine but you can make it better with 1 more step
(x1,x2) in (AxC)n(BxC)
then (x1,x2) in (AxC) and (x1,x2) in (BxC)
→ x1 in A, x2 in C and x1 in B, x2 in C
→ x1 in (AnB), x2 in C
lone elbow
ok
glossy basin
well done
lone elbow
$(A \cross C) \cap (B \cross C) \subseteq (A \cap B) \cross C \\$ Take, $x = (x_1, x_2) \in (A \cross C) \cap (B \cross C)\$ then $(x_1, x_2) \in (A \cross C)$ and $(x_1,x_2) \in (B \cross C)\$ And so, $(x_1 \in A, x_2 \in C)$ and $(x_1 \in B, x_2 \in C)\$
It follows that, $x_1 \in (A \cap B)$, $x_2 \in C\$ And thus, we conclude $(x_1, x_2) \in (A \cap B) \cross C$
clever fjordBOT
Renato
lone elbow
like this dude?
glossy basin
yes
glossy basin
yes I understand, words are better at explaining
odd edgeBOT
odd edgeBOT
Available help channel!
hoary fjord
can someone help me with just like .. anything? i’ve struggled with math since primary school, i believe i have dyscalculia but i’m not sure. i’ve never struggled with any other subjects, just math. i don’t even know my times tables, if anyone has a solution to this please do tell. i’m not self diagnosing with dyscalculia, i just think it’s something to keep in mind. i can’t do basic math sometimes. if this isn’t the right channel or i should post here, please tell me!
stoic cloud
well, you opened a help channel
Is there a direct, singular problem or math question you are dealing with?
hoary fjord
not necessarily, i’m sorry 
crystal charm
can someone help me with just like .. anything? i’ve struggled with math since p...
you should probably get diagnosment if you believe you have dyscalculia
hoary fjord
you should probably get diagnosment if you believe you have dyscalculia
i’m working on that at the moment! ^_^
stoic cloud
not necessarily, i’m sorry <:04_fb_sweat:1352368060949860372>
It’s okay!
gleaming acorn
can someone help me with just like .. anything? i’ve struggled with math since p...
maybe you just never had a good source of teaching, have you tried understanding it or studying it
gleaming acorn
yep
stoic cloud
I learn personally from discussing, but some people like to learn while being active, some like to listen, some like examples
<@&268886789983436800>
gleaming acorn
bru
hoary fjord
maybe you just never had a good source of teaching, have you tried understanding...
i don’t think it’s that at all, i’ve had nearly 40 teachers / tutors combined and nothing works. i’ve tried everything i could and i still don’t grasp simple math. this isn’t an issue with language arts or any other subject, and i even scored the highest in my grade for state testing last year (language arts), it’s only an issue in math for me.
gleaming acorn
i don’t think it’s that at all, i’ve had nearly 40 teachers / tutors combined an...
then your assumption about dyscalculia is probably right
can you say an example w smt you struggle w and we could try explaining it simply
im lowk curious
if you want tho
hoary fjord
hmm, i struggle with a lot of things but the thing i’m most concerned about is fractions / decimals.
(for context : i’m in grade 10, so not knowing something like fractions or decimals is a bit humiliating )
like uh im fine adding & subtracting decimals, but that’s about it
gleaming acorn
(for context : i’m in grade 10, so not knowing something like fractions or decim...
oh dw i just finished 10th grade LOL
gleaming acorn
like uh im fine adding & subtracting decimals, but that’s about it
hmmmmm what exactly don’t you get
division ?
merry finch
hmm, i struggle with a lot of things but the thing i’m most concerned about is f...
Practice!
hoary fjord
division ?
yeah, i think i understand multiplication okay enough, but division is really tricky
merry finch
Division of fractions is just flip the second thing upside down
hoary fjord
what ..
gleaming acorn
she means decimals
merry finch
${a \over b} \div {c \over d} = {a \over b} \times {d \over c}$
hoary fjord
she means decimals
-# he*
hoary fjord
no worries ^_^
clever fjordBOT
frosst
merry finch
Division of decimals is put it in a calculator
gleaming acorn
Division of decimals is put it in a calculator
sometimes you don’t got a calc tho
hoary fjord
Division of decimals is put it in a calculator
-# that’s not necessarily an option for me
gleaming acorn
the trick is to multiply by 10
merry finch
Well, division of decimals is very hard
But we do know how to divide fractions
So we need to learn how to turn decimals into fractions
Then we know how to divide them
hoary fjord
yeah
gleaming acorn
For the basic decimal division just multiply 10
merry finch
Then practice your basic fundamentals first!!
hoary fjord
For the basic decimal division just multiply 10
wdym?
