yeah, this week all we did was take a bunch of ap exams, again.. but it's okay because i am getting better at them. for this blog i am going to write about riemann summs.
The first formula you need to know is x=(b-a)/n [a,b] with n subintervals. You will need to know this because each of the next formulas require that you know what x is.
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)]
RRAM- 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)]
i still have trouble with related rates, in my opinion, that is the hardest part of the ap tests we take, and it is on almost every free response section, so some help on that would be appreciated.
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we never have related rates! so taht could be why it's hard for you..but if your talking about the things filling up with oil, or something like taht i can show it to you in class.
ReplyDeleteall you have to think is PVA position, velocity, acceleration..and as you go across the acroynm you take the derivative.
Related Rates:
ReplyDelete1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation
related rates are always a long paragraph. explainging how oil is spilling in the ocean or filling up a tank or something. the most common first thing given is ... THE RATE AT WHICH OIL IS SPILLING IN THE OCEAN IS v(t)=whatever, v representing velocity.
ReplyDeleteand it will tell you a bunch of other stuff that is usually important. just write it all down on the side.
also, for related rates.... 9/10 times on free response. part A says something like the rate at which the oil spills from time = 0 to time =2. whenever it gives you an interval, you should INTEGRATE according to that interval. *calculators*
:)
Related Rates:
ReplyDelete1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation
ima post the steps like everyone else :)
ReplyDelete1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation