Answer to Question #253508 in Calculus for Roger

Question #253508
In the temperature range between 0 degrees * C and 700 ^ 0 * C the resistance R [in ohms] of a certain platinum resistance

thermometer is given by

R = 10 + 0.04124T - 1.779 * 10 ^ - 5 * T ^ 2 where 7 is the temperature in degrees Celsius. Where in the interval from 0 °C to 700 ^ 0 * C is the resistance of the thermometer most sensitive and least sensitive to temperature changes? [/lint: Consider the size of dR / d * T in the interval 0 <= T <= 700.1
1
Expert's answer
2021-10-20T04:12:04-0400
R=10+0.04124T1.779×105T2R=10+0.04124T-1.779\times 10^{-5}T^2

dRdT=0.041243.558×105T\dfrac{dR}{dT}=0.04124-3.558\times10^{-5}T

The function dRdT\dfrac{dR}{dT} decreases for T[0°C,700°C].T\in[0\degree C, 700\degree C].


dRdTT=0°C=0.04124 Ω/°C\dfrac{dR}{dT}|_{T=0\degree C}=0.04124\ \Omega /\degree C

dRdTT=700°C=0.016334 Ω/°C\dfrac{dR}{dT}|_{T=700\degree C}=0.016334\ \Omega /\degree C

The resistance is most sensitive to temperature changes at T=0°C,T=0\degree C, least sensitive at T=700°C.T=700\degree C.



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