gleaming acorn
4.5 : 1.5 then make it 45 : 15 and that is 3
merry finch
Don’t try to learn more advanced stuff without getting the basics down pat
hoary fjord
Don’t try to learn more advanced stuff without getting the basics down pat
that’s not an option for me, i have my decimals pretest tomorrow and then my actual test on monday
hoary fjord
4.5 : 1.5 then make it 45 : 15 and that is 3
oh!!
merry finch
Your test is not the end of the world
gleaming acorn
he wants to do his best!
merry finch
If you fail this next test because you’re preparing your fundamentals to do better in the future, that’s fine
hoary fjord
if i don’t pass this test, i may get kicked off my hockey team, i want to get at least a basic understanding
merry finch
It’s not ideal if you’re behind to just keep slapping Band-Aid fixes one after another
Anyway then, the point aboit 4.5/1.5 is that we can multiply this fraction by 1 and it’s the same
${4.5 \over 1.5} = {4.5 \over 1.5} \times 1 = {4.5 \over 1.5} \times {10 \over 10} = {4.5\times 10 \over 1.5\times 10} = {45 \over 15} = 3$
clever fjordBOT
frosst
merry finch
Here I’m just rewriting 1 as 10/10
Then sending each part to the top and bottom to “get rid” of the decimals
If you have more decimals like ${6.25 \over 1.25}$ then you multiply the top and bottom by 100 instead
clever fjordBOT
frosst
hoary fjord
.close
odd edgeBOT
odd edgeBOT
Available help channel!
noble oasis
How is this 3?
odd edgeBOT
How is this 3?
pastel orbit
How is this 3?
factor 3 out from the numerator, and use the fact that |4 - x| = -(4 - x) when x > 4
noble oasis
factor 3 out from the numerator, and use the fact that |4 - x| = -(4 - x) when x...
Why are they equal when x>4, is that because -(4 - x) would have x be greater than the 4 and then do a double positive?
pastel orbit
Why are they equal when x>4, is that because -(4 - x) would have x be greater th...
|x| is defined to equal x when x > 0, and -x when x < 0
replace x with 4 - x in this situation, and you have that |4- x| = 4 - x when 4 - x > 0 i.e. 4 > x, and |4 - x| = -(4 - x) when 4 - x < 0, i.e. when 4 < x
and when we're considering the limit x -> 4+, that means that we're looking at the limit as x approaches 4 from above, i.e. x > 4
noble oasis
.close
odd edgeBOT
odd edgeBOT
Available help channel!
low mesa
How do I simplify #19? So far I have y= 3+sqr-x^2 but its wrong on desmos
unkempt lichen
i think you can try completing the square
cursive hollow
How do I simplify #19? So far I have y= 3+sqr-x^2 but its wrong on desmos
you can't distribute a square root like that
for instance, sqrt(1+1) = sqrt(1)+sqrt(1) = 2
but sqrt(2) < 2
try squaring both sides and see if that equation is familiar
unkempt lichen
I don't know how to graph imaginary numbers
why do you need to? you can cleanly factor the quadratic inside
are you asked to graph or simplify?
unkempt lichen
I don't know how to graph imaginary numbers
then why this response. i was of the idea i am giving you a way to simplify
anyway
low mesa
oh mb
unkempt lichen
have you learnt about how to complete the square?
low mesa
no?
unkempt lichen
hm
low mesa
you can't distribute a square root like that
for instance, sqrt(1+1) = sqrt(1)+...
so far using this I have y^2=9-x^2
is that on the right track
ivory raven
yes, move the x^2 to the other side and you might recognise that this is the standard form of something
take care with the square root afterwards though
unkempt lichen
oh that counts as simplification?
ivory raven
well, the question looks like "match the graph to the equation"
I wouldn't call it simplifying though
low mesa
I have y=x+3 now I think something went wrong
unkempt lichen
where did all the squares go?
unkempt lichen
well, the question looks like "match the graph to the equation"
ok now this would make sense and i now see the answer
wanton bison
where did all the squares go?
they got squared
ivory raven
$\sqrt{x^2+y^2}\ne x+y$
unkempt lichen
this is what is meant by "be careful with the square root afterwards"
clever fjordBOT
Desync
unkempt lichen
ivory raven
do you recognise this as the standard form of any geometric shapes?
ivory raven
(x^2+y^2=r^2)
low mesa
I recognize a circle
ivory raven
yes, so this is the equation of a circle
low mesa
I see
ivory raven
but we've added some extra values by squaring the original equation
we originally had $y=\sqrt{9-x^2}$
clever fjordBOT
Desync
ivory raven
are there any values that y can't be?
low mesa
x?
ivory raven
not quite
unkempt lichen
what can't a square root be?
low mesa
undefined?
unkempt lichen
not in the right direction
specifically, what can't a principal square root be?
if you have ever heard of this term
low mesa
not yet
unkempt lichen
fair enough
ok let's look at it this way
when you square a number, what will the result be?
