Problem 2 (20 points): Provide a sketch of the function f(x) shown to the right and explain why it does or does not have a limit at x = 10. Use the e - d definition of a limit to accomplish this task.
Problem 6 (10 points): Explain the Intermediate Value Theorem. Included a labeled sketch of an example function to augment your explanation.
If f(x) is continuous over a, b and N lies between f(a) and f(b), then there exists at least one point c that lies between a and b.
Problem 7 (10 points): Explain the Squeeze (sandwich) Theorem and provide a sketch of two example NON LINEAR functions "sandwiching" a third NON LINEAR function. Include the equations of the functions!
Problem 8 (10 points):
a) Explain the three parts for the continuity test at a point x = c for the function f(x).
- f(c) exists
- the limit of f(x) as x --> c exits
- f(c) = the limit of f(x) as x --> c exits
b) Explain what is required for a function to be continuous over a domain.
-IT IS CONTINUOUS AT EACH POINT IN ITS DOMAIN.
c) Provide grahical examples of a removeable and non removeable discountinuitites.
