conversation_id int64 1 206k | help_channel stringlengths 6 7 | __rowid__ stringlengths 32 32 | author_id int64 62,061,868B 1,071,443,446B | author_name stringlengths 2 32 | timestamp stringlengths 19 19 | content stringlengths 0 3.97k | reference.messageId stringclasses 3
values | reference.channelId stringclasses 3
values | reference.guildId stringclasses 1
value | url stringlengths 0 591 | fileName stringlengths 0 513 | student int64 0 1 | helper int64 0 1 | references.id float64 62,061,868B 1,071,056,124B ⌀ | references.name stringlengths 2 32 ⌀ | references.discriminator stringlengths 4 4 ⌀ | references.nickname stringlengths 1 32 ⌀ | references.isBot bool 2
classes |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:16:00 | we need bounds | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:16:30 | And what bounds do we choose? Well a is arbitrary and irrelevant (most people choose it to be 0), but the important part is the x upper bound | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 334,482,942,506,041,340 | Zybikron | 01/30/2022 03:16:54 | everything is with respect to x, there is a t in the integration as a dummy variable because having and the variable x as your bound, and as the variable in your function is.... problematic. | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:17:36 | yea i know | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:17:54 | @s_chanch Think about it, F takes in a number x and gives you the area under the curve from 0 to x | 0 | 1 | 510,789,298,321,096,700 | TeXit | 0796 | TeXit | true | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:18:06 | 0? | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:18:10 | If you take the derivative of that function, you get f back | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:18:28 | (Just think of it as 0 for now, the important part is that it’s irrelevant, you’ll see why in the proof) | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:19:49 | yea i know why it’s irrelevant | 1 | 0 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:20:32 | Ok | 0 | 1 | 334,482,942,506,041,340 | Zybikron | 5611 | Zybikron | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:21:41 | I sorta think I get why you don’t get it | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:22:32 | When we say “derivative of f” what are we saying?
It’s a new function f’ such that f’(x) is the slope of the tangent line to the graph of f at x | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:23:43 | When we say “integral of f” what are we saying? It’s a new function $F(x)$ such that $$F(x) = \int_a^x f(t)dt$$ | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 510,789,298,321,096,700 | TeXit | 01/30/2022 03:24:02 | **abs\_0** | 307070375735459842.png | 0 | 1 | null | null | null | null | null | ||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:24:23 | @s_chanch FTC1 establishes that f’ and F are opposites, according to these above definitions | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:24:47 | the hell | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:24:51 | Translating to colloquial language, you can say “derivatives and integrals are opposites” | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:25:13 | Did that make any sense at all lol | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:26:14 | not really | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:26:20 | Dksichdiejf | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:26:31 | (i’ve been asking this for 3 days) | 1 | 0 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:26:37 | Really | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:26:41 | (yes) | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:26:50 | \:( | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:26:53 | oiiii | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:26:58 | Help me :c | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:27:07 | @Ansh_ use another channel | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:27:09 | It's relevant to the topic! | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:27:12 | Oh | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:27:13 | 1 | 0 | null | null | null | null | null | ||||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:27:30 | repulsive: starvation | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:27:43 | @s_chanch I think part of it is that your question requires us to understand something you don’t get in your head | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:27:52 | yea i guess | 1 | 0 | 706,934,233,012,371,600 | Ansh_ | 3502 | Arya | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:28:04 | if it doesn’t bother you..? | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:28:13 | maybe i should try? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:28:23 | though i have no idea what's already been discussed | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:28:24 | I will say that I don’t really get exactly what you don’t get, like sorta but not really lol | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:28:48 | or rather, what's already been tried | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:29:21 | The integral of a function is the area under the curve! ✓ I can see that visually.. and it's fine!
But ..