low mesa
that number times itself
unkempt lichen
sure, but what about the sign of the answer?
low mesa
positive
unkempt lichen
that's a key
low mesa
a sqroot cant be inside a sqroot
unkempt lichen
by squaring, no matter if the original number was positive or negative, they all turn positive
low mesa
o
unkempt lichen
a sqroot cant be inside a sqroot
this restriction does not exist, but that's a talk for another day
unkempt lichen
**Desync**
anyway, from here
low mesa
by squaring, no matter if the original number was positive or negative, they all...
yeah thats true
unkempt lichen
you know how we do +/- when we take the square root of both sides?
low mesa
no?
unkempt lichen
oh, hm. guess i'll skip this part then
but the gist of this part is that because both negative and positive numbers square to become positive, when square rooting both sides, you must consider both the positive and negative roots (hence the +/-)
however, here, you are not square rooting both sides. you are given a square root up front
when you are given a direct square root like this, this is, unless otherwise stated, always taken to mean the positive square root
(also known as the principle square root)
low mesa
I see
unkempt lichen
so the square root must be positive, which means y must be...?
low mesa
positive
unkempt lichen
exactly!
low mesa
thats why its half
unkempt lichen
also fyi (other helpers can correct me if i'm wrong)
low mesa
o
unkempt lichen
these kinds of solutions where you introduce extra solutions via an operation like squaring that are NOT valid solutions to the original problem
they are called extraneous
be careful of these
always check against what you are originally given
unkempt lichen
should thank desync more hahah, they sparked the idea in me about what's actually going on
odd edgeBOT
odd edgeBOT
Available help channel!
somber river
odd edgeBOT
feral beacon
@somber river 85th?
somber river
How to do the substitution???
somber river
<@1334809641930068018> 85th?
ya
feral beacon
just put x in the equation, this is the simplest way
somber river
bruh , that will take 10 yrs
amber schooner
did you try solving for x
you’ll something nice
i’m assuming you know complex numbers
somber river
ehhh I don't
amber schooner
eulers formula?
amber schooner
e^{ix} = cos(x) + isin(x)
somber river
Nope no idea
amber schooner
bruh
fluid tundra
$11x^3 + 8x^2 + 8x - 2 = 11(x + 1)^3 - 25x^2 - 25x - 13 = \dotsb$
clever fjordBOT
Mqnic_
fluid tundra
identify (x + 1)^2 = x, etc
somber river
sure
fluid tundra
expand and you get x^2 + x + 1 = 0, yes?
somber river
Ya
somber river
sure
fluid tundra
ok so you can just take this and subtract off instances of x^2 + x + 1 from 11x^3 + 8x^2 + 8x - 2
because A - 0 = A for any A
somber river
okay?
fluid tundra
you want to find 11x^3 + 8x^2 + 8x - 2 so you repeatedly subtract zero
if this makes sense to you then you can solve the problem
x^3 + x^2 + x = 0
x^2 + x + 1 = 0
somber river
yes
amber schooner
that’s nice
odd edgeBOT
@somber river Has your question been resolved?
dreamy totem
how do I start this question..
odd edgeBOT
how do I start this question..
wooden python
try u := e^x if you haven't already.
golden sonnet
let denominator be t, thne differentiate and find the relation b/w dt and dx. now substitute this relation into the original differential, and then integrate
maybe my method id long but i guess it wont be much helpful
whole gyro
let denominator be t, thne differentiate and find the relation b/w dt and dx. no...
no its quite quick actually
whole gyro
well on second look i made a mistake oops
wide oasis
you could write it as $[1 - \frac{e^{2x}}{e^{2x} + 1}]$
whole gyro
its still fast tho
wooden python
you could write it as $[1 - \frac{e^{2x}}{e^{2x} + 1}]$
don't put a space before the last dollar
clever fjordBOT
Prathamesh
wide oasis
don't put a space before the last dollar
thanks
wooden python
@dreamy totem still here or is your internet shitting itself again?
mental swan
is this approach invalid
how did you split it
wooden python
$\int \frac{1}{f(x)} \dd{x} \neq \frac{1}{f'(x)} \ln(f(x))$ in general.
clever fjordBOT
Ann
wooden python
also your substitution was done improperly. you were supposed to work out du/dx and do the integral in terms of u entirely.
so uhhhhhh yeah unfortunately basically none of what you just sent is correct.
