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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:28:47
of that RHS
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755
help-10
ab0af503f3a94036abe335a5065d1e08
510,789,298,321,096,700
TeXit
02/18/2022 12:28:55
**Shuri2060**
https://cdn.discordapp.c…119171756033.png
321445119171756033.png
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:29:01
What do you mean 'not include'
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:29:07
I have not missed anything out
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:29:13
The sum of all the terms is the original polynomial
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
466,621,653,514,846,200
sauxing
02/18/2022 12:29:28
Like how do you know to use those three and not the first three
1
0
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help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:29:31
???????????/
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help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:29:32
=================================== A polynomial in one variable (let's say x) consists of terms that are summed together. Each term consists of a single **power of x** multiplied by a **constant**. Different terms consist of different powers of x. The **constant** is known as the coefficient
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help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:29:45
===================================
0
1
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help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:29:50
Understand the definition first before asking.
0
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755
help-10
ab0af503f3a94036abe335a5065d1e08
466,621,653,514,846,200
sauxing
02/18/2022 12:30:01
Ok
1
0
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:30:19
If you still don't understand then I suggest looking up a video/page explaining the same thing to you
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:30:26
you could search up 'what is a polynomial'
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
466,621,653,514,846,200
sauxing
02/18/2022 12:30:33
Okay thanks for your help anyway
1
0
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755
help-10
ab0af503f3a94036abe335a5065d1e08
466,621,653,514,846,200
sauxing
02/18/2022 12:30:55
One last thing
1
0
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755
help-10
ab0af503f3a94036abe335a5065d1e08
466,621,653,514,846,200
sauxing
02/18/2022 12:31:45
@Shuri2060
1
0
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:31:49
Like I am just rephrasing what I know
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1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:31:54
A book will be better
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:31:57
And more precise
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1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
466,621,653,514,846,200
sauxing
02/18/2022 12:32:05
My friend did this. Is it correct
https://cdn.discordapp.c…7330CE0E5BFE.jpg
435E2597-34EA-48DF-A0CF-7330CE0E5BFE.jpg
1
0
null
null
null
null
null
755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:32:20
idk
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:32:27
You should ask them how they did it
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:32:32
If they understand.
0
1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
466,621,653,514,846,200
sauxing
02/18/2022 12:32:40
Can You check to see if he made a mistake
1
0
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755
help-10
ab0af503f3a94036abe335a5065d1e08
321,445,119,171,756,000
Shuri2060
02/18/2022 12:33:07
no.
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1
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755
help-10
ab0af503f3a94036abe335a5065d1e08
466,621,653,514,846,200
sauxing
02/18/2022 12:33:15
Ok fair enough
1
0
null
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null
755
help-10
ab0af503f3a94036abe335a5065d1e08
466,621,653,514,846,200
sauxing
02/18/2022 12:33:21
.close
1
0
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null
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756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:49:00
Can someone explain what I'm missing in this problem? $$\int \frac{\sqrt{1-x^2}}{x}$$ my thought process is to make a trig sub for $$x = \sin(t)$$, then you get $$\int \frac{\sqrt{1-\sin(t)^2}{\sin(t)} = \int \frac{\sqrt{\cos(t)^2}{\sin(t)} = \int \frac{\cos(t)}{\sin(t)} = \ln(\sin(t)) +C = \ln(\sqrt(x))+C I looked ...
1
0
321,445,119,171,756,000
Shuri2060
9525
a μ-er
false
756
help-10
75606f9562f543ceb11e372a92b04abd
510,789,298,321,096,700
TeXit
02/18/2022 12:51:56
**Carl** Compile Error! Click the :errors: reaction for more information. (You may edit your message to recompile.)
https://cdn.discordapp.c…528508952576.png
412086528508952576.png
0
1
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756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:52:56
$$\int \frac{\sqrt{1-x^2}}{x}$$ $$x = \sin(t)$$ $$\int \frac{\sqrt{1-\sin(t)^2}{\sin(t)} = \int \frac{\sqrt{\cos(t)^2}{\sin(t)} = \int \frac{\cos(t)}{\sin(t)} = \ln(\sin(t)) +C = \ln(\sqrt(x))+C$$ $$\sqrt{1-x^{2}}-\left(\operatorname{arctanh}(\sqrt{1-x^{2}})\right)$$
1
0
null
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756
help-10
75606f9562f543ceb11e372a92b04abd
510,789,298,321,096,700
TeXit
02/18/2022 12:52:58
**Carl** ```latex $$\int \frac{\sqrt{1-x^2}}{x}$$ $$x = \sin(t)$$ $$\int \frac{\sqrt{1-\sin(t)^2}{\sin(t)} = \int \frac{\sqrt{\cos(t)^2}{\sin(t)} = \int \frac{\cos(t)}{\sin(t)} = \ln(\sin(t)) +C = \ln(\sqrt(x))+C$$ $$\sqrt{1-x^{2}}-\left(\operatorname{arctanh}(\sqrt{1-x^{2}})\right)$$ ```Compilation error:```! File en...
