# Practice Problems

Site: | Saylor Academy |

Course: | MA005: Calculus I |

Book: | Practice Problems |

Printed by: | Guest user |

Date: | Tuesday, July 23, 2024, 4:21 AM |

## Description

Work through the odd-numbered problems 1-41. Once you have completed the problem set, check your answers.

## Practice Problems

In problems 1 – 3, use the values in Table 1 to estimate the areas.

x | f(x) | g(x) | h(x) |
---|---|---|---|

0 | 5 | 2 | 5 |

1 | 6 | 1 | 6 |

2 | 6 | 2 | 8 |

3 | 4 | 2 | 6 |

4 | 3 | 3 | 5 |

5 | 2 | 4 | 4 |

6 | 2 | 5 | 2 |

1. Estimate the **area** between and for .

3. Estimate the **area** between and for .

5. Estimate the area of the island in Fig. 13.

In problems 7 – 17, sketch the graph of each function and find the **area **between the graphs of and for in the given interval.

In problems 19 – 21, use the values in Table 1 to estimate the average values.

19. Estimate the average value of on the interval .

21. Estimate the average value of on the interval .

In problems 23 – 31, find the **average value** of on the given interval.

33. Calculate the average value of on the interval for . What is the pattern?

35. Fig. 15 shows the number of telephone calls per minute at a large company. (a) Estimate the average number of calls per minute from 8 am to 5 pm. (b) From 9 am to 1 pm.

37. (a) How much work is done lifting a 20 pound bucket from the ground to the top of a 30 foot building with a cable which weighs 3 pounds per foot? (b) How much work is done lifting the same bucket from the ground to a height of 15 feet with the same cable?

39. (a) How much work is done lifting a 10 pound calculus book from the ground to the top of a 30 foot building with a cable which weighs 2 pounds per foot? (b) From the ground to a height of 10 feet? (c) From a height of 10 feet to a height of 20 feet?

41. How much work is done lifting an 60 pound injured child to the top of a 15 foot hole using a stretcher weighing 10 pounds and a cable which weighs 2 pound per foot?

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-5.8-First-Applications-of-Definite-Integrals.pdf

This work is licensed under a Creative Commons Attribution 3.0 License.

### Answers

1. between 11 (using left endpoints of intervals) and 6 (using right endpoints)

3. between 4 (using left endpoints of intervals) and 6 (using right endpoints)

5. Using left endpoint widths:

Right endpoint widths and average widths give the same result . All of these are reasonable methods for estimating the area of the island.

19. Estimate using midpoints of unit intervals: . About .

21. Estimate using midpoints of unit intervals: . About 5.

33.

35.

37.

39.