@dreamy totem hi are you still alive or what
whole gyro
i can confirm that my method will cook
dont see how it works
wooden python
the integral will become $\int \frac{1}{u(1+u^2)} \dd{u}$ and then you partial-fraction it and it becomes very nice
clever fjordBOT
Ann
whole gyro
bruh its occupied
whole gyro
the integral will become $\int \frac{1}{u(1+u^2)} \dd{u}$ and then you partial-f...
theres a simpler partial fraction if you substitute the entire denominator as dhairya did
wooden python
sure ig
vocal tide
can u answer my question
wooden python
can u answer my question
!occupied
odd edgeBOT
can u answer my question
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
wooden python
take your own channel please
vocal tide
oh sorry
whole gyro
should have been softer eh
wooden python
???
whole gyro
mb
odd edgeBOT
@dreamy totem Has your question been resolved?
keen scroll
How do I simplify #19? So far I have y= 3+sqr-x^2 but its wrong on desmos
am i having osme mental retardisim or
y = sqrt((3-x)**2) = 3-x
narrow crypt
Wrong
keen scroll
wtu
narrow crypt
Also !occupied
narrow crypt
${(a+b)^2 = a^2 + \color{red}{2ab} \color{black}{+ b^2}}$
clever fjordBOT
k
keen scroll
is that for me?
clever fjordBOT
k
inner swift
no its quite quick actually
hi
inner swift
.close
odd edgeBOT
mental swan
In a right angled triangle, the largest side or the hypotenuse is to the opposite of the right angled vertex and base forms the base of the 90 degree vertex and perpendicular is the straight line to the 90 degree vertex (or whatever angle you take except the 90 degree the base of it is the base and the side opposite to it is the perpendicular) so if base is AB, perpendicular BC and hypotenuse AC , AC^2=AB^2+BC^2
mental swan
what is pythagoras theorem
answer to ur question
odd edgeBOT
Available help channel!
icy inlet
how would i go about sketching an angle like 2pi/9 in standard positition?
subtle raft
What angle is 2π/9?
icy inlet
im not sure what your asking
subtle raft
You said you wanted to draw the angle, right?
crystal charm
sounds like you need to use a protractor for that, if you want it accurately
icy inlet
sketch
and i dont think the teacher expects it to be perfect since we cant use one
is it just supposed to be relatively close and obviously inside the proper quadrant?
left violet
probably yeah
subtle raft
Yeah basically
left violet
might be worth trying to split it into thirds, into thirds again, and then counting two
subtle raft
There is a way you can make it with a very high accuracy
oblique wadi
can anyone help me with this:
Evaluate the integral:
∫₀^(π/2) [ (sin³(x)) * arcsin(1 / sin²(x)) ] dx
wooden python
oblique wadi
hello
oblique wadi
no thats the lower limit
wooden python
$\int_0^{\pi/2} \sin^3(x)\arcsin\paren{\frac{1}{\sin^2(x)}}\dd{x}$
clever fjordBOT
Ann
wooden python
is it this
wooden python
are you 100% sure it was written exactly like this
oblique wadi
i am 100% sure this is the question my math teacher gave me
oblique wadi
thats where im confused
south plume
i am 100% sure this is the question my math teacher gave me
photo?
wooden python
well right now we cannot give you anything other than "undefined"
oblique wadi
well right now we cannot give you anything other than "undefined"
undefined or 0?
wooden python
undefined.
oblique wadi
okay
wooden python
but also yes send us a photo of the original question if you have one.
wooden python
and you're 120% sure that you didn't fuck up
south plume
Ah.
wooden python
ok then you are not sure enough
come back when you have a question whose veracity you're certain about
oblique wadi
well my math teacher has less tolerance
its just the way it is
if he finds out that i copied the question wrong, im cooked
anyways ty for helping
.solved
odd edgeBOT
mystic nova
if he finds out that i copied the question wrong, im cooked
Why don't you ask your classmate to send the question
odd edgeBOT
Available help channel!
grand marten
What is implicit defferention
odd edgeBOT
What is implicit defferention
tacit wasp
Differentiating both sides of an equation, without isolating the dependent variable
tacit wasp
Huh?
grand marten
Then
potent nexus
Eg y^3=sinx, then 3y^2 dy/dx = cosx
crystal charm
Means
as an example, imagine you had y + xy + x^2 = x
we would use implicit differentiation for that
potent nexus
Usually it’s when you can’t get it in the form y=f(x)
grand marten
Like
potent nexus
wdym like
grand marten
Ex
grand marten
Ohhh like x and -x
tacit wasp
??
crystal charm
?
grand marten
1/2 sqrt x and -(1/2 sqrt x
tacit wasp
???
crystal charm
no, that's wrong
grand marten
Then
potent nexus
U sure
crystal charm
https://www.youtube.com/watch?v=LGY-DjFsALc&pp=ygUYaW1wbGljaXQgZGlmZmVyZW50aWF0aW9u. learn it from this, about it
grand marten
Yes
tacit wasp
Yes
potent nexus
Alright
tacit wasp
No
potent nexus
(y+xy’)
tacit wasp
sec^2(xy) (xy)’=0?
This is correct @grand marten
potent nexus
(xy)’ would be differentiated using product rule
crystal charm
https://www.youtube.com/watch?v=LGY-DjFsALc&pp=ygUYaW1wbGljaXQgZGlmZmVyZW50aWF0a...
