Where do they get the 1/5 from? 1. (3 points.) Consider a bar (or rod) of length

Question

Where do they get the 1/5 from?

1. (3 points.) Consider a bar (or rod) of length 5, with both endpoints insulated. Recall that the temperature u(x, t) satisfies the PDE ?2uzz-ut. Suppose Q2 2 3, 0SEvaluate lim u(, t) and u(z,0-1 K 5. t->oo 13 13 9 (D) 0 Correct answer: A. Your answer:C. 0 out of 3 points received Solution. The insulated endpoints correspond to zero Neumann boundary conditions. Hence the temperature at each point converges to the constant value c0/2 as t ? oo (see the formula sheet). The value co/2 equals the average of the initial temperature u(x, 0), which is ^ /u(x, 0) dx

Explanation / Answer

The function u(X,0) is defined in the interval [0, 5]. Since the value of c_O /2 is equals the average of the initial temperature u(X, 0) which is defined over the time interval [0, 5] so to find the average over the time interval of length 5, the total value should be divided by 5. For this reason 1/5 come here.

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