Post 27

Yay...school tomorrow.

Anyway, here's the steps for implicit derivatives for those of you who have forgotten.


1. Take the derivative of both sides (implicit derivatives usually have an equals sign)

2. When you take a derivative of a y term, state that. Do so by putting y prime or dy/dx. Like ( taking the derivative of y^2 would be 2y(dy/dx) )

3. Move all of the terms that don't have a dy/dx in them to one side. Factor out a dy/dx out of all the terms that do have it, then divide to finish solving for dy/dx.

That's basically all it is. Just make sure when you are doing these is like...say you are doing product rule with like sin's and cos's...make sure you put cos(x) where its supposed to and cos(y) where its supposed to. It would really mess up problems if you mix this up. So take these longer derivatives slow and just avoid making silly mistakes.

As for what else I can explain...hmm

Riemann Sums, yay.

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 this is the most accurate of the Riemann summs. x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]

all of the above is assuming that x is delta x which is (b-a)/(subintervals)


Anyway, just wanted to mention two things people still miss.

Have a good day :-P