mikeion/dissertation_data_with_split · Datasets at Hugging Face

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770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 07:56:52	And visually what we are doing as x is growing			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 07:58:20		https://cdn.discordapp.c…0216/unknown.png	unknown.png	1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 07:58:21	so with 1			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 07:58:24	we'd have infinitely many aps			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 07:58:32	because 1*x (x in R) never hits a multiple pi?			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 07:58:48	as pi is irrational			1	0	510,789,298,321,096,700	TeXit	0796	TeXit	true
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 07:58:50	?			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 07:59:51	well it does			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 07:59:54	cus x is real			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 07:59:56	not integer			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:00:09	But that doesn't matter, because we will keep spinning around the circle			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:00:21	I always confuse things lol			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:00:25	I thought x is rational for a second			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:00:29	Thats partially my bad			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:00:41	You will hit every point on the unit circle a infinite number of times			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:00:43	Since x is real			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:00:51	So they are definitely AP for sure.			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:01:21	One way to think of this is b describes the speed at which you spin			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:01:47	If b is positive, then you spin anticlockwise If b is negative, clockwise			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:02:04	Let's say your x is increasing at a constant rate (let's say 1 per second)			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:02:34	b = 1 vs b = 2			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:02:45	You spin twice as fast with b = 2			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:03:05	Handwavy explanation for the visualisation			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:04:39	https://i.imgur.com/myto5TA.gif			0	1	321,445,119,171,756,000	Shuri2060	9525	a μ-er	false
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:05:04	`b = 1, 2.5, -1` for those examples			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:06:19	You can see those dots will never converge to any point as `a` (a in desmos, x in your question) goes to infinity			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:06:52	The only case they could converge is when your spinning speed is 0			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:08:24	so the limit is non determinate			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:09:32	doesnt exist yes			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:09:36	$$\lim_{x\to\infty}\frac{1}{x}e^{ix}$$			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	510,789,298,321,096,700	TeXit	02/19/2022 08:09:48	Shuri2060	https://cdn.discordapp.c…119171756033.png	321445119171756033.png	0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:09:53	Can you imagine what this will look like?			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:10:03	0?			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:10:11	right, but whats the path you are taking			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:10:16	As x is growing			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:10:54	$$\lim_{x\to\infty}\frac{1}{x}e^{ix} = \lim_{x\to\infty} \frac{1}{x} \cdot \lim_{x\to\infty} e^{ix} = 0 \cdot n = 0$$			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	214,429,100,880,691,200	MallocSamuel	02/19/2022 08:10:55	how is that 0?			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:11:08	Sure that's how to work it out algebraically			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	510,789,298,321,096,700	TeXit	02/19/2022 08:11:12	illuminator3	https://cdn.discordapp.c…706186420224.png	391270706186420224.png	0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:11:17	But there is something to visualize too			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:11:23	hm			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:11:25	also thats not 0 . n			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:11:36	lim x -> infty e^ix is not convergent (as we just worked out now)			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:11:44	oh			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:11:44	right			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	214,429,100,880,691,200	MallocSamuel	02/19/2022 08:11:57	this is not 0 man			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:12:03	it is 0			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:12:08	But not in the way you worked out - you don't split the product			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	214,429,100,880,691,200	MallocSamuel	02/19/2022 08:12:10	e is exponential			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:12:16	@MallocSamuel you're not being helpful. shuri is already helping me			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:12:21	😂			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:12:30	no no			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:12:34	e is exponential yes			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:12:43	but are you familiar with complex exponential			0	1	510,789,298,321,096,700	TeXit	0796	TeXit	true
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:12:52	i is sqrt -1, so this is different			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:13:08	So algebraically, this is a slight pain			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:13:21	You might justify it by saying the modulus goes to 0			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:13:30	therefore, the limit must be 0 regardless of what the argument is doing			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:13:38		https://cdn.discordapp.c…119171756033.png	321445119171756033.png	0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:13:52	But you can also visualize what this is doing as x changes			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:14:03	in the same way as we did here			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:15:17	so it's like a spiral			1	0	214,429,100,880,691,200	MallocSamuel	6528	MallocSamuel	false
