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# A machinist is required to manufacture a circular metal disk with area 1000 $cm^2$. (a) What radius produces such a disk? (b) If the machinist is allowed an error tolerance of $\pm 5 cm^2$ in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius? (c) In terms of the $\varepsilon$, $\delta$ definition of $\displaystyle \lim_{x \to a} f(x) = L$, what is $x$? What is $f(x)$? What is $a$? What is $L$? What value of $\varepsilon$ is given? What is the corresponding value of $\delta$?

## (a) $r \approx 17.8412 cm$(b) Radius must be within $0.0445 cm$(c) $x$ is the radius, $f(x)$ is the area, $a$ is the target radius given in part (a), $L$ is the target area $(1000), e$ is the tolerance in the$\operatorname{arca}(5),$ and $\delta$ is the tolerance in the radius given in part (b).

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