## Practice Problems

Work through the odd-numbered problems 1-21. Once you have completed the problem set, check your answers.

### Problems

1. Use the functions and defined by the graphs in Fig. 10 to determine the following limits.

3. Use the function defined by the graph in Fig. 11 to determine the following limits.

5. Label the parts of the graph of (Fig. 12) which are described by

7. Use the function defined by the graph in Fig. 14 to determine the following limits.

9. The Lorentz Contraction Formula in relativity theory says the length of an object moving at miles per second with respect to an observer is where is the speed of light (a constant).

a) Determine the "rest length" of the object .

Problems 13 and 15 require a calculator.

13. (a) What does represent on the graph of ?

(It may help to recognize that )

(b) Graphically and using your calculator, determine .

15. Use your calculator (to generate a table of values) to help you estimate

17. Describe the behavior of the function in Fig. 16 at each integer using one of the phrases:

(a) "connected and smooth", (b) "connected with a corner",

(c) "not connected because of a simple hole which could be plugged by adding or moving one point", or

(d) "not connected because of a vertical jump which could not be plugged by moving one point".

19. This problem outlines the steps of a proof that

Statements below refer to Fig. 18. Assume that and justify why

each statement is true.

(c) The line through the points and has slope , so and the area of (base)(height)

(d) Area of area of sector area of .

(Suggestion: Let and pick so for every Then pick so for every ).

Source: Dave Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-2.3-Properties-of-Limits.pdf

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