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:15:23	that goes inward as x increases			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:16:42	yes exactly			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:16:49	https://i.imgur.com/yzD7aJ0.gif			0	1	214,429,100,880,691,200	MallocSamuel	6528	MallocSamuel	false
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:16:57	And we see the only accumulation point is 0			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:17:39	never really thought about solving problems visually hm			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:17:41	Where possible, it is usually helpful to try thinking about these limits geometrically			0	1	391,270,706,186,420,200	illuminator3	0001	illuminator3	false
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:17:46	yeah			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	321,445,119,171,756,000	Shuri2060	02/19/2022 08:17:50	Sometimes you get an ugly expression and you can't, ofc			0	1	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:28:43	alright thanks for the help			1	0	null	null	null	null	null
770	help-10	07fac3c5fb2449ab82562d5b132c3ff1	391,270,706,186,420,200	illuminator3	02/19/2022 08:28:44	.close			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 08:31:20	Hello			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 08:34:31	Let $h: \mathbb{R}^4 \to \mathbb{R}$ be a function with the following properties: the domain of h is $\mathbb{R}^4$ and all partial derivatives of h from of 2 or lower exist and have the same domain as h. Let $H: \mathbb{R}^2 \to \mathbb{R}$ be a function defined by $H(x,y) = h(-3, e^{xy}, x^2 + y^2, y-x)$.			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 08:35:41	How can I prove that the partial derivative $\frac{\partial H}{\partial x}$ exists?			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	510,789,298,321,096,700	TeXit	02/19/2022 08:36:54	veganlatina	https://cdn.discordapp.c…106945417258.png	608759106945417258.png	0	1	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 08:38:00	My idea was to prove $\lim_{h \to 0} \frac{H(x+h,y) - H(x,y)}{h}$ exists, but I don't know how I can prove this limit exists			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	510,789,298,321,096,700	TeXit	02/19/2022 08:38:03	veganlatina	https://cdn.discordapp.c…106945417258.png	608759106945417258.png	0	1	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	510,789,298,321,096,700	TeXit	02/19/2022 08:41:00	veganlatina	https://cdn.discordapp.c…106945417258.png	608759106945417258.png	0	1	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 08:44:49	@Helpers			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 09:03:09	@Helpers anyone?			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	692,654,133,785,657,300	Alexander42	02/19/2022 09:10:55	use the chain rule			0	1	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 09:14:37	But how?			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	692,654,133,785,657,300	Alexander42	02/19/2022 09:19:09	write H as the composite of two partial differentiable function, then H has also a partial derivative \|\|one is the two functions is h\|\|			0	1	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 09:25:57	So something like $\frac{ \partial H}{\partial x} = \frac{ \partial H}{\partial h} \frac{\partial h}{\partial x} + \frac{\partial H}{\partial ?} \frac{\partial ?}{\partial x}$?			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	510,789,298,321,096,700	TeXit	02/19/2022 09:25:59	veganlatina	https://cdn.discordapp.c…106945417258.png	608759106945417258.png	0	1	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	692,654,133,785,657,300	Alexander42	02/19/2022 09:30:31	if H(x,y)=h(g(x,y)) with $g(x,y)=(g_1(x,y),g_2(x,y),g_3(x,y),g_4(x,y))$, then $\frac{ \partial H}{\partial x} = \frac{ \partial h}{\partial g_1} \frac{\partial g_1}{\partial x} + \frac{\partial h}{\partial g_2} \frac{\partial g_2}{\partial x}+\frac{ \partial h}{\partial g_3} \frac{\partial g_3}{\partial x} + \frac{\pa...			0	1	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	510,789,298,321,096,700	TeXit	02/19/2022 09:30:34	Alexander42	https://cdn.discordapp.c…133785657375.png	692654133785657375.png	0	1	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 09:31:19	ooooh			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 09:31:27	thank you so much!			1	0	null	null	null	null	null
771	help-10	0d8f75a4686f4d7ab4b4c2fc3ff47e71	608,759,106,945,417,200	veganlatina	02/19/2022 09:59:52	.close			1	0	null	null	null	null	null
772	help-10	7cd4655a7b264a6d94c1af9ad5e18c14	720,651,983,643,738,100	DeltzX	02/19/2022 10:25:17	not quite sure why q = f(p)	https://cdn.discordapp.c…10_23_12_Pro.jpg	WIN_20220219_10_23_12_Pro.jpg	1	0	null	null	null	null	null
772	help-10	7cd4655a7b264a6d94c1af9ad5e18c14	411,882,877,933,060,100	Ｈｅｒｅｌｓ	02/19/2022 10:27:19	P is a point of the curve of f			0	1	null	null	null	null	null
772	help-10	7cd4655a7b264a6d94c1af9ad5e18c14	411,882,877,933,060,100	Ｈｅｒｅｌｓ	02/19/2022 10:27:42	so it's obvious that his coordinate verify q = f(p)			0	1	null	null	null	null	null
772	help-10	7cd4655a7b264a6d94c1af9ad5e18c14	720,651,983,643,738,100	DeltzX	02/19/2022 10:30:29	ok			1	0	null	null	null	null	null
772	help-10	7cd4655a7b264a6d94c1af9ad5e18c14	720,651,983,643,738,100	DeltzX	02/19/2022 10:30:40	.close			1	0	null	null	null	null	null
773	help-10	d0ef48004630404188fa0844059ae384	735,546,509,986,234,400	dan can	02/19/2022 10:32:42	I'm trying to understand the derivation of the Length of the spiral formed within a regular polygon https://mathworld.wolfram.com/PolygonalSpiral.html. Does the equation of the total length of the spiral $L=\frac{1 }{ 2}s\sum_k \cos^k(\pi/n)$ immediately follow from the previous step on the ratio $r/R$? Or are there v...			1	0	null	null	null	null	null
773	help-10	d0ef48004630404188fa0844059ae384	510,789,298,321,096,700	TeXit	02/19/2022 10:32:45	tuturuuu	https://cdn.discordapp.c…509986234418.png	735546509986234418.png	0	1	null	null	null	null	null
773	help-10	d0ef48004630404188fa0844059ae384	376,014,466,585,722,900	Arthek	02/19/2022 11:36:36	Problem 1 : The input is 2 values, that can be in a scale between [-3.89, 10.66] And i need to compare the difference between an oldValue (A) and a newValue (B). So i want to create a variable that express this difference. Let say : ``` A = -2 B = 3 diff = ? ``` If i do a simple substraction it doesn't ca...			0	1	null	null	null	null	null
773	help-10	d0ef48004630404188fa0844059ae384	376,014,466,585,722,900	Arthek	02/19/2022 11:36:43		https://cdn.discordapp.c…37744946/idp.png	idp.png	0	1	null	null	null	null	null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 07:56:52

