Finding the limit of Newton's law of cooling as t approaches 0

[nycmathdad]

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?

 

[jonah1]

Beer soaked ramblings follow.

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.

 

[nycmathdad]

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.

 

[jonah1]

Beer soaked suggestion follows.

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.