Finding Complex Roots: Can You Trust Your Calculator?.

The use of technology raises interesting questions and presents unique opportu nities for in-depth classroom investiga tions. These opportunities can open a whole new world of understanding to our students. Trying to understand a calculator an swer that may he different from the answer in the back of the text or what the class determines is the "correct" answer can be a powerful motivator. Technology also occasionally gives incorrect, or at best highly misleading, information. For example, enter nDeriv(abs(x),x,0) on a TI-83 and it returns a value of 0, in spite of the fact that the derivative of |x| at = 0 does not exist. Technology can also give our students a false sense of familiarity with and understanding of certain concepts. Ask a student to evaluate 3^ and you will quickly (assuming their calculator is handy) get an answer of "about 4.73." Persist by asking what the expression means and you are likely to get a blank stare. Some of us at tended high school and college without the aid of scientific or graphing calculators. We had the advan tage of using calculus texts in which the authors were careful to talk about ax only in the context of a > 0 and rational until, for example, ln(x) could be defined in terms of an integral, e* defined as its inverse, and the Intermediate Value theorem in voked to give meaning to e*, when is irrational.