Finding the Area of a Region

We find the area of the region where | |x + y| - y| ≤ |x - y| ≤ 3.
00:00 First inequality |x - y| ≤ 3
01:42 Second inequality x + y ≥ 0
06:35 Second inequality x + y ≤ 0
11:25 Finding the intersection

[@user-cd9dd1mx4n]

I really appreciate the step-by-step approach. Your way of explaining things is really effective. Thank you very much❤

[@russelltownsend6105]

Another absolutely brilliant delivery, I just love your clarity and timing.

[@vvop]

That was so enjoyable. I can't wait until next week, now! Thank you.

[@ronbannon]

First, a trivial (by inspection) solution is x = y = 0. Second, two simple lines emerge from | x-y | = 3. From this, you get y = x + 3 and y = x - 3, which can be used to solve | |x + y| - y| = |x - y | for points of intersection. A series of lines emerge, forming regions that can be tested for shading.

[@boringextrovert6719]

I live in Korea. Every Friday after I leave work, I open KZbin, and it recommends me your videos. Good way to end my week

[@vvop]

I live in Australia, same for me, a great way to end the work week!

[@brendanmccann5695]

Nice job. Very clean. Thank you.

[@magicmeatball4013]

Has a week really passed again??

[@gael8828]

For the case x+y>0 (7:47), I think the point where you're closest to -2y than -y is -3/2*y, not -y/2 as you mentionned.

[@davidcroft95]

The singular y is with a plus sign, and the mean between y and -2y is (y-2y)/2=-y/2

[@gael8828]

@@davidcroft95 You're perfectly right, my eyes saw a minus sign where there was not...

[@davidcroft95]

@@gael8828 ahah don't worry, it got me fooled too, I had to stop the video and do the math in my head 😂

[@ShanBojack]

Dang man this was nice stuff really 👏

[@jim3129]

clear explanation

[@lenskihe]

Excellent presentation and explanation, as always 👏 But I personally do not find these absolute value inequalities very interesting. They just boil down to a lot of case differentiations. Still a very valuable lesson for people who have never seen this kind of thing before.

[@user-wu8yq1rb9t]

The beautiful mind is here ... Now I should go (I have exam) ... Then I'm back and watch it. Thank you dear Dr Barker

[@andriworld]

Can this be solved with integrals?

[@jbrecken]

Is absolute value called modulus now?

[@brendanmccann5695]

in the UK, yes

[@davidcroft95]

Within real numbers they are synonyms, things start changing with complex numbers (and vectors ofc)

[@psiphiorg]

@@brendanmccann5695, I had never heard this term applied to the absolute value before, so I was also very confused at first, because I didn't know how the absolute value applied to modular arithmetic. After thinking about it, I can see a similarity between the absolute value and the modulo operator, since one is a distance from zero and the other is a distance from a multiple of the divisor. But 19 % 5 = 4, not 1, so they're not quite the same. Is "absolute value" just the American way of saying this, or do British people use both terms interchangeably? I tried some Googling to see if I could answer this question myself first, and from the queries I did, it looks like most sources in the UK use only modulus and not absolute value. I did find a few, but now I'm wondering if these might be from Americans working on British websites.

[@BUY_YOUTUB_VIEWS_2273]

I wish I had found your channel earlier. Amazing! 😃