Let g(x) = √x for x ≥ 0.

a. Find the average rate of change of g(x) with respect to x over the intervals [1, 2], [1, 1.5] and [1, 1 + h].

b. Make a table of values of the average rate of change of g with respect to x over the interval [1, 1 + h] for some values of h approaching zero, say h = 0.1, 0.01, 0.001, 0.0001, 0.00001, and 0.000001.

c. What does your table indicate is the rate of change of g(x) with respect to x at x = 1?

d. Calculate the limit as h approaches zero of the average rate of change of g(x) with respect to x over the interval [1, 1 + h].