And visually what we are doing as x is growing

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 07:58:20

https://cdn.discordapp.c…0216/unknown.png

unknown.png

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 07:58:21

so with 1

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 07:58:24

we'd have infinitely many aps

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 07:58:32

because 1*x (x in R) never hits a multiple pi?

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 07:58:48

as pi is irrational

1

0

510,789,298,321,096,700

TeXit

0796

TeXit

true

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 07:58:50

?

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 07:59:51

well it does

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 07:59:54

cus x is real

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 07:59:56

not integer

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:00:09

But that doesn't matter, because we will keep spinning around the circle

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:00:21

I always confuse things lol

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:00:25

I thought x is rational for a second

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:00:29

Thats partially my bad

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:00:41

You will hit every point on the unit circle a infinite number of times

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:00:43

Since x is real

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:00:51

So they are definitely AP for sure.

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:01:21

One way to think of this is **b** describes the speed at which you spin

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:01:47

If **b** is positive, then you spin anticlockwise If **b** is negative, clockwise

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:02:04

Let's say your **x** is increasing at a constant rate (let's say 1 per second)

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:02:34

**b** = 1 vs **b** = 2

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:02:45

You spin twice as fast with **b** = 2

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:03:05

Handwavy explanation for the visualisation

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:04:39

https://i.imgur.com/myto5TA.gif

0

1

321,445,119,171,756,000

Shuri2060

9525

a μ-er

false

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:05:04

`b = 1, 2.5, -1` for those examples

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:06:19

You can see those dots will never converge to any point as `a` (a in desmos, x in your question) goes to infinity

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:06:52

The only case they could converge is when your spinning speed is 0

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:08:24

so the limit is non determinate

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:09:32

doesnt exist yes

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:09:36

$$\lim_{x\to\infty}\frac{1}{x}e^{ix}$$

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

510,789,298,321,096,700

TeXit

02/19/2022 08:09:48

**Shuri2060**

https://cdn.discordapp.c…119171756033.png

321445119171756033.png

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:09:53

Can you imagine what this will look like?

