CALCULUS BC EXTRA TOPICS

1
CALCULUS BCEXTRA TOPICS

• Developed by
• Susan Cantey and her students
• at
• Walnut Hills High School
• 2006

2
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?
3
Explain
Calculus rocks!
4
This is the Logistic Equation, where k Growth
rate K Carrying Capacity
5
Logistic Solution P(t) ?
6
Where
7
Next term using Eulers Method ?
Oiler
8
Previous
(at previous (x,y))
Estimated Change
9
Length of a curve defined by f(x)i.e. arc length
Curve length
10
How long is it?
11
Length of a parametric curve
12
(No Transcript)
13
Formula for Speed in Parametric equation?
Speedy the lightning bolt
14
That is, speed is the rate of change along the
curvethe derivative of the integral for arc
length, i.e. the integrand by itself.
15
Formula for Speed in Motion Problems?
16
(No Transcript)
17
Length of a polar curve
(Polar)
18
(No Transcript)
19
area of a region inside a polar graph...
20
Master polar of equations
21
(Parametric)
More change
22
(No Transcript)
23
(Parametric)
The change of the change
24
(No Transcript)
25
(Polar)
Polar Bear
26
(No Transcript)
27
? if you forget the formula for the polar
derivative, you can always derive it using x
rcos? and y rsin? along with the product
rule and
28
(Parametric)
Surface
Area
29
About Y-axis
About X-axis
30
(Reg. Function)
31
About X-axis
About Y-axis
32
(No Transcript)
33
Where x, y, and z are treated the same as
parametric equations
34
Another notation for a vector function is
What is the formula for the velocity and
acceleration vectors?
35
Velocity vector Acceleration vector
(or use the i, j, k notation) also...most AP
vector problems will be 2-dimensionalso the
third (z) component will be omitted.
36
Work ?
37
Force dx
38
Work in stretching and/or contracting springs?
39
Where a length of the spring when the work
begins minus the springs natural length b
length of the spring when the work ends minus
the springs natural length 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 its natural length
40
Work in pumping liquids
41
Density g area of cross section distance
dy
Density g weight
42
Average Value of J
43
Youre done!
44
Created by Robert Jiang Jake Ober
45
Class of 07 rocks all. Stay in school, kids.
46
Be sure to study the power points for 1)
Integrals 2) Derivatives 3) Pre-Calc Topics (on
a separate page) 4) Sequences and Series 5)
Miscellaneous Topics