## 490 Reputation

14 years, 280 days

## Perfect!...

@Carl Love As always, when I get an answer to a question here, I often learn a lot more than I expected to. Thanks much!

## Sorry...

@acer Sorry about the ambiguity, I was thinking the former. Would it matter, though?

## Complement?...

@acer Supposing we have a universal set of all reals, could this method be adapted to work with complements? For example, how could I do the intersection of the complement of A and B?

## Perfect!...

@acer Thanks so much. Just what I needed!

## Perfect...

@Kitonum This is exactly what I needed. Thanks!

## I was looking at the wrong package......

@rlopez Okay, it appears I was looking at the wrong package. This is exactly what I was looking for! Thanks!

## Perfect......

@tomleslie Just what I was looking for. Thank you!

## On the contrary......

@tomleslie A path is a walk in which no vertices are repeated. So, with regard to your example, an undirected graph with three vertices would have a longest path of length 2: A-B-C, C-A-B, etc. For a cycle, only the initial and terminal vertices are allowed to be the same. Again, from your example, a couple cycles are C-A-B-C, A-C-B-A, all of length 3. Hope this clarifies my question.

## Does the job!...

@mmcdara Thank you. This does what I need it to do!

## Just need it to work......

@acer Well, I've been playing around with the density option, but I am not getting it to work consistently. Maybe I'm not using it correctly.

For a 10x10 matrix, I don't think speed will be much of an issue. Although, it would be nice to have a solution that is scalable for larger matrices.

## Thanks...

@vv Yes, I find it a bit perplexing that Maple attempts the same methods for both, but is only able to evaluate one of them. The rewriting you've done is what is typically taught in a standard integration techniques unit, which facilitates a straightforward substitution.

Moreover, I observe a similar behavior when attempt to evaluate comparable integrals involving powers of tangent and secant. Risch is being employed, I believe.

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## Why......

I know how to get Maple to perform the integration, the question is why does the second integral require more? By hand, the same approach to integration works, particularly under the assumptions you stated. Other CASs, for example Mathematica, is able to handle both integrals easily.

## Definition...

@Carl Love The standard definition of continuity of a real-valued function, in a first semester calculus course is as follows. A function f:A->B, where A and B are subsets of R, is continous at a in A if:

(1) f(a) exists,

(2) lim f(x) as x->a exists, and

(3) (1) = (2)

Many books refer to this as a `continuity checklist`. This can then be modified using one-sided limits to reflect right- or left-continuity.

## Agree...

@nm I completely agree with this. How do we make suggestions to the Maple engineers?

## Yes.....

@Carl Love Ideally, I would like to restrict the domain and codomain to R. I didn't know is there was a system-wide way of achieving this. This isn't specific to just the sqrt function. It is true also for arcsine and arccosine. I have first-year college students exploring properties such as continuity using Maple. In these classes we use only the real number system, not the complex one. So, some of these results are initially confusing for the students. The follow-up discussion tends to be a good one, however. Thanks for your help!

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