The fee per ton of pollution is given by A(x) = F(x)=x. Write a piecewise
de�nition of A(x). What is the limit of A(x) as x approaches 4,000 tons? As x
approaches 8,000 tons?
http://www.jiskha.com/display.cgi?id=1298565394
A(x)=20x/x
A(x)=80,000/x
To write a piecewise definition of A(x), we need to define the function A(x) for different ranges of x.
Given that A(x) = F(x) = x, we can write the piecewise definition as follows:
For x < 0, A(x) is undefined (since negative pollution does not make sense).
For 0 ≤ x < 4,000 tons, A(x) = x.
For 4,000 ≤ x < 8,000 tons, A(x) = x.
For x ≥ 8,000 tons, A(x) = x.
Regarding the limits as x approaches 4,000 tons and 8,000 tons:
1. Limit as x approaches 4,000 tons:
To find the limit as x approaches 4,000 tons, we substitute 4,000 into the function A(x):
lim(x→4,000) A(x) = lim(x→4,000) x = 4,000.
Therefore, the limit of A(x) as x approaches 4,000 tons is 4,000.
2. Limit as x approaches 8,000 tons:
To find the limit as x approaches 8,000 tons, we substitute 8,000 into the function A(x):
lim(x→8,000) A(x) = lim(x→8,000) x = 8,000.
Therefore, the limit of A(x) as x approaches 8,000 tons is 8,000.