Problem 1 (10 points): Given the composite function

where:

Sketch h(x) and state it's domain and range.

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 3 (25 points): Find the following five (5) limits analytically. You may use numerical or graphical methods to confirm your answers.

Problem 4 (10 points): Given the limit:

find d > 0 such that

whenever

Problem 5 (5 points): Graph (sketch) the function:

over the domain

Problem 5 (10 points): Explain the Intermediate Value Theorem. Included a labeled sketch of an example function to augment your explanation.

CONTINUED ON REVERSE PAGE

Problem 6 (10 points): Explain the Squeeze Theorem and provide a sketch of two example NON LINEAR functions "sandwiching" a third NON LINEAR function. Include the equations of the functions!

Problem 7 (10 points):

• Explain the three parts for the continuity test at a point x = c for the function f(x).
• Explain what is required for a function to be continuous over a domain.
• Provide graphical examples of a removable and non-removable discontinuities.

Bonus (10 points): Derive the instantaneous rate of change h'(x)equation for h(x).

using: