# calculus

A state charges polluters an annual fee of \$20 per ton for each ton of pollutant
emitted into the atmosphere, up to a maximum of 4,000 tons. No fees are charged
for emissions beyond the 4,000-ton limit. Write a piecewise de�nition of the fees F(x)
charged for the emission of x tons of pollutant in a year. What is the limit of F(x) as
x approaches 4,000 tons? As x approaches 8,000 tons?

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1. F(x) is a continuous function governed by F(x)=20x for 0<x≤4000
=80000 for 4000<x
Note that
Lim x->4000- F(x)=Lim x->4000+ F(x) = 80000

See if you can find Lim x->8000 F(x).

Post your answer for confirmation if you wish.

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2. 80,000

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3. 80000

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