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1) Estimate T'(3). Show the work that leads to your answer. Include units of measure. ) Write an integral expression in terms of T(c) for the average temperature of the cable. Estimate the average temperature of the cable using a trapezoidal sum with the four subintervals indicated by the data in the table. Indicate units of measure. :) Find T'(c)dc, and indicate units of measure. Explain the meaning of T'(c)dc in terms of the temperature of the cable.

1) Estimate T'(3). Show the work that leads to your answer. Include units of measure. ) Write an integral expression in terms of T(c) for the average temperature of the cable. Estimate the average temperature of the cable using a trapezoidal sum with the four subintervals indicated by the data in the table. Indicate units of measure. :) Find T'(c)dc, and indicate units of measure. Explain the meaning of T'(c)dc in terms of the temperature of the cable.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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An aluminum cable of length 10 inches is heated at one end. The table shows some values of the temperature T(dc), in degrees Fahrenheit, of the cable c inches from the heated end. T(c) is a twice-differentiable function. 0 2 Temperature T(c) ('F) 120 106 4 7 10 Distance c inches 94 80 60 (a) Estimate T'(3). Show the work that leads to your answer. Include units of measure. (b) Write an integral expression in terms of T(c) for the average temperature of the cable. Estimate the average temperature of the cable using a trapezoidal sum with the four subintervals indicated by the data in the table. Indicate units of measure. (c) Find "T'(c)dc, and indicate units of measure. Explain the meaning of f," T'(c)de in terms of the temperature of the cable. (d) Are the data in the table consistent with the assertion that T"(c) > 0 for every x in the interval 0 <c< 10? Explain.
Transcribed Image Text:An aluminum cable of length 10 inches is heated at one end. The table shows some values of the temperature T(dc), in degrees Fahrenheit, of the cable c inches from the heated end. T(c) is a twice-differentiable function. 0 2 Temperature T(c) ('F) 120 106 4 7 10 Distance c inches 94 80 60 (a) Estimate T'(3). Show the work that leads to your answer. Include units of measure. (b) Write an integral expression in terms of T(c) for the average temperature of the cable. Estimate the average temperature of the cable using a trapezoidal sum with the four subintervals indicated by the data in the table. Indicate units of measure. (c) Find "T'(c)dc, and indicate units of measure. Explain the meaning of f," T'(c)de in terms of the temperature of the cable. (d) Are the data in the table consistent with the assertion that T"(c) > 0 for every x in the interval 0 <c< 10? Explain.
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