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28. In Exercise 14 in Section 7.1 we considered a 95°C cup of cof- fee in a 20°C room. Suppose it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C. (a) What does the differential equation become in this case? (b) Sketch a direction field and use it to sketch the solution curve for the initial-value problem. What is the limiting value of the temperature? (c) Use Euler's method with step size h = 2 minutes to estimate the temperature of the coffee after 10 minutes. 22. Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem у — ху — х*, у(0) — 1.

28. In Exercise 14 in Section 7.1 we considered a 95°C cup of cof- fee in a 20°C room. Suppose it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C. (a) What does the differential equation become in this case? (b) Sketch a direction field and use it to sketch the solution curve for the initial-value problem. What is the limiting value of the temperature? (c) Use Euler's method with step size h = 2 minutes to estimate the temperature of the coffee after 10 minutes. 22. Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem у — ху — х*, у(0) — 1.

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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9. A population is modeled by the differential equation dP P dt 4200 (a) For what values of P is the population increasing? (b) For what values of P is the population decreasing? (c) What are the equilibrium solutions? 20. A direction field for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step sizes h = 1 and h = 0.5. Will the Euler estimates be under- estimates or overestimates? Explain. y A 2 1 2 x
Transcribed Image Text:9. A population is modeled by the differential equation dP P dt 4200 (a) For what values of P is the population increasing? (b) For what values of P is the population decreasing? (c) What are the equilibrium solutions? 20. A direction field for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step sizes h = 1 and h = 0.5. Will the Euler estimates be under- estimates or overestimates? Explain. y A 2 1 2 x
28. In Exercise 14 in Section 7.1 we considered a 95°C cup of cof- fee in a 20°C room. Suppose it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C. (a) What does the differential equation become in this case? (b) Sketch a direction field and use it to sketch the solution curve for the initial-value problem. What is the limiting value of the temperature? (c) Use Euler's method with step size h = 2 minutes to estimate the temperature of the coffee after 10 minutes. 22. Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem у — ху — х*, у(0) — 1.
Transcribed Image Text:28. In Exercise 14 in Section 7.1 we considered a 95°C cup of cof- fee in a 20°C room. Suppose it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C. (a) What does the differential equation become in this case? (b) Sketch a direction field and use it to sketch the solution curve for the initial-value problem. What is the limiting value of the temperature? (c) Use Euler's method with step size h = 2 minutes to estimate the temperature of the coffee after 10 minutes. 22. Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem у — ху — х*, у(0) — 1.
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