1. CALCULUS BC EXTRA TOPICS
Developed by
Susan Cantey and her students at
Walnut Hills High School
2006

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

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

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

5. How long is it?

6. Length of a parametric curve…

8. Formula for Speed in Parametric equation?
Speedy the lightning bolt

9. 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.

10. Formula for Speed in Motion Problems?

12. Length of a polar curve…

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

15. Master polar of equations

16. (Parametric)
More change

18. (Parametric)
The change of the change

20. (Polar)
Polar Bear

21. (using prod. Rules:)

22. (Reg. Function)

23. About X-axis
About Y-axis

24. (Parametric)
Surface
Area

25. About Y-axis
About X-axis

26. What is the formula for the velocity and acceleration vectors?
Another notation for a vector function is:
What is the formula for the velocity and acceleration vectors?

27. (or use the i, j, k notation)
Velocity vector:
Acceleration vector:
(or use the i, j, k notation)
also...most AP vector problems will be
2-dimensional…so the third (z) component
will be omitted.

28. Work in stretching and/or contracting springs?
(Hooke’s Law)

29. a = length of the spring when the work begins minus
Where:
a = length of the spring when the work begins minus
the spring’s natural length
b = length of the spring when the work ends minus
k = a constant peculiar to the spring in question
kx = force needed to maintain the spring at a length x units longer (or shorter) than it’s natural length

30. Explain:
Calculus rocks!

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