Chapter 5.1, Problem 14E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

The table shows speedometer readings at 10-second intervals during a 1-minute period for a car racing at the Daytona International Speedway in Florida.

(a) Estimate the distance the race car traveled during this time period using the velocities at the beginning of the time intervals.

Time (s) | Velocity (mi/h) |

0 | 182.9 |

10 | 168.0 |

20 | 106.6 |

30 | 99.8 |

40 | 124.5 |

50 | 176.1 |

60 | 175.6 |

(b) Give another estimate using the velocities at the end of the time periods.

(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.

**(a)**

To determine

**To Estimate:**

The distance travelled by the car using the velocities at the beginning of time intervals.

Explanation

**Given information:**

The number of intervals

Each interval value is

**Calculation:**

The expression to find the total distance travelled by the car

Here, the velocity at time

Substitute 6 for *n* in Equation (1).

Substitute 182.9 mi/h for

(b)

To determine

**To Estimate:**

The distance travelled by the car using the velocities at the end of time intervals.

(c)

To determine

**To Check:**

The upper or lower estimates are obtained in part (a) and part (b).

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