we learned are between curves and we also learned disks and washers
To find area between curves:
The formula you use is b(int)a (top eq.) - (bottom eq.).
If a and b is not already given to you, then you much set the equations equal to each other and solve.
You find which equation is top/bottom by graphing both and simply looking to see which one is on top.
If the area is on the y-axis, then the a and b values need to be set as y-values, and the equations must be solved for x.
First of all: Disks are solid objects with one equation bounded by the equation and usually an axis. Washers are objects bounded by two equations.
Formula for Disk:
(Pi) b(int)a [R(x)]^2.
Formula for Washers:
(Pi) b(int)a (top eq.)^2 - (bottom eq.)^2 dx.
Washers:
volume by washers is basically the same concept except that it is not just one formula squared, it is pie times the top equation squared minus the bottom equation squared. You figure out which formula is the top and bottom by graphing the equation by hand or on your calculator, once you figure that out, you then square the functions and integrate them and solve. Again, the same rules apply to the bounds.
limit rule is something good to hold onto
limits:
Rules for Limits:…
1. if the degree of top equals the degree of bottom, the answer is the top coefficient over bottom coefficient
2. if top degree is bigger than bottom degree, the answer is positive or negative infinity
2. if top degree is less than bottom degree, the answer is 0
some things im not too great on is related rates and and all the mram rram and lram is confusing to me somehow lol
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these are the steps for related rates:
ReplyDelete1. Identify all of the variables and equations
2. Identify what you are looking for
3. sketch and lable a graph
4. create an equation using all of the variables
5. Take derivative with respect to time
6. substitute back in
7. solve
I actually understand RRAM. So, I'll attempt to explain.
ReplyDeleteRRAM is the right hand approximation. The formula: delta x[f(a+deltax)+...+f(b)].
delta x is b-a/n
The problem should have a point [a,b] and then give you n which is the subintervals.
You take your a and add delta x. Then take whatever you got and add delta x to that. (If your subinterval is 4 then you do it 4 times.) You should end up with b as your last number.
Then you plug into the equation they give you with each one. Add them all and make sure to multiply by delta x!