Wow, lucky number 13, eh?
I'm so glad I was up writing, because I forgot all about this. 0=]
Alright, this week, we worked on Integration a bit. I sorta understand it, but I have to be glued to my notes in order to remember what to do. I really hope that John was right when he said you understand it with more practice.
I would attempt to explain it, but I don't want to sound like a fool, so let's move on to something I understand better! :)
Hmm....how about...Implicit Derivatives!!
1. Don’t move anything! Just take the Derivative like normal, except that after EACH term, add a d(insert term here)/dx. Don’t forget to do it on BOTH SIDES!
2. Then solve for d(insert term here)/dx!
Very very simple
Example!
Find the Implicit Derivative of 6y^2+3x=7x^3-8y^2
1. 12y(dy/dx) + 3(dx/dx) = 21x^2(dx/dx) - 16y (dy/dx)
2. 12y(dy/dx) + 16y(dy/dx) = 21x^2(dx/dx)-3(dx/dx)
3. 28y(dy/dx) = 21x^2(dx/dx)-3(dx/dx)
4. (Dy/dx) = (21x^2(dx/dx)-3(dx/dx)) / 28y
For what I don't understand:
I THINK I understand integration a little bit, I just would like someone to go over the homework for this weekend and see if I made any major mistakes. I have trouble with Definite Integration more than Indefinite for some reason...I stopped half-way through the assignment because I really don't think I was doing them right. Can someone help me with that? :)
Oh! I almost forgot! I, for some reason, also have trouble with LRAM, RRAM, MRAM, and Trapezoidal Integration. Not sure why, I just do. I think the graphs blew my mind and I think I can't do it anymore because of the graph? I'm not sure, but I also need help with those. v.v
Anndd…linearization! I’m iffy on that…can someone explain (short and sweet) the simple steps?
Thanks!!!!
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For LRAM, RRAM, MRAM, and Trapezoidal, you just have to what the fomrula is for each.
ReplyDeleteFirst you need to find delta x which is b-a/n
LRAM is left hand approximation
delta x [f(a) + f(a + delta) + ... f(b- delta x)
It is easier to see whats going on with an example so:
x^2-3 [1,4] n=3
delta x = 4-1 / 3 = 1
now plug in: 1[ f(1)+ f(2)+ f(3]
1[-2 + 1 + 6] = 5
RRAM: delta x [ f(a+ delta x) + ... + f(b)]
1[ f(2) + f(3) + f(4)]
1[ 1 + 6 + 13] = 20
MRAM: delta x [ f(mid) + f(mid)...]
To find the midpoints, you add the first two numbers then divide by two, then the second and third numbers and divide by two, and so on
Your midpoints are: 3/2, 5/2, and 7/2
1[f(3/2) + f(5/2) + f(7/2)]
1[ -3/4 + 13/4 + 37/4] = 47/4
Trapezoidal: delta x/2 [f(a) + 2f(a+ delta x) + 2f ( a + 2 delta x) +... f(b)]
1/2 [ f(1) + 2 f(2) + 2f( 3) + f(4)]
1/2 [ -2 + 2(1) + 2(6) + 13] = 25/2
Remember for trapeziodal: the will always be one more term than their is for the rest