The approximations to e corresponding to h = 0.04 , 0.02 , and 0 .01 .

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Answer 1

Question

Chapter 4.2, Problem 11ES

a.

To determine

The approximations to e corresponding to $h=0.04,0.02, and 0.01$ .

b.

To determine

An $O(h3)$ approximation to e corresponding with $h=0.04$ assuming that $e=(1+h)1h+K1h+K2h2+K3h3+⋯$ .

c.

To determine

Whether the assumption in part (b) is correct.

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Temperature measurements are based on the transfer of heat between the sensor of a measuring device (such as an ordinary thermometer or the gasket of a thermocouple) and the medium whose temperature is to be measured. Once the sensor or thermometer is brought into contact with the medium, the sensor quickly receives (or loses, if warmer) heat and reaches thermal equilibrium with the medium. At that point the medium and the sensor are at the same temperature. The time required for thermal equilibrium to be established can vary from a fraction of a second to several minutes. Due to its small size and high conductivity it can be assumed that the sensor is at a uniform temperature at all times, and Newton's cooling law is applicable. Thermocouples are commonly used to measure the temperature of gas streams. The characteristics of the thermocouple junction and the gas stream are such that λ = hA/mc 0.02s-1. Initially, the thermocouple junction is at a temperature Ti and the gas stream at…

Answer 2

Question

Chapter 4.2, Problem 11ES

a.

To determine

The approximations to e corresponding to $h=0.04,0.02, and 0.01$ .

b.

To determine

An $O(h3)$ approximation to e corresponding with $h=0.04$ assuming that $e=(1+h)1h+K1h+K2h2+K3h3+⋯$ .

c.

To determine

Whether the assumption in part (b) is correct.

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Answer 3

Question

Chapter 4.2, Problem 11ES

a.

To determine

The approximations to e corresponding to $h=0.04,0.02, and 0.01$ .

b.

To determine

An $O(h3)$ approximation to e corresponding with $h=0.04$ assuming that $e=(1+h)1h+K1h+K2h2+K3h3+⋯$ .

c.

To determine

Whether the assumption in part (b) is correct.

Expert Solution & Answer

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Answer 4

Question

Chapter 4.2, Problem 11ES

a.

To determine

The approximations to e corresponding to $h=0.04,0.02, and 0.01$ .

b.

To determine

An $O(h3)$ approximation to e corresponding with $h=0.04$ assuming that $e=(1+h)1h+K1h+K2h2+K3h3+⋯$ .

c.

To determine

Whether the assumption in part (b) is correct.

Expert Solution & Answer

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Answer 5

Chapter 4.2, Problem 11ES

a.

To determine

The approximations to e corresponding to $h=0.04,0.02, and 0.01$ .

b.

To determine

An $O(h3)$ approximation to e corresponding with $h=0.04$ assuming that $e=(1+h)1h+K1h+K2h2+K3h3+⋯$ .

c.

To determine

Whether the assumption in part (b) is correct.

Answer 6

Chapter 4.2, Problem 11ES

a.

To determine

The approximations to e corresponding to $h=0.04,0.02, and 0.01$ .

Answer 7

Chapter 4.2, Problem 11ES

a.

To determine

The approximations to e corresponding to $h=0.04,0.02, and 0.01$ .

Answer 8

b.

To determine

An $O(h3)$ approximation to e corresponding with $h=0.04$ assuming that $e=(1+h)1h+K1h+K2h2+K3h3+⋯$ .

Answer 9

b.

To determine

An $O(h3)$ approximation to e corresponding with $h=0.04$ assuming that $e=(1+h)1h+K1h+K2h2+K3h3+⋯$ .

Answer 10

c.

To determine

Whether the assumption in part (b) is correct.

Answer 11

c.

To determine

Whether the assumption in part (b) is correct.

Answer 12

Expert Solution & Answer

Answer 13

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Answer 14

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Answer 15

Ch. 4.1 - Use the forward-difference formulas and...Ch. 4.1 - The data in Exercise 1 were taken from the...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - Use the most accurate three-point formula to...Ch. 4.1 - The data in Exercise 5 were taken from the...Ch. 4.1 - The data in Exercise 6 were taken from the...Ch. 4.1 - Prob. 9ES Ch. 4.1 - Use the formulas given in this section to...Ch. 4.1 - The data in Exercise 9 were taken from the...Ch. 4.1 - Prob. 12ES

The approximations to e corresponding to h = 0.04 , 0.02 , and 0 .01 .

Solution Summary: The author explains the approximations to e corresponding to h=0.04,0.02,and 0 .01.

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The approximations to e corresponding to $h=0.04,0.02, and 0.01$ .

An $O(h3)$ approximation to e corresponding with $h=0.04$ assuming that $e=(1+h)1h+K1h+K2h2+K3h3+⋯$ .

Whether the assumption in part (b) is correct.

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Chapter 4 Solutions

The approximations to e corresponding to h = 0.04 , 0.02 , and 0 .01 .

Solution Summary: The author explains the approximations to e corresponding to h=0.04,0.02,and 0 .01.

Concept explainers

Videos

The approximations to e corresponding to h=0.04,0.02, and 0.01<m:math><m:mrow><m:mi>h</m:mi><m:mo>=</m:mo><m:mn>0.04</m:mn><m:mo>,</m:mo><m:mn>0.02</m:mn><m:mo>,</m:mo><m:mtext> and 0</m:mtext><m:mtext>.01</m:mtext></m:mrow></m:math>.

Whether the assumption in part (b) is correct.

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Chapter 4 Solutions

The approximations to e corresponding to $h=0.04,0.02, and 0.01$ .