CALCULUS BC EXTRA TOPICS

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Presentation transcript:

CALCULUS BC EXTRA TOPICS Developed by Susan Cantey and her students 2006

They will tend to be a little harder to remember!! Here come some questions on the extra topics not covered in the AB course. They will tend to be a little harder to remember!! When you think you know the answer, (or if you give up ) click to get to the next slide to see if you were correct. Ready?

Explain: Calculus rocks!

This is the Logistic Equation, where k= Growth rate K= Carrying Capacity

Logistic Solution P(t) = ?

Where:

Next term using Euler’s Method = ? “Oiler”

Previous (at previous (x,y)) Estimated “Change”

Length of a curve defined by f(x)…i.e. arc length… Curve length

How long is it?

Length of a parametric curve…

Formula for Speed in Parametric equation? Speedy the lightning bolt

That is, speed is the rate of change along the curve…the derivative of the integral for arc length, i.e. the integrand by itself.

Formula for Speed in Motion Problems?

Length of a polar curve…

area of a region “inside” a polar graph...

Master polar of equations

(Parametric) More change

(Parametric) The change of the change

(Polar) Polar Bear

♪ if you forget the formula for the polar derivative, you can always derive it using: x = r·cosӨ and y = r·sinӨ along with the product rule and

What is the formula for the velocity and acceleration vectors? A vector function is: What is the formula for the velocity and acceleration vectors?

Velocity vector: Acceleration vector:

Average Value of J(x)?

You’re done!

Class of ’07 rocks all. Stay in school, kids.

Be sure to study the power points for : 1) Integrals 2) Derivatives 3) Sequences and Series 4) Miscellaneous Topics