The derivative of the integral,i.e., the derivative of the area under the curve.... returns the function ;-; how do you visualize that? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:29:29 | Ok @s_chanch for this person can you just try to phrase your question in the most exact words you can | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:29:37 | bottom text | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:29:42 | It’s very difficult | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:29:54 | and that *maybe* answers my question | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:30:01 | I spent a while trying to force my brain to accept it, and it’s just plainly an unintuitive concept | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:30:07 | :p | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:30:29 | Unintuitive** | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:31:01 | is it really that unintuitive? | 0 | 1 | 706,934,233,012,371,600 | Ansh_ | 3502 | Arya | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:31:26 | The tangent slope doing the opposite of the area under the function? I mean | 0 | 1 | 706,934,233,012,371,600 | Ansh_ | 3502 | Arya | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:31:37 | Call me crazy but those sound like totally different things lol | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:31:54 | it seems to me that between $\int_a^x$ and $\int_a^{x+h}$ where $h$ is small, all you're doing is adding an infinitesimal rectangle of height $f(x)$ and width $h$ | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 510,789,298,321,096,700 | TeXit | 01/30/2022 03:31:56 | **Camilleone** | 569167697925898261.png | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | ||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 239,501,588,589,182,980 | Ray | 01/30/2022 03:32:05 | what i think about is a rectangle. length f(x). side length dx. integral u get the area so it's f(x)dx. derivative u divide by dx u get back f(x). and then i think about riemann sum | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:32:38 | and that is exactly the rate of change of the area | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:32:48 | But whenever you think about how they’re opposites, you must go through this thought process every time | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:32:50 | At least, for me | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:33:07 | Intuitive means I don’t have to go through any thought process at all, I just get it in my gut | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:33:09 | Oooooooooo omg that's smart >_< | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:33:29 | like one way to view, is change of area | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:33:32 | and dumb of me at the samee time :bearlain: T_T | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:33:36 | what about ‘area function when you input the tangent line’????? | 1 | 0 | 569,167,697,925,898,240 | Camilleone | 1596 | Camilleone | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:33:37 | wtf | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:33:45 | :this: | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:34:22 | the what? | 0 | 1 | 569,167,697,925,898,240 | Camilleone | 1596 | Camilleone | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:34:27 | this explains d/dx (int), not int (d/dx) | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:34:32 | i must have missed that | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:34:42 | How does the "derivative is the slope of tangent to a function at some point" comes into equation here :catThink:
Does it have to do with, slope of tangent being a rate of change of function 👀 | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:34:47 | Yes I believe | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:35:09 | oh i see | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:35:44 | Yes, the slope of the tangent is “instantaneous rate of change” | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:36:10 | (Really, rate of change as h, the distance between the points, approaches 0) | 0 | 1 | 510,789,298,321,096,700 | TeXit | 0796 | TeXit | true | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 706,934,233,012,371,600 | Ansh_ | 01/30/2022 03:36:26 | Got that... now the int(d/dx) part plz... as chromium asked | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:37:33 | the first problem with any argument of int (d/dx) is the introduction of a constant which leads to many antiderivatives | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:38:29 | Changing areas makes sense… area under changes doesn’t | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:38:37 | like, many functions all differing by constants have the same tangent function | 0 | 1 | 701,895,792,763,600,900 | s_chanch | 2633 | s_chanch | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:39:15 | i believe this is what's making the arguments hard to understand intuitively | 0 | 1 | 706,934,233,012,371,600 | Ansh_ | 3502 | Arya | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:41:56 | so to understand this we have to go back to $\int_a^x$ | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 510,789,298,321,096,700 | TeXit | 01/30/2022 03:41:59 | **Camilleone** | 569167697925898261.png | 0 | 1 | null | null | null | null | null | ||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:42:15 | the derivative, as you know, is the rate of change function | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:42:59 | so let's say you start with a function f, and then you differentiated it to find the derivative f' | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:43:53 | the integral of f' can be understood as infinitesimal addition of all the little rates of changes at each point | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:46:17 | huh..? | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:46:48 | which means that now to get $\int_a^x f'(x) dx$, what you want is the total sum of all the little changes of $f$ from $a$ to $x$, which ends up as the difference between $f(x)$ and $f(a)$, i.e. $f(x) - f(a)$ | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 510,789,298,321,096,700 | TeXit | 01/30/2022 03:47:41 | **Camilleone** | 569167697925898261.png | 0 | 1 | null | null | null | null | null | ||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:47:46 | i can’t visualise this | 1 | 0 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:48:04 | Ohhh cause a rectangle with 0 with is the same as the height basically right | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:48:18 | yeah | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:48:27 | Wait no that doesn’t make sense | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:48:32 | well | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:48:33 | You’d be adding up infinitely many values | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:48:38 | It would diverge | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:48:39 | i admit it isn't that well-worded | 0 | 1 | 569,167,697,925,898,240 | Camilleone | 1596 | Camilleone | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:48:44 | what i should have said was | 0 | 1 | 307,070,375,735,459,840 | abs_0 | 8527 | a.b.s._.0. | false | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:49:02 | take for example a rate of change at a point $x$ | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 510,789,298,321,096,700 | TeXit | 01/30/2022 03:49:04 | **Camilleone** | 569167697925898261.png | 0 | 1 | null | null | null | null | null | ||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:49:59 | for h small, between x and x+h you basically add an infinitesimal "increase" of the function by that rate of change - of course if the rate of change is negative your function decreases, but that's not important | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:50:42 | the point is, by adding all these infinitesimal increases you end up with the total increase of the original function | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:52:08 | Hold up | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 569,167,697,925,898,240 | Camilleone | 01/30/2022 03:52:14 | so in terms of an integral $f(x) = \int_a^x f'(t) \,dt$, you're adding all the infinitesimal increases from $a$ to $x$, which ends up as the total increase from $f(a)$ to $f(x)$ | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 307,070,375,735,459,840 | abs_0 | 01/30/2022 03:52:26 | By “the function” you mean any general function f, or the derivative function? | 0 | 1 | null | null | null | null | null | |||||
365 | help-10 | d8b842f4e0a64afb952cef54909e6d8e | 701,895,792,763,600,900 | s_chanch | 01/30/2022 03:54:50 | (please use f’(t) dt) | 1 | 0 | null | null | null | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.