2. This is practice with using convolution-existence criteria. (a) Both signals are left-sided, so by the second criterion (Criterion 7.5 in the monograph) their convolution exists. (b) x1 is a bounded signal and x2 is an L1-signal i.e. x2 is absolutely integrable. To see this, note that Z 1 1 |x2(t)|dt = Z 0 1 e3tdt = 1/3 . Accordingly, the third criterion (Criterion 7.6 in the monograph) applies, and x1 x2 exists. (c) x1 is bounded (i.e. x1 2 L1) and x2 is absolutely integrable (i.e. x2 2 L1), as you can check easily. By the third criterion (Criterion 7.6 in the monograph), x1 x2 exists. (d) x1 has finite duration (graph it), so by the first criterion (Criterion 7.4 in the monograph) x1 x2 exists. (e) We saw in (b) that x1 is an L1-signal. As for x2, note that |x2(t)| 1 for all t, so x2 is bounded. Accordingly, Criterion 7.6 in the monograph applies once again, and x1 x2 exists