Limit of Newton's Law of Cooling....2

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SUMMARY

The limit of Newton's Law of Cooling, represented by the equation u(t) = (u_0 - T)e^(kt) + T, approaches u_0 as t tends to 0 from the right side. This conclusion is derived from evaluating the limit of the exponential term as t approaches zero. Additionally, the discussion raises the question of whether this law can be graphed, indicating interest in visualizing the cooling process. Participants emphasize the importance of providing complete problem details for effective assistance.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with exponential functions
  • Knowledge of Newton's Law of Cooling
  • Basic graphing skills for mathematical functions
NEXT STEPS
  • Study the derivation of limits in calculus
  • Explore graphing techniques for exponential decay
  • Learn about the applications of Newton's Law of Cooling in real-world scenarios
  • Investigate related problems in calculus, such as Problem 1.5.75 from the discussion
USEFUL FOR

Students studying calculus, educators teaching mathematical concepts, and anyone interested in the practical applications of Newton's Law of Cooling.

nycmathdad
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Given u(t) = (u_0 - T)e^(kt) + T, find the limit of u(t) as t tends to 0 from the right side.

The answer is u_0. How is the answer found? Seeking a hint or two.
Can this Law of Cooling be graphed? If so, what does the graph look like?
 
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Beer soaked ramblings follow.
nycmathdad said:
Given u(t) = (u_0 - T)e^(kt) + T, find the limit of u(t) as t tends to 0 from the right side.

The answer is u_0. How is the answer found? Seeking a hint or two.
Can this Law of Cooling be graphed? If so, what does the graph look like?
Problem 1.5.75.b.
Some details left out.
Suggest you post a screenshot of the entire problem instead of making helpers guess the condition for k.
 
Look at 75 parts (a) and (b). You are not helping by telling me to go back to the question. I want to learn how this is done.

Screenshot_20210402-184607_Drive.jpg
 
Beer soaked suggestion follows.
nycmathdad said:
Look at 75 parts (a) and (b). You are not helping by telling me to go back to the question. I want to learn how this is done.

View attachment 11043
Do us all a favor and post a screenshot of your problem so we don't have to task our imagination with sloppy typing.
 

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