https://cdn.discordapp.c…528508952576.png
412086528508952576.png
0
1
null
null
null
null
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756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:53:42
$$\int \frac{\sqrt{1-x^2}}{x}$$ $$x = \sin(t)$$ $$\int \frac{\sqrt{1-\sin(t)^2}}{\sin(t)} = \int \frac{\sqrt{\cos(t)^2}}{\sin(t)} = \int \frac{\cos(t)}{\sin(t)} = \ln(\sin(t)) +C = \ln(\sqrt{x})+C$$ $$\sqrt{1-x^{2}}-\left(\operatorname{arctanh}(\sqrt{1-x^{2}})\right)$$
1
0
null
null
null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
510,789,298,321,096,700
TeXit
02/18/2022 12:53:45
**Carl**
https://cdn.discordapp.c…528508952576.png
412086528508952576.png
0
1
null
null
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null
756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:54:39
Well, I guess one error I'm seeing already is that it should be ln(x) not ln(sqrt(x))
1
0
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null
null
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756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:54:41
$\int \frac{\sqrt{1 -x^2}}{x} \dd x$ is your problem?
0
1
null
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null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
510,789,298,321,096,700
TeXit
02/18/2022 12:54:45
**Chromium**
https://cdn.discordapp.c…792763600896.png
701895792763600896.png
0
1
null
null
null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:54:45
Yeah
1
0
null
null
null
null
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756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:55:14
so you used trig sub?
0
1
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756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:55:17
Yeah
1
0
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756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:55:44
hm
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1
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756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:55:48
there's a better way to do it
0
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756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:55:51
are you forced to do trig sub
0
1
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756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:56:29
Yeah, forced to do trig sub. Full disclosure I'm a TA for a calc class I'm working on an example for trig subs. Trying to work through one myself and checking that my results are correct
1
0
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756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:56:57
oh so this is a problem you came up with lol
0
1
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help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:57:20
More or less. I'm taking ideas from their homework
1
0
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756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:57:24
might wanna use $\int \frac{1}{\sqrt{1 - x^2}} \dd x$ instead
0
1
null
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null
756
help-10
75606f9562f543ceb11e372a92b04abd
510,789,298,321,096,700
TeXit
02/18/2022 12:57:27
**Chromium**
https://cdn.discordapp.c…792763600896.png
701895792763600896.png
0
1
null
null
null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:57:33
i don't think there's a way out except for trig sub
0
1
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null
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756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:57:50
(so that you can show its ✨ superiority✨ )
0
1
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756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 12:58:10
?
0
1
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756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 12:58:18
Almost all integrals are not doable by hand
0
1
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help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 12:58:32
If I wrote random numbers/functions it would almost always be impossible
0
1
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756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:58:43
Sure, but I would expect this one to be possible.
1
0
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null
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756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 12:58:46
All integration questions you see are handcrafted so they are possible.
0
1
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756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 12:58:51
By no means is that guaranteed
0
1
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null
756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:58:52
$\int_0^{\infty} \frac{\sin x}{x} \dd x$ :bleak:
0
1
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756
help-10
75606f9562f543ceb11e372a92b04abd
510,789,298,321,096,700
TeXit
02/18/2022 12:58:55
**Chromium**
https://cdn.discordapp.c…792763600896.png
701895792763600896.png
0
1
null
null
null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 12:59:06
You should check in wolfram to see if it is even possible first.
0
1
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help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:59:13
That's exactly what I did
1
0
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756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:59:27
Sorry, i think my first messgae got buried after I tried to fix my TeX
1
0
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756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:59:27
integral-calculator.com does a more specific job imo
0
1
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756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 12:59:43
My problem is that wolfram disagrees with the answer I'd expect to get, and I'm not sure where I'm going wrong
1
0
412,086,528,508,952,600
Carl
8124
Carl
false
756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 12:59:44
free steps
0
1
null
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null
756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 12:59:54
you should compare your answers on desmos
0
1
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null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 12:59:57
to check for equivalence
0
1
null
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null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 13:00:00
Already did
1
0
null
null
null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 13:00:14
sometimes the problem lies in the + C
0
1
null
null
null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 13:00:22
https://cdn.discordapp.c…t_1.00.05_PM.png
Screen_Shot_2022-02-18_at_1.00.05_PM.png
1
0
null
null
null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 13:00:22
The constants of integration are not necessarily the same
0
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null
null
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null
756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 13:00:28
ok, that is different.
