Hi I have this D'Alembert's question. What I've done seems easy so I wanted to clarify just in case I'm missing something, cus it seems so easy. Second part I don't understand and would appreciate a guidance.

(PART A)

D'Alembert's Solution is:

of the one dimensional wave equation:

with "c" a constant, when the initial conditions are:

Evaluate the solution if F(x)=0 for and

(PART B)

Show the values of z(x,t) for t>0 in different regions of the (x,t)- plane. Show that the value of z(x,t) is continuous for all values of x and t, gives the correct initial value of and as |x|

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SOLUTION TO PART A:

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GRAPH:

Working out region 1:

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Working out region 2:

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Region 2 = 0.

Working out region 3:

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FINAL SOLUTION:

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Thats part a done. As far as I know that's all there is to evaluating the question. Is there anythin else I need to add???

PART B: any ideas on this please?