**Q1: **

Suppose that and . Find two estimates of to three decimal places using the left and then the right endpoint methods with 8 rectangles.

- A7.769, 7.843
- B7.843, 7.686
- C0.7689, 0.686
- D7.769, 7.686
- E7.686, 7.769

**Q2: **

Calculate the midpoint rule estimate of with subintervals. Is the result an overestimate or underestimate of the actual value?

- A16, an underestimate
- B48, an overestimate
- C28, an overestimate
- D28, an underestimate
- E16, an overestimate

**Q3: **

Calculate the right endpoint estimate of with subintervals. Is the result an overestimate or underestimate of the actual value?

- A48, an underestimate
- B16, an underestimate
- C16, an overestimate
- D48, an overestimate
- E13, an underestimate

**Q4: **

The table gives sampled values of an increasing function . Use the data to give a lower and upper bound for .

10 | 13 | 16 | 19 | 22 | 25 | |

1 | 4 | 8 | 10 |

- Alower bound: , upper bound: 66
- Blower bound: , upper bound: 3
- Clower bound: , upper bound: 20
- Dlower bound: , upper bound: 60
- Elower bound: , upper bound: 1

**Q5: **

The table gives sampled values of an increasing function . Use the data to give a lower and upper bound for .

12 | 14 | 16 | 18 | 20 | 22 | |

1 | 6 | 15 |

- Alower bound: , upper bound: 20
- Blower bound: , upper bound: 46
- Clower bound: , upper bound: 6
- Dlower bound: , upper bound: 12
- Elower bound: , upper bound: 23

**Q6: **

Calculate the left endpoint estimate of with subintervals. Is the result an overestimate or underestimate of the actual value?

- A16, an overestimate
- B18, an underestimate
- C48, an underestimate
- D16, an underestimate
- E48, an overestimate