I recommend you watch this video first so you can understand implicit differentiation @grand marten
grand marten
Ok
lament rune
2.b help
wooden python
,rccw
clever fjordBOT
wooden python
!status
odd edgeBOT
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
.close
odd edgeBOT
wooden python
...do you want help or not
reef tartan
you scared him 😭
ivory dock
Bro came in with a question picture and ya'll started rotating it and calling status, scary fr
wooden python
i mean if he doesnt want to get help bc WOW SCARY LADY INTERROGATED ME thats his loss
odd edgeBOT
Available help channel!
left loom
odd edgeBOT
half sleet
i think it would help if you showed/typed the original problem
odd edgeBOT
@left loom Has your question been resolved?
mild rampart
which question number?
left loom
<@1388575253856518236> Has your question been resolved?
No
left loom
which question number?
Everything
mild rampart
i am really sorry but i am not able to interpret this, can you write in better writing please, it will help to solve
left loom
Ok
mild rampart
do you know how to differentiate implicit functions?
left loom
mild rampart
now ok
left loom
do you know how to differentiate implicit functions?
As in chain rule ? Quotient differentiation or like parametric form?
mild rampart
As in chain rule ? Quotient differentiation or like parametric form?
no, can you differentiate x^y - y^x = 0
left loom
Yea with log right
mild rampart
u did lil long
and worry, was doing imp work
take everyhting in RHS
1 = (a^b)/(x^y) + (y^x)/(x^y)
then log on both side
division property of log
then book
u got answer
mention if any otehr help
mild rampart
68 is parameteric form
differentiate wrt t
and manually solve that x + y/x-y
both result will be ok
mild rampart
62 also parameteric form
mild rampart
Is my differentiation crct?
having some doubt, le me solve myself
the formula i told do not hold for implicit function
you will have to do that manually
your substitution way is ok
found one more way without substition or log
odd edgeBOT
@left loom Has your question been resolved?
left loom
No
mystic saffron
odd edgeBOT
fluid tundra
u + x = pi/2
odd edgeBOT
odd edgeBOT
Available help channel!
odd edgeBOT
nocturne belfry
,calc 4 * (3 ^ 5)
clever fjordBOT
Result:
972
@marsh bridge is that a good enough hint
okay
rewrite it like this
$\frac 13 \sqrt[6]{ 4 \cdot 3^5 }$
clever fjordBOT
jan Niku
clever fjordBOT
jan Niku
tacit wasp
$\sqrt[6]{\frac{1}{3}} = \sqrt[6]{\frac{3^5}{3^6}} = \sqrt[6]{\frac{1}{3^6}} \cdot\sqrt[6]{3^5} = \frac{1}{3} \sqrt[6]{3^5}$
clever fjordBOT
Alberto Z.
marsh bridge
Ok but what about with the 4/3
rough birch
If you multiply 2 nth roots, you can take the nth root of the product instead
So if we write 1/3 as an nth root, we can multiply it with the nth root of 972
Oh sorry that’s the opposite of what Alberto did, I’m referring to working with the bottom expression to get to the top one
But it’s a similar logic, we can write the root of 4/3 as the root of 4 * the root of 1/3
And then pull a 1/3 out by doing some rationalizing, which is what Alberto did by manipulating the top and bottom of the fraction under the root
tacit wasp
Exactly
odd edgeBOT
odd edgeBOT
Available help channel!
shy adder
Hi, I just started my analysis pre-requisite class, and it's been a while since I've worked on math problems. Since the material we're working with in class is more advanced than high school level, the course assumes that you already know the "elementary" level stuff but honestly for me I forgot a lot of what I learned a few years ago in high school.
So I'm working on the "Preliminary" unit of our exercise book seen in the appended image. I was able to fairly easily work through problems A, B, C, and D in exercise 1 but in problem E I encountered the -1 exponent and I simply don't remember what it means or how to work with it. I think what I'd need to review are the properties of exponentiation and roots. Later on, I can see, for example in problem h of exercise 1 that I'll be working with the 3rd root? of -27/8 which I'm completely lost on and in problem l I'll be working with fractional exponents.
