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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Monday, December 05, 2005

Blogging On Differentiation rule

In this Chapter, I found the most difficult stuff was relates rates problems.
We need to read the question and find a formula, or even probably two relate to the information that question told us. We need to know everything that might relate to the question, and solve the problem.
Exp: Water is flowing into a cone-shaped tank at the rate of 5 cubic inches per second. If the cone has an attitude of 4 inches and a base radius of 3 inches, how fast is the water level rising when the water is 2 inches deep?
The problem is given us the rate of change volume, dv/dt =5, r = 3, and asked to determine the rate change of height when h is 2, dh/dt when h=2.
We know the formula for conical volume is: V = 1/3 pai (r)^2 h
By similar triangle we have r/3=h/4,
So, r=3/4 h
V=1/3 pai r^2 h
V=1/3 pai (3/4h)^2 h
V= 1/3 pai 9/16 h^2 h
V= 3/16 pai h^3
Defferentiate implicitly:
dv/dt = 3/16*pai* 3h^2 (dh/dt)
5 = 3/16 pai 3(2)^2 (dh/dt)
20/9pai = dh/dt
The water level is rising at a rate of 20/9pai inches per second when the water is 2 inches deep.



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