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A crystal growth furnace is used in research to determine how best to manufacture crystals used in electronic components for the space shuttle. For proper growth of the crystal, the temperature must be controlled accurately by adjusting the input power. Suppose the relationship is given by$$T(\omega) = 0.1\omega^2 + 2.155\omega + 20$$where $T$ is the temperature in degrees Celsius and $\omega$ is the power input in watts. (a) How much power is needed to maintain the temperature at $200^{\circ}C$?(b) If the temperature is allowed to vary from $200^{\circ}C$ by up to $\pm 1^{\circ}C$, what range of wattage is allowed for the input power?(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) $w=32.998$(b) from 32.884 to 33.112 watts(c) see explanation

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Idaho State University

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DM
Oklahoma State University

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Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Michael J.

Idaho State University

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