LIMIT RULES:
1. If the degree of the top is larger than the degree of the bottom, the limit approaches infinity
2. If the degree of the bottom is larger than the degree of the tip, the limit approaches zero
3. If the degree of the bottom is equal to the degree of the top, then you make a fraction out of the coefficients in front of the largest degree.
linearization.
The steps for solving linearization problems are:
1. Pick out the equation
2. f(x)+f`(x)dx
3. Figure out your dx
4. Figure out your x
5. Plug in everything you get
implicit derivatives:
First Derivative:
1. take the derivative of both sides
2. everytime you take the derivative of y note it with dy/dx or y^1
3. solve for dy/dx
i dont understand lram,
I dont understand rram
i dont understand trapiziodal
and m ram
can somebody help me with these i need help with these. Somebody help!!! It will be much appreciated.
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LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
ReplyDeleteRRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
*delta x=b-a/number of subintervals
Okay so here we go again..
ReplyDeleteLRAM is left hand approximation. The formula is
delta x [f(a) + f(a+delta x) +....f(b-delta x)]
Example: Find area of f(x)=x-3 o n the interval [0,3] with three sub intervals.
The first step is to find delta x which is b-a / n
delta x=3-0/3 which equals 1
Then plug into the formula
1[f(0)+f(0+1)+f(1+1)]
1[(-3)+(-2)+(-1)] = -6
RRAM is right hand approximation and the formula is
delta x[f(a+delta x) + .... + f(b)]
Using the same example: 1[f(1)+f(2)+f(3)]
1[(-2)+(-1)+(0)] = -3
MRAM formula is delta x[f(mid)+ f(mid) +...]
You start in a then add delta x until b
0 , 1, 2, 3
Now take the midpoint of each
0+1/ 2 = 1/2
1+2/2 = 3/2
2+3/2 = 5/2
Then plug into formula
1[f(1/2) + f(3/2) + f(5/2)]
1[(-5/2) + (-3/2) + (-1/2) = -9/2
And finally the formula for trapezoidal is
delta x/2[f(a)+2f(a+delta x) + 2f(a+2 delta x) +.... f(b)]
1/2 [f(0) + 2f(1) + 2f(2) + f(3)]
1/2[(-3) + 2(-2) + 2(-1) + 0]
1/2[-9] = -9/2
It's quite simple if you know the formulas.
LRAM-left handed approximation
ReplyDeletedelta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-right handed approximation
delta x[f(a+delta x)+...f(b)]
MRAM-middle approximation
delta x[f(mid)+f(mid)+...]
Trapezoidal
delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
I'm not going to do an example because chelsea already did, but this concept is extremely easy because you just follow the formula exactly. All you have to do is take some time to memorize them and know the difference between the four and you'll never have to worry about it again.
LRAM, RRAM, MRAM, and TRAM are actually pretty easy because you just plug into the formula. The only tricky part you may encounter is remembering the formulas themselves or doing the algebra.
ReplyDeleteRRAM: deltax [f(a + deltax) + ... + f(b)]
LRAM: deltax [f(a) + f(a + deltax) +... + f(b - deltax)]
MRAM: deltax [f(mid) +f(mid) + ...]
TRAM: deltax/2 [f(a) + 2f(a +deltax) + 2f(a + 2deltax) + ... + f(b)]
LRAM- left hand approximation. (this puts the rectangles used to find the area on the left side of the curve) x[f(a)+f(a+x)+...f(b)]
ReplyDeleteRRAM- right hand approximation. (this puts the rectangles used to find the area on the right side of the curve) x[f(a+x)+...f(b)]
MRAM- approximation from the middle. (this puts the rectangles right on top of the curve, so that the curve goes through the middle of each one) x[f(mid)+f(mid)+...]
Trapezoidal- this does not use squares, instead it uses trapezoids to eliminate most of the empty space inside the curve, and I think this is the most accurate. x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]