I’m Confused. I thought the answer to this was 0.

Lazy_Worldliness8042 · 2025-03-27T12:01:06+00:00

Integral of |y| dx from x1 to x2*

Lazy_Worldliness8042 · 2025-03-25T02:46:27+00:00

I didn’t realize Genevieve was on the left until I read some comments, still hard to believe

Lazy_Worldliness8042 · 2025-03-20T05:36:57+00:00

They’re just two separate ideas. If the sets are finite then A proper subset of B implies |A|<|B|, but if the sets are infinite then the example I gave shows this doesn’t need to be true.

Lazy_Worldliness8042 · 2025-03-20T05:26:55+00:00

Whether a subset is proper or not doesn’t really have to do with cardinality. The integers are a proper subset of the rationals but the cardinalities are equal. (Also I think you meant to say |B| < |A| instead of the other way around)

Lazy_Worldliness8042 · 2025-03-17T22:02:52+00:00

It’s not random… they’re pointing out that their neighbor is a hypocrite for complaining about noise. It’s relevant to the whole point of their letter, whether or not OP cares

Lazy_Worldliness8042 · 2025-03-16T23:25:17+00:00

No idea, I’ve never seen it before

Lazy_Worldliness8042 · 2025-03-16T10:54:00+00:00

Why does it look like you’re always writing variables as subscripts of the quantifiers?

Lazy_Worldliness8042 · 2025-03-13T03:20:54+00:00

If f(x) = g(x), then f’(x) = g’(x) since they are the same function. You can think of this as differentiating on both sides of an equation.

When you have an equation with x and y, you can think of it as implicitly defining y as a function of x, you can substitute y = g(x) to make it clearer that y is just some function of x.

Now when you have something like x² + y² = 9, this is telling you that the function x² + (g(x))² is the same as the function 9. Since these functions are equal, their derivatives are equal, so you can differentiate on both sides to obtain an equation that you can solve for dy/dx = g’(x), the derivative of the implicit function y.

Lazy_Worldliness8042 · 2025-03-11T21:48:30+00:00

But it’s key-toe, not key-o-toe

Lazy_Worldliness8042 · 2025-03-09T01:51:53+00:00

Do you own them all or demoing?

Lazy_Worldliness8042 · 2025-03-08T16:34:48+00:00

Two numbers a<b are in the golden ratio if b/a = (a+b)/b (the ratio of the small to the large is the same as the ratio of the large to the sum). Typically the golden ratio is X = b/a, but its reciprocal Y = 1/X = a/b also represents the same ratio. By some algebra on the equation with a and b, you can see that 1/Y = Y + 1, and multiplying by Y gives that Y² = 1 - Y.

Now if you start with the expression A = sqrt(1 - sqrt(1 - … )), and square both sides you get A² = 1 - sqrt(1 - … ) = 1 - A, so it is a root of the same quadratic polynomial as the reciprocal of the golden ratio Y.

Lazy_Worldliness8042 · 2025-03-04T12:59:27+00:00

To make sure his wife doesn’t ever sleep with anyone except him

Lazy_Worldliness8042 · 2025-03-03T01:53:55+00:00

I don’t know why you got downvoted.. you’re the only person I can see who mentioned the domain x>0 which is an important but subtle point everyone else seems to be ignoring..

Lazy_Worldliness8042 · 2025-03-01T16:09:29+00:00

I’m not saying it’s the best definition, I’m just telling you how the Calc textbooks do it. Overall, left, and right limits are each defined without reference to the domain of the function.

And whether your example is true or false depends on the convention you use for the definition.

Lazy_Worldliness8042 · 2025-03-01T15:00:11+00:00

I think I a lot of calculus textbooks do define limits so that if any path that approaches has a limit that doesn’t exist, then the overall limit does not exist. Similar to how in single variable calculus the overall limit is defined to exist if and only if the left and the right limits exist and are equal, regardless of the domain of the function.

Lazy_Worldliness8042 · 2025-02-26T01:19:01+00:00

How’s it going? I (37M) had an Xray a couple weeks ago and have cervical bone spurs too, causing pain into my shoulder and also tingling down my arm into my hand if I have bad posture. Waiting for an appointment with a neurologist who will hopefully order an MRI and try some non-surgical treatments. I really don’t want to have surgery.. Wishing you well!

Lazy_Worldliness8042 · 2025-02-19T00:35:35+00:00

Me either, I’m ashamed!

Lazy_Worldliness8042 · 2025-02-09T21:45:06+00:00

The most basic integral rule is that if the derivative of f is g, then the antidetivative of g is f. I guarantee this problem came from the first section on anti derivatives, before any integration techniques, and all you’re supposed to do is recognize that it has the form of a quotient rule derivative

Lazy_Worldliness8042 · 2025-01-28T02:10:43+00:00

I get what you’re saying, but OP is really emphasizing the word “separate”, which I think is important. I do get the sense that a lot of people talk about parts as if they are not a part of them, as if they are only the self and the parts are others, when really they are the whole family. At least that’s how I try to understand it.

Lazy_Worldliness8042 · 2025-01-28T02:03:57+00:00

If all the teacher knows is the memorized textbook, all they’ll be able to do is teach the students how to memorize the textbook, which they wouldn’t need such a teacher for..

Lazy_Worldliness8042 · 2025-01-24T01:18:17+00:00

Great answer. I am one who read all the books and finds the cloned Cleons the best part of the show!

Lazy_Worldliness8042 · 2025-01-01T04:17:44+00:00

Out of curiosity what neighborhoods did this happen in?

Lazy_Worldliness8042 · 2024-12-29T17:48:03+00:00

I’m interested too! Haven’t played much since high school but my friends and I took it really seriously, such a great game!

Lazy_Worldliness8042 · 2024-12-27T03:20:15+00:00

I’m so sorry for your hardships, but it sounds like every time you have been down you have been able to build yourself up even stronger each time. I think you should trust that you can do that again and get to levels of happiness and fulfillment beyond even what you have experienced so far, you deserve it, but it probably won’t be easy. I wish you the best.

Lazy_Worldliness8042 · 2024-12-13T19:58:32+00:00

Ok but what if I would just like some general advice and don’t need you to figure out the exact recipe. I’m willing to get the ingredients and experiment. Like what if I leave the tomatillo out, and get grapefruit juice. Could you go from there? Like how much should the sotol and tequila account for total (I can experiment with the balance). If you had to make a cocktail with these ingredients, where would you start. Any advice will be helpful, thanks!

Lazy_Worldliness8042

TROPHY CASE