Paper and Pencil Time!! It doesn't count as practice unless you really DO it.

What to Do

Each practice problem has a button which will bring up a pop-up window with the answer in it. Some answers also have a full calculation or further explanation in the window.

Feel free to discuss problems with your fellow students, be it in person, via email, over the telephone, or using a Hypernews group if one exists. And don't forget about your instructors - their JOB is to help you!

Expected Study Time

Stage 4 Skills

You are finished with Stage 4 when you can do the following:

Continuity

• Translate statements about continuity into statements about limits.

• Identify and classify points of discontinuity from a table of values, a graph, and/or a (piecewise) algebraic description of a function. For removable discontinuities, determine what value is needed to remove the discontinuity.

• Give examples of functions with given discontinuities.

• Describe and use the continuity properties of Field Guide Functions.

Evaluate Limits

• Compute limits of continuous functions by evaluating at a limit point. Also available: More challenging examples. The above examples include:
  • Evaluating limits of rational functions.
  • Recognizing and identifying indeterminate forms.
  • Computing limits involving sin(x)/x as x approaches zero.
  • Applying the "algebraic limit laws" to compute limits of combinations of Field Guide Functions.
  • Applying the "algebraic limit laws" to functions, knowing only the limits of the individual components.

• State and apply the squeeze law.

Know the Theorems

• Apply the Intermediate Value and Intermediate Zero Theorems, clearly identifying the necessary hypotheses, and explain why these theorems do not apply in a given situation.

• Apply the Extreme Value Theorem, identifying the necessary hypotheses.