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

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The discussion revolves around finding the limit of the cooling function u(t) = (u_0 - T)e^(kt) + T as t approaches 0 from the right, which is determined to be u_0. Participants seek hints on how to arrive at this answer and inquire about the graph of Newton's Law of Cooling. There is a suggestion to provide a complete screenshot of the problem for clarity, as incomplete information hinders understanding. The conversation emphasizes the importance of clear communication in problem-solving. Overall, the focus is on understanding the mathematical principles behind the 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.
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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