I've lost count.

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

So for implicit derivatives...its pretty easy. You are going to be using this when you have like y^2 + x^2 = 4. It will ask for dy/dx. So what you do is you take the derivative like normal...but whenever you take the derivative of y you write dy/dx. So the above would be 2y (dy/dx) + 2x = 0. Now you solve for dy/dx. To do this, minus over 2x and then divide by 2y. So the answer would be

dy/dx = -x/y.

Some people have been asking about related rates!!!!!!!!!!!!! SO HERE IS an EXAMPLE!!!

Um let's see...
The steps for related rates are:
1. Pick out all variables
2. Pick out all equations
3. Pick out what you are looking for
4. Sketch a graph and label
5. Create an equation with your variables
6. Take the derivative respecting time
7. Substitute back into the derivative
8. Solve

Okay so first derivative refers to slope of position..which is velocity.
Second derivative is slope of velocity...or acceleration.
Third derivative would be the slope of acceleration which I believe is jerk.
Past that, its just the rate of change of whatever was before...so...yeah.


Anyway, think this is around 285 words so...see you guys tomorrow.
Posted by XxDohxX at 8:30 PM 0 comments
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post of holidays..3
IMPLICIT DERIVATIVES:
1. Take the derivative like normal.
2. For each y-term, you put y' or dy/dx behind it.
3. Solve for dy/dy or y'.

36x^2 + 2y = 9
36x + 2(dy/dx) = 0
2(dy/dx) = -36x
-36x/2
dy/dx = -18x



steps to SECOND IMPLICIT DERIVATIVES
1. Take the derivative of the first derivative
2. Put d^2y/dx^2 for dy/dx
3. Simplify
4. Plug in values

so an example using the same equation is:
we take the first implicit derivative first
36x^2 + 2y = 9
36x + 2(dy/dx) = 0
2(dy/dx) = -36x
-36x/2
dy/dx = -18x


You have to identify what you are looking for and what you are given. Not only does this make it easier on you, it's kind of necessary, especially when you want those points on free response questions (or so I'm told). You also have to realize that when you are doing related rates, you have to put dy/dt or dx/dt or whatever whenever you are taking the derivative of some variable in relation to time (hence the t). So given that:

Given xy = 4

you want to know what dy/dt equals given x = 8 and dx/dt=10.

Take the derivative (product rule):

dx/dt y + dy/dt x = 0
Plug in everything:

dy/dt = -10y/8

= -5y/4

Obviously, I'm not doing perfect, and I don't know everythin, so here's my trouble areas:

1. I can't remember when to use washers and disks-and i switch up the equations.
2. Slope Fields!!!! I get the one we did on the free response,,,just none like on the practice tests..if that makes any sense.
3. my e integrating skills have something to be desired...

any suggestions?