# Practice Problems

Site: | Saylor Academy |

Course: | MA005: Calculus I |

Book: | Practice Problems |

Printed by: | Guest user |

Date: | Tuesday, July 23, 2024, 4:53 AM |

## Description

Work through the odd-numbered problems 1-9. Once you have completed the problem set, check your answers for the odd-numbered questions.

## Problems

1. What is the slope of the line through and for and ? ? ? What happens to this last slope when is very small (close to 0)? Sketch the graph of for near .

3. What is the slope of the line through and for and ? ? ? What happens to this last slope when is very small? Sketch the graph of for near .

5. Fig. 9 shows the temperature during a day in Ames.

(a) What was the average change in temperature from 9 am to 1 pm?

(b)
Estimate how fast the temperature was rising **at **10 am and **at **7 pm?

(a) What was the average velocity of the car from to seconds?

(b) What was the average velocity from to seconds?

(c) About how fast was the car traveling at seconds? at at ?

Problem 9 defines new functions in terms of AREAS bounded by the functions and . This may seem a strange way to define a functions , but this idea will become important later in calculus. We are just getting an early start here.

9. Define to be the area bounded by the and y axes, the horizontal line , and the vertical line at (Fig. 13). For example, is the area of the 4 by 3 rectangle.

a) Evaluate and .b) What area would represent in the figure?

c) Graph for .

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-2.1-Tangent-Lines-Velocities-Growth.pdf

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

## Answers

If , then . When is very small (close to 0, is very close to 6.

If , then When is very small, is very close to 5.

5. All of these answers are approximate. Your answers should be close to these numbers.

(a) average rate of temperature change per hour.

(b) at 10am, temperature was rising about per hour.

at 7pm, temperature was rising about per hour (falling about per hour).

7. All of these answers are approximate. Your answers should be close to these numbers.

(a) average velocity feet per second.

(b) average velocity feet per second.

(c) at seconds, velocity feet per second (between 20 and .

at seconds, velocity feet per second.

at seconds, velocity feet per second.

(b) the area of the rectangle bounded below by the -axis, above by the line , on the left by the vertical line , and on the right by the vertical line .