3.48. *** If we measure three independent quantities x, y, and z and then calculate a function such as q = (x + y)/(x + z), then, as discussed at the beginning of Section 3.11, a stepwise calculation of the uncertainty in q may overestimate the uncertainty ͉q. (a) Consider the measured values x = 20 ± 1, y = 2, and z = 0, and for simplicity, suppose that ͉y and ͉z are negligible. Calculate the uncertainty ͉q correctly using the general rule (3.47) and compare your result with what you would get if you were to calculate ͉q in steps. (b) Do the same for the values x = 20 ± 1, y = -40, and z = 0. Explain any differences between parts (a) and (b).