0
1
null
null
null
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null
756
help-10
75606f9562f543ceb11e372a92b04abd
701,895,792,763,600,900
s_chanch
02/18/2022 13:00:28
they're referring to differenti constants altogether
0
1
null
null
null
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null
756
help-10
75606f9562f543ceb11e372a92b04abd
321,445,119,171,756,000
Shuri2060
02/18/2022 13:00:49
You can plot each step of your working as well
0
1
null
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null
null
null
756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 13:05:04
Figured it out. I forgot to substitute my 'dx' when I sub'd the 'x'
1
0
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null
756
help-10
75606f9562f543ceb11e372a92b04abd
412,086,528,508,952,600
Carl
02/18/2022 13:07:26
.close
1
0
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null
757
help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:14:10
Hello, I am asked to prove by recurrence this expression
https://cdn.discordapp.c…4336/unknown.png
unknown.png
1
0
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:14:20
Previously we have established that
https://cdn.discordapp.c…3438/unknown.png
unknown.png
1
0
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757
help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:14:36
So in the correction, the recurrence passes by this formula but I struggle to understand why
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:14:45
https://cdn.discordapp.c…2984/unknown.png
unknown.png
1
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:15:26
Because technically, here the recurrence happens every 2 steps, right? My question is, how can we use 2n-1 instead of 2n to establish recurrence, I thought that was illegal
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help-10
3f9a2167445444539ec2b9d0789fe337
474,549,305,777,061,900
Euler2
11/07/2021 10:18:11
What’s your concern?
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help-10
3f9a2167445444539ec2b9d0789fe337
474,549,305,777,061,900
Euler2
11/07/2021 10:18:34
The even terms of the sequence are redundant
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help-10
3f9a2167445444539ec2b9d0789fe337
474,549,305,777,061,900
Euler2
11/07/2021 10:19:09
If you know the first term, you know the third, then you know the 5th and so on
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help-10
3f9a2167445444539ec2b9d0789fe337
474,549,305,777,061,900
Euler2
11/07/2021 10:19:31
So you can use induction to prove the claim just for the odd terms
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:20:24
Ah, I thought we only could do one n at a time and the n itself can be odd
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:20:38
if.. that makes sense?
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:21:00
that the number we calculate for n can be odd itself
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:21:07
but we must pass by every step of n
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:21:53
Basically I dont see how a formula that only proves every 2nd term can prove the whole thing
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help-10
3f9a2167445444539ec2b9d0789fe337
474,549,305,777,061,900
Euler2
11/07/2021 10:22:40
You’re not asked to prove it for the whole thing, you’re asked to prove it only for the odd terms
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help-10
3f9a2167445444539ec2b9d0789fe337
474,549,305,777,061,900
Euler2
11/07/2021 10:23:05
The statement is false for the even terms, you’re approximating square root of 2 with this sequence
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help-10
3f9a2167445444539ec2b9d0789fe337
474,549,305,777,061,900
Euler2
11/07/2021 10:23:17
The even terms squared will be bigger than 2
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:23:36
Oh, because It's 2n+1?
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help-10
3f9a2167445444539ec2b9d0789fe337
474,549,305,777,061,900
Euler2
11/07/2021 10:23:44
Yeah that’s just the odd terms
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:23:51
ah, okay, that makes sense
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:23:59
I have another small question
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:24:01
In the same vein
1
0
474,549,305,777,061,900
Euler2
3796
Euler2
false
757
help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:24:15
I am asked to prove
https://cdn.discordapp.c…8298/unknown.png
unknown.png
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:24:24
And we find that
https://cdn.discordapp.c…1196/unknown.png
unknown.png
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help-10
3f9a2167445444539ec2b9d0789fe337
227,858,073,497,108,480
rice
11/07/2021 10:24:39
...because we computed xn+1 into the formula we found previously, right?
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help-10
3f9a2167445444539ec2b9d0789fe337
474,549,305,777,061,900
Euler2
11/07/2021 10:24:55
That’s just using the recursion yeah
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