Lec #18 Pt.2 Ch 11.10 Taylor & Maclaurin Series

I kept an X here because it was a defined interval this time. I put a what I just inserted that number in front. Now we have to get the The first two terms you can write them as fractions or decimals up here so that I can write them as fractions or glasses. What is the first number? I'm going to write them as fractions. What is the charge of the first three? The first term connecting a 0 to 1 is a 0. what 0 factor one what ispoint 5 to 2 times 0 plus 3, plus 2 times n plus 3 is, so there's my first term. I'll write it like this and then you can take out any constant, what is that in the counter? 0.5 cubed over 3 let me know if I have it but I will write very small below this is a 5 cubed 25 cubed over 3 would come out as a point and it is as a point 0 4 I want to write the decimal correctly oh yeah when will I have the address still? stay calm, they want the first returns, this posture is this: very important now, when you notice that we have 1 a.m. negative here, that will make it alternate, the first one was positive, now you put a 1 here and see.

I'll put the - here comes the second term 0.5 al - 2 + 3 that's enough, yes - up in one you escape 5 what is 1 factorial 1 what is 2 times 1 + r/n times a really small number that number NGJ well that one It's a point 5 out of 5, okay, like in some places, wait zero zero six two five, we're getting close, but that's not smaller than that, so I'll continue, that was positive, negative, this is the only capsule , TRUE? the first three terms, what are you getting here? continue, this is, give me a break, let's go to point five, connect a - hey, keep in mind I'm ready, there's nothing wrong with these fractions.

I'll give you enough space or anyone here could write it. the long decimal readings of these three notes are completely fun, it only goes as far as you have a company, it doesn't mean you have to write it in fractional language, now it's point five to seven, who doesn't forget that. arrogant what is 2 factorial 2 if I have no other term what is 3 factorial is not 3 remember 3 factorial means 3 times 2 times 1 just in case where is the fact of a night here where is the factorial oh it's mass go to math and a narrative PRB in case you want to check this out if you ever wanted to get that thing right.

We just know it's easy, we can do it in our head to factor, it's like 2 times 1, what is 3? factor in your head 3 times 2 times 1 6 what is the order of four operations? you'll probably do it 4 times 3 times 3 times 1 right, it's always good to know about the first five girls, but this would be 2 times 7 or whatever 14 yeah, and you thank me. here positive this is negative this is positive but it is designed to choose the notation a 45.58 negative 45.58 right here in fact 5.59 competing for that means a decimal place with how many jurors 0 0 0 head up five all are less than this so by the theorem of alternating

series

estimation I just have to get this precision I just have to add which to know this is all I have to write in my blank room, but I'm going to make it clear what happens if I add this to this just make it more precise, like this Don't worry if you say, oh God, what happens if I add three more terms?

It's just going to make it more precise, they just want this, you actually know less than this, so let's Write this answer now, well, how many decimals are we going to do, let's say for this one and we're going to go out and write it to four decimal places, so now I will remember that you wrote this accurately. four is definitely like that and your community that - that on the screen and I'm going to write the whole number point five key number three - physical positive let's write everything else I'm just going to say the moment I'm like I don't have to add that so that this actress be right, of course, what is that zero three five four one six and how is something okay with that 468 now, if you see the four decimals, then I'm just going to write? one doesn't help me well, by the way, I go there, right at point zero, three, five and that's a year after four, so I rounded up or kept it ahead, there you go, that's what I put my answer , they look good.

Anson can pour decimals there we go there has to be less air than s what we cut about four dozen terms yes senator actually now you have your peppers let's see what you get where do we go? I want to make sure you understand the whole problem you have with where I'm going now. I want to make sure this works from what I did. All this. I'm not doing anything and I get the same number. It's not very good evidence. I did all of primary school. Alright. do it math nine nine and one you can do math nine function integrate like so x squared where e is I'll send two places negative precision less than that, it's the same as everyone gets point zero three five nine these first three numbers right there and that would be the action less than that, let's say we get point zero three, so even there we only had that precision let's see what is happening here we're getting this to what extent O 3 5 so we get two point zero three five nine now why is it slightly different because we only get to the air?

You know, we had the accidents, this is what I want you to see by the way. I wanted to know about 54 with you the real number on my calculator that says dot zero three five nine four zero three when I add Andrews calories add these two and it says dot zero three five then the four and eleven movie i1z so you might be thinking if I did something wrong oh we didn't do anything wrong we just got the oxy what they said come up like this and when you see what's happening we have point zero three and I was like five four right we had those things but if we wanted to be more , but get 5 and 9, what would we do?

We would simply add more terms. Hi Nicholas, it will work, so when you write your life in mind, that depends. like we said, we have different programs in this format, you have people, you have your new model evidence, so you have x squared, let's again integrate x squared e to the negative square point X 0, okay, I'll write that on the board. I would do it so people could see this when I was going through this one to finish by doing a math line and I hit it and then I was writing there is a function integrate and x squared they both won it's a carat and then it was a negative comment of x squared .

X comma comma zero point five and I know it, but again I want you to see something before leaving what appeared here in the calculator that will have eight precision digits, so the reason why I got a bit weird here is because only usa, I'll take that, does that make sense? let's do it are you sure you did it right great great job tomorrow we will do 1111 which is amazing basically the same thing we just wrote has polynomials these are polynomials are polynomials every day