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:10:03

0?

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:10:11

right, but whats the path you are taking

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:10:16

As x is growing

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:10:54

$$\lim_{x\to\infty}\frac{1}{x}e^{ix} = \lim_{x\to\infty} \frac{1}{x} \cdot \lim_{x\to\infty} e^{ix} = 0 \cdot n = 0$$

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

214,429,100,880,691,200

MallocSamuel

02/19/2022 08:10:55

how is that 0?

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:11:08

Sure that's how to work it out algebraically

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

510,789,298,321,096,700

TeXit

02/19/2022 08:11:12

**illuminator3**

https://cdn.discordapp.c…706186420224.png

391270706186420224.png

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:11:17

But there is something to visualize too

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:11:23

hm

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:11:25

also thats not 0 . n

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:11:36

lim x -> infty e^ix is not convergent (as we just worked out now)

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:11:44

oh

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:11:44

right

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

214,429,100,880,691,200

MallocSamuel

02/19/2022 08:11:57

this is not 0 man

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:12:03

it **is** 0

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:12:08

But not in the way you worked out - you don't split the product

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

214,429,100,880,691,200

MallocSamuel

02/19/2022 08:12:10

e is exponential

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:12:16

@MallocSamuel you're not being helpful. shuri is already helping me

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:12:21

😂

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:12:30

no no

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:12:34

e is exponential yes

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:12:43

but are you familiar with complex exponential

0

1

510,789,298,321,096,700

TeXit

0796

TeXit

true

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:12:52

i is sqrt -1, so this is different

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:13:08

So algebraically, this is a slight pain

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:13:21

You might justify it by saying the modulus goes to 0

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:13:30

therefore, the limit must be 0 regardless of what the argument is doing

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:13:38

https://cdn.discordapp.c…119171756033.png

321445119171756033.png

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:13:52

But you can also visualize what this is doing as x changes

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:14:03

in the same way as we did here

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:15:17

so it's like a spiral

1

0

214,429,100,880,691,200

MallocSamuel

6528

MallocSamuel

false

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:15:23

that goes inward as x increases

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:16:42

yes exactly

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:16:49

https://i.imgur.com/yzD7aJ0.gif

0

1

214,429,100,880,691,200

MallocSamuel

6528

MallocSamuel

false

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:16:57

And we see the only accumulation point is 0

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:17:39

never really thought about solving problems visually hm

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:17:41

Where possible, it is usually helpful to try thinking about these limits geometrically

0

1

391,270,706,186,420,200

illuminator3

0001

illuminator3

false

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:17:46

yeah

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

321,445,119,171,756,000

Shuri2060

02/19/2022 08:17:50

Sometimes you get an ugly expression and you can't, ofc

0

1

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:28:43

alright thanks for the help

1

0

null

770

help-10

07fac3c5fb2449ab82562d5b132c3ff1

391,270,706,186,420,200

illuminator3

02/19/2022 08:28:44

.close

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 08:31:20

Hello

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 08:34:31

Let $h: \mathbb{R}^4 \to \mathbb{R}$ be a function with the following properties: the domain of h is $\mathbb{R}^4$ and all partial derivatives of h from of 2 or lower exist and have the same domain as h. Let $H: \mathbb{R}^2 \to \mathbb{R}$ be a function defined by $H(x,y) = h(-3, e^{xy}, x^2 + y^2, y-x)$.

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 08:35:41

How can I prove that the partial derivative $\frac{\partial H}{\partial x}$ exists?

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

510,789,298,321,096,700

TeXit

02/19/2022 08:36:54

**veganlatina**

https://cdn.discordapp.c…106945417258.png

608759106945417258.png

0

1

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 08:38:00

My idea was to prove $\lim_{h \to 0} \frac{H(x+h,y) - H(x,y)}{h}$ exists, but I don't know how I can prove this limit exists

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

510,789,298,321,096,700

TeXit

02/19/2022 08:38:03

**veganlatina**

https://cdn.discordapp.c…106945417258.png

608759106945417258.png

0

1

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

510,789,298,321,096,700

TeXit

02/19/2022 08:41:00

**veganlatina**

https://cdn.discordapp.c…106945417258.png

608759106945417258.png

0

1

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 08:44:49

@Helpers

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 09:03:09

@Helpers anyone?