I'm pretty hazy on all of this, so what I'm looking for is mainly a reference to any online resources or books I can use to review this topic. I'd appreciate if anyone can refer me to one. Thanks!
mortal trench
shy adder
If I were to just say the problem, you wouldn't understand my question. If you don't want to read a question, then don't be in a help channel.
rough birch
i think khan academy would be helpful
it targets a lot of concepts in a focused way
esp for prealgebra style stuff
shy adder
Thanks, yeah I was thinking of going there too. What specific topic would I need to look into for this type of stuff?
in high school they called it properties of exponents and roots but
rough birch
i think u can look up exponents on the website and u will get a lot of stuff
same for roots and factoring
odd edgeBOT
odd edgeBOT
Available help channel!
lone elm
Use Cramer's theorem to investigate the number of solutions to the system of equations depending on the parameter p
px+2y+4z=-6
x-y+pz=3
-px+3z=5
i know i need to use matrix but i have no idea how, i dont know how to solve this and i cant find any info online on problems like this with parametr
lone elm
i also have a second one
px + y + 2z − t = 0
2px − 2y + z + 2t = −9
−3px + y + 2z + 3t = −p
4px + 6y + 7z − 4t = 5
im not sure if they both apply to the same rule
forest sky
what is cramer's theorem?
lone elm
cramers rule? im not sure how its called in english im sorry its my second language
lone elm
yes its that!
lone elm
i also have a second one
px + y + 2z − t = 0
2px − 2y + z + 2t = −9
−3px + y + ...
but also if you know how to solve this in any way it would be helpful. Since this one doesnt state that the cramers rule is requiered
forest sky
is it something like this?
well we can see that cramer's rule gives us exactly one solution, unless D = 0 in which case it fails
odd edgeBOT
@lone elm Has your question been resolved?
lone elm
im sorry but i still dont really understand? i know that d cant be 0 but it doesnt really help me solve this problem, i know how to use cramers rule without the parametr but this question has it in it and probably requieres a different approach
low locust
frozen musk
odd edgeBOT
frozen musk
find radius and interval of convergence
i did ratio test and got lim k to inf (k/(k+1)5^k)|x-1|
limit of the k stuff goes to zero though which surely is wrong
oh
nvm
.close
shy grove
How do I find the angle X?
I encontered similar problems many times, but I've never managed to find the missing angle, even if it is obviously uniquely defined
manic sleet
look at triangle ACB
you can figure out angle ACB by the sum of interior angles of a triangle being 180deg
clever fjordBOT
Result:
108
manic sleet
Great! Now you can write CED in terms of x, how would you go about doing that?
manic sleet
awesome!
just one more fact clears this up
the sum of interior angles of a quadrilateral is...? 
manic sleet
and so a little algebra gets us our answer, we have all the angles at the foru corers
oh wait...
shy grove
and x and -x cancels
shy grove
oh wait...
yeah 😔
manic sleet
yeah I defined that angle in terms of the other, brainfart moment
manic sleet
okay hang on, I gotta take a moment to think about this, geometry problem shouldn't be this hard but I'm kidna rusty 
shy grove
I have a feeling law of cosines is going to work but I tried it before and it didn't
so Ill try again I guess
odd edgeBOT
@shy grove Has your question been resolved?
orchid torrent
Are you sure that this was typed correctly? Because if we let $AB=\sin 108^{\circ}$ without loss of generality, then $AC=\sin 25^{\circ}$ and $BC=\sin 47^{\circ}$. \ \ Hence, by the law of sines again, $CE=\frac{\sin(25^{\circ}) \sin(32^{\circ})}{\sin 76^{\circ}}$ and $CD=\frac{\sin(47^{\circ}) \sin(48^{\circ})}{\sin(60^{\circ})}$. \ \ Bashing with the law of cosines yields $$DE=\sqrt{\left(\left(\frac{\sin(25^\circ)\sin(32^\circ)}{\sin(76^\circ)}\right)^2+\left(\frac{\sin(47^\circ)\sin(48^\circ)}{\sin(60^\circ)}\right)^2-2\times\frac{\sin(25^\circ)\sin(32^\circ)}{\sin(76^\circ)}\times\frac{\sin(47^\circ)\sin(48^\circ)}{\sin(60^\circ)}\cos(108^\circ)\right)}$$
and thus $$x=\arcsin \left(\frac{CE \sin 108^{\circ}}{DE} \right) \approx 17.44^{\circ}$$ which is not a particularly nice number.
clever fjordBOT
Civil Service Pigeon
shy grove
I did just put in random angles
orchid torrent
shy grove
I just want to know how to get the value of x in any way
orchid torrent
well normally you have nice solutions with reflection and/or rotation if the question was designed to be done nicely
but trig bash always works ig
shy grove
but you wouldn't be able to do it that way manually right
orchid torrent
you can do everything until the end decimal conversion by hand
as you see above
if you want to leave it in exact form then you don't need a calculator at all
shy grove
well I suppose that suffices
ngl I totally forgot law of sines existed
thanks for your input 🙏
.close
odd edgeBOT
odd edgeBOT
Available help channel!
waxen goblet
An event has a 1/357 chance to occur, supposedly. In roughly 8000 attempts, the event took place 30 times. Why is this? Just luck? If so, how do you get lucky 30 times in a row?
shy grove
An event has a 1/357 chance to occur, supposedly. In roughly 8000 attempts, the ...
