A signal x(t) is defined as x(t) = r(t + 1) r(t) 2u(t) + u(t 1). (a) Plot x(t) and indicate where it has discontinuities.

A signal x(t) is defined as x(t) = r(t + 1) ˆ’ r(t) ˆ’2u(t) + u(t ˆ’ 1).

(a) Plot x(t) and indicate where it has discontinuities. Compute y(t) = dx(t)/dt and plot it. How does it indicate the discontinuities? Explain.

(b) Find the integral

and give the values of the integral when t = ˆ’1, 0, 0.99, 1.01, 1.99, and 2.01. Is there any problem with calculating the integral at exactly t = 1 and t = 2? Explain.

| y(t)dr пр(2)d