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help-10
091c72f2f8694f02ad20d870478da520
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gnu
03/14/2022 08:02:03
But I’m not sure what to do next
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vicarious
03/14/2022 08:05:17
my handwriting sucks so I can't send a pic
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gnu
03/14/2022 08:06:32
Aw :/
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ScapeProf
03/14/2022 08:08:16
\begin{align*}\sum_{n=2}^\infty\frac{1}{n^2-1}&=\frac{1}{2}\sum_{n=1}^\infty \frac{1}{n}-\frac{1}{n+2} \\ &=\frac{1}{2}\sum_{n=1}^\infty \left(\frac{1}{n}+\frac{1}{n+1}\right)-\left(\frac{1}{n+1}+\frac{1}{n+2}\right)\end{align*}
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gnu
03/14/2022 08:09:23
How did you get the 1/n - 1/n+2? Thank you btw
1
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TeXit
03/14/2022 08:09:40
**ScapeProf**
https://cdn.discordapp.c…506664136705.png
265853506664136705.png
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ScapeProf
03/14/2022 08:10:13
You have 1/(n-1)-1/(n+2)
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ScapeProf
03/14/2022 08:10:15
Index shift
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ScapeProf
03/14/2022 08:10:25
Telescoping now
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help-10
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gnu
03/14/2022 08:10:27
Oh hmmm very interesting
1
0
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gnu
03/14/2022 08:10:38
Ive never seen that but it makes sense!
1
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gnu
03/14/2022 08:10:40
Thanks
1
0
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gnu
03/14/2022 08:18:15
What changes when we do this?
1
0
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gnu
03/14/2022 08:18:20
Other than n
1
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gnu
03/14/2022 08:19:19
I’m not sure where the 1/n is from
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ScapeProf
03/14/2022 08:20:39
If you plug in n=2 in 1/(n-1) it is the same as plugging in n=1 in 1/n?
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gnu
03/14/2022 08:20:56
Ohhhh yes thanks
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Deleted User
03/14/2022 09:29:14
Can someone help me? How can I write the Euler-Lagrange equation in terms of generalized coordinates and velocities?
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Kaynex
03/14/2022 09:41:12
Question is very general
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ZED_118
03/14/2022 10:21:49
https://cdn.discordapp.c…620/IMG_0384.jpg
IMG_0384.jpg
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ZED_118
03/14/2022 10:21:52
How should I do this?
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261,933,205,387,477,000
riemann
03/14/2022 14:19:32
.close
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Mahdi M.
03/14/2022 14:42:51
Hi
1
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Mahdi M.
03/14/2022 14:43:09
https://cdn.discordapp.c…4_202205_046.jpg
IMG_20220314_202205_046.jpg
1
0
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Mahdi M.
03/14/2022 14:43:10
Here
1
0
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Mahdi M.
03/14/2022 14:43:16
In the point of inflection
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Mahdi M.
03/14/2022 14:43:31
@Deleted Account ????
1
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Mahdi M.
03/14/2022 14:44:08
@Helpers
1
0
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Mahdi M.
03/14/2022 14:44:22
In the point of inflection I
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Mahdi M.
03/14/2022 14:44:35
it has the abscissa x = -2
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Mahdi M.
03/14/2022 14:44:45
and what is y?
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Mahdi M.
03/14/2022 14:45:03
Does it f''(-2) ???
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Kaisheng21
03/14/2022 14:45:12
if it wants the point on the graph
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Kaisheng21
03/14/2022 14:45:18
then the point will be just f(2)
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Mahdi M.
03/14/2022 14:46:02
But it is point of inflection
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Mahdi M.
03/14/2022 14:46:11
Which is f''(x)
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Mahdi M.
03/14/2022 14:46:56
@Kaisheng21
1
0
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help-10
023545815120492caabba2f9c33eabc2
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Kaisheng21
03/14/2022 14:47:00
yes
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Kaisheng21
03/14/2022 14:47:32
let the point where the abcissa is be (x, y)
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Kaisheng21
03/14/2022 14:47:39
then at that point, f''(x) = 0
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Kaisheng21
03/14/2022 14:47:45
then, for that x, y = f(x)
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Mahdi M.
03/14/2022 14:48:04
ok
1
0
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Mahdi M.
03/14/2022 14:48:32
@Kaisheng21
https://cdn.discordapp.c…87e5dfd0d499.jpg
5df387e5dfd0d499.jpg
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Mahdi M.
03/14/2022 14:48:32
What about this?
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Kaisheng21
03/14/2022 14:48:43
nope
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Kaisheng21
03/14/2022 14:48:53
should be f(2), not f''(x)
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Mahdi M.
03/14/2022 14:49:24
So it should be f(-2) not f''(-2)
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Mahdi M.
03/14/2022 14:55:08
@Kaisheng21 is this true?
1
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Kaisheng21
03/14/2022 14:56:21
that's what i said
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Mahdi M.
03/14/2022 14:56:37
Ok thank you @Kaisheng21
1
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Mahdi M.
