Mr. Sorensen

AB Implicit Time 3-11

Like we discussed, purpose here to set mathematical curves in motion. Triangles. Spherical bellies. 12 foot upside-down cones. Etc. Anytime you see something moving, it is along a curve with time being inflicted upon it ... and this is how.

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Exponential Integrating Factor Intro 3-11

This is another solution method that is both a more general form of the separation of variables, and a more powerful form that extends your abilities to address other types of problems.

While the derivation is detailed, and difficult to take it all in, the resulting method is clean and aggressive. Little by little, as we progress through these things, you will see more and more of why we went through the derivation - because each step in it contains its own set of specific solutions. I know it was rough. Think back to the Fundamental Theorem discussions. They were rough too. But it is all simple now and part of your instincts and mathematical vocabulary. This stuff will progress that way also.

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AB Inv Trig Derivatives 3-6

This includes the classwork and the homework. Tried to include a description of the 'triangle' exercise also.

Download AB Inv Trig 3-6

AB Implicit Derivatives 3-3

This is actually one of the purer form of the derivative operation - the application of the derivative operator all the way across an equation, just like I showed in class. In reality, we have been doing this the whole time, just not showing the details. 

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Postings for Observations

Download AP Scope and Sequence AB

Download AP Scope and Sequence BC

Download Logistic Population

AB L'Hopital and FTCPVA 2-24

The BC group was very excited that you finally knew L'Hopital. It can make your life so much better. Not that everything is a L'Hopital trick, but it seems to come in handy in the handiest places. It probably would have solved ALL of the limit problems at the beginning of the year.

As for the FTC problem - pay close attention to the wording. It is the same as always but you should be good enough at the interpretations that we can give more attention to cleaning up the support reasoning. Most of all, since it is a FTC problem, you must cite the Fundamental Theorem when you make the connection between H' and f, and H" and f'.

Download L'Hopital Intro 2-24

Download FTCPVA 2-24

AB 2-23 99AB Practice

AP Practice 1999 1,3,5

Separation Practice II 2-23

A few more reminders of what you know:

Trig Identities

Factoring

Inverse trig functions

Partial Fractions

Don't forget the C's.

Download Separation Practice II 2-23

AB FTC and CR Practice 2-21

The FTC derivative stuff is just skill practice. The world will not end if you don't get the answers the first time through.

Your calculus world will be much more unpleasant if you do not get the derivatives on the other sheet though. You must have those. Must.

Next, you should also be able to do the integrals, or at least use it as a good learning tool because the answers to the integrals are the derivatives above ... and yes, I was quite proud of that. I also gave hints for what to use as 'u' in the chain rule integrals but do not forget to do the du substitution that makes the whole process work.

Download AB FTC and CR Practice 2-21

Slope Fields and Equilibrium Values 2-21

More matching but with a bit more style. You can easily see that these situations have multiple solution curves depending on the initial values the curves must pass through.

Download Slope Fields & Equil 2-21