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

692,654,133,785,657,300

Alexander42

02/19/2022 09:10:55

use the chain rule

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771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 09:14:37

But how?

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

692,654,133,785,657,300

Alexander42

02/19/2022 09:19:09

write H as the composite of two partial differentiable function, then H has also a partial derivative ||one is the two functions is h||

0

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771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 09:25:57

So something like $\frac{ \partial H}{\partial x} = \frac{ \partial H}{\partial h} \frac{\partial h}{\partial x} + \frac{\partial H}{\partial ?} \frac{\partial ?}{\partial x}$?

1

0

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771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

510,789,298,321,096,700

TeXit

02/19/2022 09:25:59

**veganlatina**

https://cdn.discordapp.c…106945417258.png

608759106945417258.png

0

1

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

692,654,133,785,657,300

Alexander42

02/19/2022 09:30:31

if H(x,y)=h(g(x,y)) with $g(x,y)=(g_1(x,y),g_2(x,y),g_3(x,y),g_4(x,y))$, then $\frac{ \partial H}{\partial x} = \frac{ \partial h}{\partial g_1} \frac{\partial g_1}{\partial x} + \frac{\partial h}{\partial g_2} \frac{\partial g_2}{\partial x}+\frac{ \partial h}{\partial g_3} \frac{\partial g_3}{\partial x} + \frac{\pa...

0

1

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

510,789,298,321,096,700

TeXit

02/19/2022 09:30:34

**Alexander42**

https://cdn.discordapp.c…133785657375.png

692654133785657375.png

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help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 09:31:19

ooooh

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 09:31:27

thank you so much!

1

0

null

771

help-10

0d8f75a4686f4d7ab4b4c2fc3ff47e71

608,759,106,945,417,200

veganlatina

02/19/2022 09:59:52

.close

1

0

null

772

help-10

7cd4655a7b264a6d94c1af9ad5e18c14

720,651,983,643,738,100

DeltzX

02/19/2022 10:25:17

not quite sure why q = f(p)

https://cdn.discordapp.c…10_23_12_Pro.jpg

WIN_20220219_10_23_12_Pro.jpg

1

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772

help-10

7cd4655a7b264a6d94c1af9ad5e18c14

411,882,877,933,060,100

Ｈｅｒｅｌｓ

02/19/2022 10:27:19

P is a point of the curve of f

0

1

null

772

help-10

7cd4655a7b264a6d94c1af9ad5e18c14

411,882,877,933,060,100

Ｈｅｒｅｌｓ

02/19/2022 10:27:42

so it's obvious that his coordinate verify q = f(p)

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772

help-10

7cd4655a7b264a6d94c1af9ad5e18c14

720,651,983,643,738,100

DeltzX

02/19/2022 10:30:29

ok

1

0

null

772

help-10

7cd4655a7b264a6d94c1af9ad5e18c14

720,651,983,643,738,100

DeltzX

02/19/2022 10:30:40

.close

1

0

null

773

help-10

d0ef48004630404188fa0844059ae384

735,546,509,986,234,400

dan can

02/19/2022 10:32:42

I'm trying to understand the derivation of the Length of the spiral formed within a regular polygon https://mathworld.wolfram.com/PolygonalSpiral.html. Does the equation of the total length of the spiral $L=\frac{1 }{ 2}s\sum_k \cos^k(\pi/n)$ immediately follow from the previous step on the ratio $r/R$? Or are there v...

1

0

null

773

help-10

d0ef48004630404188fa0844059ae384

510,789,298,321,096,700

TeXit

02/19/2022 10:32:45

**tuturuuu**

https://cdn.discordapp.c…509986234418.png

735546509986234418.png

0

1

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773

help-10

d0ef48004630404188fa0844059ae384

376,014,466,585,722,900

Arthek

02/19/2022 11:36:36

**Problem 1 :** The input is 2 values, that can be in a scale between [-3.89, 10.66] And i need to compare the difference between an oldValue (A) and a newValue (B). So i want to create a variable that express this difference. Let say : ``` A = -2 B = 3 diff = ? ``` If i do a simple substraction it doesn't ca...

0

1

null

773

help-10

d0ef48004630404188fa0844059ae384

376,014,466,585,722,900

Arthek

02/19/2022 11:36:43

https://cdn.discordapp.c…37744946/idp.png

idp.png

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