03/14/2022 14:57:12
How to give an feedback? @Kaisheng21
1
0
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Mahdi M.
03/14/2022 14:57:23
t!rep @Kaisheng21
1
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Tatsu
03/14/2022 14:57:23
:Reputation_Icon: **Mahdi has given @Kaisheng21 a reputation point!**
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Mahdi M.
03/14/2022 14:57:26
Ok
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Mahdi M.
03/14/2022 14:57:30
.close
1
0
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CoffeePls
03/14/2022 15:05:16
Good afternoon folks
https://cdn.discordapp.c…9402/unknown.png
unknown.png
1
0
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d9f30e0c0c9445b78184e2c117d5db7e
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BoredFromlife
03/14/2022 15:05:31
Hello guys
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BoredFromlife
03/14/2022 15:05:40
growth of a spherical tumor modeled as a function of the population of germs (g in Million) in tumor, v(g) = 1.5 g?, When the diameter of the tumor is 2V15 , and population of germs is 20m and it is growing at a rate of 2m /day. How fast is the diameter of the tumor changing at that time?
0
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d9f30e0c0c9445b78184e2c117d5db7e
901,760,990,016,835,600
BoredFromlife
03/14/2022 15:06:00
My brain froze
0
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CoffeePls
03/14/2022 15:06:00
1: Why did we need to calculate all those derivatives when we could just insert a = 1 into the taylor summation formula. 2: How did we go from the left side of the summation equation to the series?
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Kaisheng21
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BoredFromlife
03/14/2022 15:06:05
Any help?
0
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CoffeePls
03/14/2022 15:06:16
Sir this is wendy's
1
0
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Kaisheng21
03/14/2022 15:06:18
bruh
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Kaisheng21
03/14/2022 15:06:23
get outta here, someone else got here first
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Kaisheng21
03/14/2022 15:06:31
one question per channel at a time
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Kaisheng21
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BoredFromlife
03/14/2022 15:06:39
K thx
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1
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CoffeePls
03/14/2022 15:06:42
Yes, I believe this channel has been assigned to me.
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Kaisheng21
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CoffeePls
03/14/2022 15:06:46
No worries tho @BoredFromlife
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Kaisheng21
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Kaisheng21
03/14/2022 15:07:17
what do you think the taylor summation formula is
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Kaisheng21
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CoffeePls
03/14/2022 15:07:41
you sum up all the derivatives?
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Kaisheng21
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Kaisheng21
03/14/2022 15:08:10
??
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CoffeePls
03/14/2022 15:08:11
https://cdn.discordapp.c…44778/image0.jpg
image0.jpg
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Kaisheng21
03/14/2022 15:08:19
yeah so you need the derivatives to calculate it
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CoffeePls
03/14/2022 15:09:06
How can you capture the range (0 to infinity) with just 4 derivatives tho?
1
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Kaisheng21
03/14/2022 15:09:12
?
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Kaisheng21
03/14/2022 15:09:25
basically they noticed a pattern
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CoffeePls
03/14/2022 15:09:45
^
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:10:16
the zeroth derivative was 1 the first derivative was -1 the second derivative was 2! the third derivative was -3! the fourth derivative was 4! so they say that the nth derivative is gonna be (-1)^n * n!
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1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:10:37
if you have the nth derivative, the general derivative for any n, then you can get all of them
0
1
901,760,990,016,835,600
BoredFromlife
1760
BoredFromlife
false
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:11:43
Ok, so the point of derivatives is to see what values they return at a given x = a point
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0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:11:51
sure
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1
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null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:11:59
then you identify a pattern, write that into a series form
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0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:12:03
is that what they did?
1
0
null
null
null
null
null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:12:50
https://cdn.discordapp.c…2068/unknown.png
unknown.png
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1
null
null
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null
null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:12:52
you want to work out this
0
1
901,760,990,016,835,600
BoredFromlife
1760
BoredFromlife
false
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:13:00
https://cdn.discordapp.c…2378/unknown.png
unknown.png
0
1
null
null
null
null
null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:13:03
and you know this
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1
null
null
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null
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:13:11
so if you just substitute that into the first thing
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1
null
null
null
null
null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:13:12
then you get
0
1
null
null
null
null
null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:13:19
https://cdn.discordapp.c…6338/unknown.png
unknown.png
0
1
null
null
null
null
null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:15:56
so doing the derivatives lets you find out this component of the taylor series, correct?
https://cdn.discordapp.c…5669/unknown.png
unknown.png
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0
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null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:18:09
yes
0
1
null
null
null
null
null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:18:13
@Kaisheng21 sorry im jut lost on where each component fits
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0
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null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:18:43
?
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1
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null
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:18:53
i don't understand
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1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:19:21
my line of thinking is
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0
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null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:20:13
Given a fn and x =a, find the first nth derivative to find the circled component in blue, and use that to find the Taylor series of the fn.
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0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:20:28
yes
0
1
null
null
null
null
null
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:20:45
Ok
https://cdn.discordapp.c…1513/unknown.png
unknown.png
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:21:00
but how do we systematically figure out what those series of numbers equal?
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