certainly your data is wrong. It'd take on average 10^76 attempts to do it 30 times
odd edgeBOT
@waxen goblet Has your question been resolved?
waxen goblet
certainly your data is wrong. It'd take on average 10^76 attempts to do it 30 ti...
i dont fully understand it. it says if you reach the base chance with attempts, the number is divided by 2. ie 357 => 179. from there if you reach 179, its divided by 3: 179 => 119. reach 119 - divided by 4. 119 => 89. here it stops though
theres other stuff too but very small in comparison
but then it also says this so idrk 
shy grove
but then it also says this so idrk <:pepeshrug:734061079407362150>
huh
what is this about?
shy grove
i dont fully understand it. it says if you reach the base chance with attempts, ...
so if you get it once, the next time is twice as likely, and again and again until the chance gets fixed at 1 in 89?
waxen goblet
so if you get it once, the next time is twice as likely, and again and again unt...
no. the chance is 1/357. if you dont get it within 357 attempts, the chance increases to 1/179. still dont get it and reach 179 attempts (357+179 total), the chance increases again to 1/119. dry streak continues? the chance increases one final time to 1/89
shy grove
oh I see
so after 357 + 179 + 119 attempts, the chance is fixed at 1 in 89 until you get it and it resets to 1 in 357?
waxen goblet
yes exactly
bottom line is on average you should get 1 every 357 attempts, and im wondering why i got 30 in 8000 attempts, 1 in 267 
shy grove
yes exactly
well, even if the base chance was always 1 in 89, it'd still take on average 10^58 attempts to get it 30 times
wait nvm
shy grove
bottom line is on average you **should** get 1 every 357 attempts, and im wonder...
well assuming that you were expected to get it only 22 times
shy grove
statistical anomaly? or is the displayed chance just wrong
it's probably higher than 1 in 357
but it's not that rare to get these rates
using binomial probability distribution it's about 7% to get 30 or more
waxen goblet
makes sense 
when should i expect to approach the average then? 50k? 200k? a million?
shy grove
when should i expect to approach the average then? 50k? 200k? a million?
funny thing: you're always expected to be on average. So you should fail every single try until you get to 10710, which is just 30*357
waxen goblet
funny thing: you're always expected to be on average. So you should fail every s...
lol i see
but whats like a big enough number so that luck should be a non factor
shy grove
lol i see
but whats like a big enough number so that luck should be a non factor
What exactly do you mean by that?
waxen goblet
What exactly do you mean by that?
idk like
ive been lucky on my first 8000 attempts
assuming average rates from now on, how many attempts are needed for this luck to be nothing more than for example 0.1 in 22.409, the mean from earlier
shy grove
$f\left(x\right)=1-\sum_{n=0}^{s-1+\frac{x}{357}}\operatorname{nCr}\left(k+x,n\right)\left(c\right)^{n}\left(1-c\right)^{\left(k-n+x\right)}$
clever fjordBOT
S0FL
shy grove
using that formula, x is the amount of extra tries youre going to do and f(x) is the probability of the whole scenario
wait foods here 1 sec
waxen goblet
occupied
shy grove
idk like
ive been lucky on my first 8000 attempts
assuming average rates from no...
I have a very unsatisfying answer that might be wrong
using that function I calculated that it would take +14 thousand attempts to reach 20%
waxen goblet
using that function I calculated that it would take +14 thousand attempts to rea...
20%?
shy grove
to reach a scenario that has a 20% chance of happening
assuming youre average from 8000 on
desmos is having a bad time
waxen goblet
shy grove
<a:MONKAW:1080463390285246535>
I think the problem here is that you're essentially asking "how big of a perfectly average set of tries do I have to add on top of what I got so that the whole sequence is average", and the answer is infinity
it's like if you had 1 liter of strawberry juice on a pool and wanted to make it so that the pool had 100% water by only adding liters of water
waxen goblet
I think the problem here is that you're essentially asking "how big of a perfect...
yeah
thats why not average but close to
like within 1% maybe?
idk how this works 
shy grove
the actual more likely scenario is that, just as you got very lucky in the first 8000 attempts, some time in the future you'll get very unlucky and things will cancel out
shy grove
yeah
thats why not average but close to
like within 1% maybe?
idk how this works...
within 1% might take millions of perfectly average tries
shy grove
the actual more likely scenario is that, just as you got very lucky in the first...
but ngl, I have no clue how to calculate that
shy grove
within 1% might take millions of perfectly average tries
or quinvigintillions, idk
tight maple
I am utterly and fully lost here
shrewd trellis
this is an indefinite integral right?
is it safe to say we dont need to include the -infinity and +infinty?
warped grove
huh why is this in the available section
shy grove
is it safe to say we dont need to include the -infinity and +infinty?
