1. Experimental evidence suggests that the response y of the body to the concentration x of injected adrenalin is given by

y = x/a + bx

where a and b are experimental constants.

(a) Is this function continuous for all x?

(b) On the basis of your conclusion in part (a) and the fact that in the context of the application x ≥ 0 and y ≥ 0, must a and b be both positive, be both negative, or have opposite signs?

2. Suppose that the cost C of removing p percent of the impurities from the waste water in a manufacturing process is given by

C(p) = 9800p / 101 - p

Is this function continuous for all those p-values for which the problem makes sense?