1- The graph of the function f is given.

2 - The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the

table. Find lower and upper estimates for the distance (in ft) that she traveled during these three seconds.

3 - Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table.

4 - Use this graph and a midpoint Riemann sum with six equal subintervals to estimate the distance traveled (in feet) by the car while the brakes are applied.

5- Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.

6- Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.

7- Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.

8- Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.

9- Determine a region whose area is equal to the given limit. Do not evaluate the limit.

10 - Determine a region whose area is equal to the given limit. Do not evaluate the limit.

11- Let A be the area under the graph of an increasing continuous function f from a to b, and let L,, and R, be the approximations to A with n subintervals using left and right endpoints, respectively.

(a) How are A. L., and R. related?

12- Exercise (a)

Estimate the area under the graph of f(x) = 3 cos(x) from x = 0 to x = x/2 using four approximating rectangles and right endpoints. Is your estimate an underestimate or an overestimate?

Exercise (b)

Estimate the area under the graph of f(x) = 3 cos(x) from x = 0 to x = x/2 using four approximating rectangles and left endpoints. Is your estimate an underestimate or an overestimate?