?Crystal growth furnaces are used in research to determine how best to manufacture

Chapter 2, Problem 12

(choose chapter or problem)

Crystal growth furnaces are used in research to determine how best to manufacture crystals used in electronic components. For proper growth of a crystal, the temperature must be controlled accurately by adjusting the input power. Suppose the relationship is given by

\(T(w)=0.1 w^{2}+2.155 w+20\)

where \(T\) is the temperature in degrees Celsius and \(w\) is the power input in watts.

(a) How much power is needed to maintain the temperature at \(200^{\circ} \mathrm{C}\) ?

(b) If the temperature is allowed to vary from \(200^{\circ} \mathrm{C}\) by up to \(\pm 1^{\circ} \mathrm{C}\), what range of wattage is allowed for the input power?

(c) In terms of the \(\varepsilon, \delta\) definition of \(\lim _{x \rightarrow a} f(x)=L\), 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 \(\delta\)?

Equation Transcription:

℃

℃

Text Transcription:

T(w)=0.1w^2+2.155w+20

T

w

200 degree celsius

xaf(x)=L

f(x)

lim_x right arrow a f(x)=L

f(x)

delta

L

pm 1 degree celsius