Given the difference equation x(k) - x(k-1) + x(k 2) = e(k) - where e(k)= 1 for

Given the difference equation

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x(k) - x(k-1) + x(k 2) = e(k) - where e(k)= 1 for k 0. (a) Solve for x(*) as a function of k, using the z-transform. Give the values of x(0), x(1), and x(2). (b) Verify the values x(0), x(1), and x(2), using the power-series method. (c) Verify the values x(0), x(1), and x(2) by solving the difference equation directly. (d) Will the final-value property give the correct value for x()?