Chapter 1: Problem 25
Find the limit. \(\lim _{x \rightarrow-3}(2 x+5)\)
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Chapter 1: Problem 25
Find the limit. \(\lim _{x \rightarrow-3}(2 x+5)\)
These are the key concepts you need to understand to accurately answer the question.
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Environmental cost The cost \(C\) (in millions of dollars) of removing \(x\) percent of the pollutants emitted from the smokestack of a factory can be modeled by $$C=\frac{2 x}{100-x}$$ (a) What is the implied domain of \(C ?\) Explain your reasoning. (b) Use a graphing utility to graph the cost function. Is the function continuous on its domain? Explain your reasoning. (c) Find the cost of removing \(75 \%\) of the pollutants from the smokestack.
Find the limit (if it exists). \(\lim _{\Delta x \rightarrow 0} \frac{2(x+\Delta x)-2 x}{\Delta x}\)
Find the limit (if it exists). \(\lim _{x \rightarrow-1} \frac{x^{3}-1}{x+1}\)
The cost (in dollars) of removing \(p \%\) of the pollutants from the water in a small lake is given by \(C=\frac{25,000 p}{100-p}, \quad 0 \leq p<100\) where \(C\) is the cost and \(p\) is the percent of pollutants. (a) Find the cost of removing \(50 \%\) of the pollutants. (b) What percent of the pollutants can be removed for \(\$ 100,000 ?\) (c) Evaluate \(\lim _{p \rightarrow 100^{-}} C .\) Explain your results.
Find the limit (if it exists). \(\lim _{x \rightarrow 2} \frac{|x-2|}{x-2}\)
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