22. Find the average velocity over the interval 0 S t S 0.2,

and estimate the velocin at t = 0.2 of a car whose posi-

tion. .9. is given by the following table. t(scc) 0 0.2 0.4 0.6 0.8 1.0

5(ft) 0 0.5 1.3 3.8 6.5 9.6 Use algebra to evaluate the limits in Problems 25— 26. 2 3

25_ um W 26, um (1_+’l)__1.

h—m h h—HD h

Homework (3) l. The table shows values of ﬁre) = :03 near a = 2 (to

three decimal places). Use it to estimate f ’ (2). a: 1.998 1.999 2.000 2.001 2.002

x3 1.976 7.988 8.000 8.012 8.0%: 3. The income that acompany receives from selling an item

is called the revenue. Production decisions are based.

in part, on how revenue changes if the quantity sold

changes; that is, on the rate of change of revenue with

respect to quantity sold. Suppose a company‘s revenue.

in dollars. is given by R{q) = 100:; — 10:12, where q is

the quantity sold in kilograms. (a) Calculate the average rate of change of R With re-

spect to q over the intervals 1 S q S 2 and

2gq5& (b) By choosing small values for h, estimate the instan-

taneous rate of change of revenue with respect to

change in quantity at q = 2 kilograms. 1]. Figure 2.19 shows the graph of 1". Match the derivatives in the table with the points a, b, c, d, e. Figure 2.19