# The fee per ton of pollution is given by A(x) = F(x) = x. Write a piecewise definition of A(x)....

## Question:

The fee per ton of pollution is given by A(x) = F(x) = x.

Write a piece-wise definition of A(x).

What is the limit of A(x)?

1. as x approaches 4,000 tons

2. as x approaches 8,000 tons

## Limits:

From the limit of the expression or function is taken from any input, the expression can either converge or diverge to a function value based on the behavior of the expression.

Given: {eq}A(x) = F(x) = x {/eq}

From the given information, the piece-wise function can expressed as {eq}A(x) = \left\{\begin{matrix} x & if\ -\infty \leq x \leq \infty \\ \end{matrix}\right. {/eq}

1. As {eq}x {/eq} approaches {eq}4,000 {/eq}:

{eq}\begin{align*} \lim_{x \rightarrow 4,000} A(x) &= \lim_{x \rightarrow 4,000} x \\ &= 4,000 \\ \end{align*} {/eq}

2. As {eq}x {/eq} approaches {eq}8,000 {/eq}:

{eq}\begin{align*} \lim_{x \rightarrow 8,000} A(x) &= \lim_{x \rightarrow 8,000} x \\ &= 8,000 \\ \end{align*} {/eq}