indefinite just means you don't define the limits. having -∞ and +∞ is defining them
warped grove
.close
odd edgeBOT
shy grove
lmao
warped grove
.reopen
waxen goblet
yeah mb
odd edgeBOT
✅
shy grove
xd
warped grove
okay nickfarmer it's your channel
waxen goblet
i dont need it anymore i just came to close as i remembered
shrewd trellis
mb Ill make a new help channel
shrewd trellis
i dont need it anymore i just came to close as i remembered
oh nvm
waxen goblet
.close
odd edgeBOT
warped grove
okay yea h make another one
odd edgeBOT
Available help channel!
shy grove
$\lim_{a\to\infty}\int_0^{a}f(x)\ dx + \lim_{b\to-\infty}\int_{b}^{0}f(x)\ dx \neq \lim_{a\to\infty}\int_{-a}^{a}f(x)\ dx$
shy grove
what is an example that illustrates this inequality?
clever fjordBOT
S0FL
amber schooner
what is an example that illustrates this inequality?
x
shy grove
hm
frigid canopy
x
That integral doesn't converge though, so would the improper integral even be defined
amber schooner
both integrals would be divergent
amber schooner
That integral doesn't converge though, so would the improper integral even be de...
thats the point
shy grove
both integrals would be divergent
which ones
plush ingot
$\infty - \infty = NaN$ i thought
frigid canopy
which ones
the ones on the left
shy grove
huh
narrow crypt
Indeterminate
clever fjordBOT
Mirror
amber schooner
huh
to make it more clear you can choose a b in terms of a
that doesn't have the same rate in the limiting sense
plush ingot
Indeterminate
indeterminate is NAN tho yeah?
narrow crypt
**Mirror**
Indeterminate form ):
plush ingot
or am i confusing them
shy grove
I can't understand this
i dont get the application of how one indeterminate form is different from the other indeterminate form
narrow crypt
indeterminate is NAN tho yeah?
Ye? I think so?
plush ingot
**S0FL**
what about f(x) = sin x
or something that repeats
that might also diverge tho
narrow crypt
x
Using this
[ \lim_{a \to \infty} \int_0^a x \dd x+ \lim_{b \to -\infty} \int_b^0 x \dd x = \infty - \infty = 0]
clever fjordBOT
k
narrow crypt
Wtf is this
plush ingot
but infty - infty ≠ 0
shy grove
is the inequality ever true for non-indeterminate values on LHS and RHS?
plush ingot
idts because we can just directly substitute
shy grove
so what makes it true is only a lack of formalization of the indeterminate forms? Were we operating on extended hyperreal wtv, would it possibly be false?
shy grove
So \neq is reasonable..
but where did that 0 come from?
amber schooner
is the inequality ever true for non-indeterminate values on LHS and RHS?
yes
amber schooner
consider 1/(1 + x^2)
arctan has horizontal asymptotes of pi/2 and -pi/2
oh wait
no yea that works
$\lim_{a \to -\infty} \int_a^0 \frac{1}{1 + x^2} \dd{x} + \lim_{b \to \infty} \int_0^b \frac{1}{1 + x^2} \dd{x} = \lim_{a \to -\infty}(\arctan 0 - \arctan a) + \lim_{b \to \infty} (\arctan b - \arctan 0)$
clever fjordBOT
knief
amber schooner
you get pi here
and if you instead did lim a to infty with the lower limit being -a and upper limit being a youd get lim a to infty arctan(a) - arctan(-a) = pi
shy grove
is there a command to run wolfram alpha from here
amber schooner
comma w
shy grove
,w Limit[(40)Integrate[(40)Divide[1,1+Power[x,2]](41),{x,0,a}](41),a->∞]+Limit[(40)Integrate[(40)Divide[1,1+Power[x,2]](41),{x,b,0}](41),b->-∞]
clever fjordBOT
Requested by s0fl
shy grove
awesome
,w lim_(a->∞) integral_0^a 1/(1 + x^2) dx + lim_(b->-∞) integral_b^0 1/(1 + x^2) dx
clever fjordBOT
amber schooner
,w \lim_{a \to -\infty} \inta^0 \frac{1}{1 + x^2} \dd{x} + \lim{b \to \infty} \int0^b \frac{1}{1 + x^2} \dd{x}
clever fjordBOT
amber schooner
bruh
shy grove
lol
amber schooner
,w int -inf to inf of 1/(1 + x^2)
clever fjordBOT
amber schooner
maybe they will clarify cauchy principal value if we do x
,w int -inf to inf of x
clever fjordBOT
shy grove
hm
amber schooner
its giving the cauchy principal value
shy grove
,w Limit[ArcTan[0] - ArcTan[a], a -> -Infinity] + Limit[ArcTan[b] - ArcTan[0], b -> -Infinity]
clever fjordBOT
amber schooner
😭
shy grove
why doesnt it work
clever fjordBOT
