In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by the following function, where x is the percentage (expressed as a decimal fraction) of the total contaminant removed. Complete parts (A) through (E). P(x) = 7x / (1 - x) 0 ≤ x < 1
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In Silicon Valley, a number of computer-related manufacturing firms were contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the monetary pool (in millions of dollars) for the testing and cleanup is given by $$P(x)=\frac{2 x}{1-x} \quad 0 \leq x<1$$ where $x$ is the percentage (expressed as a decimal) of the total contaminant removed. (A) How much must be in the pool to remove $90 \%$ of the contaminant? (B) How much must be in the pool to remove $95 \%$ of the contaminant? (C) Find $\lim _{\text {limit. }} x \rightarrow 1^{-} P(x)$ and discuss the implications of this limit.
Limits and the Derivative
Infinite Limits and Limits at Infinity
In Silicon Valley, a number of computer-related manufacturing firms were contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the monetary pool (in millions of dollars) for the testing and cleanup is given by $$ P(x)=\frac{2 x}{1-x} \quad 0 \leq x<1 $$ where $x$ is the percentage (expressed as a decimal) of the total contaminant removed. (A) How much must be in the pool to remove $90 \%$ of the contaminant? (B) How much must be in the pool to remove $95 \%$ of the contaminant? (C) Find $\lim _{-1} P(x)$ and discuss the implications of this limit. $\lim _{x \rightarrow 1^{-}} P(x)$
Eleni K.
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