Some Analyzer* Activities

1. Plot and on the domain and then on the domain . What do you conclude ?
2. Using Analyzer*, find the approximate solution of the inequality

   

3. Plot the graph of . Where can we restrict so that it has a well defined inverse function? (We'd like as big a set as possible...) Can you find an argument without the computer for why this is true ?
4. Plot the graph of . Estimate again where we can restrict so that it has a well defined inverse function? (A non-computer assisted argument is much harder here ...)
5. Consider the function . Using the ``Draw Tangent'' feature of Analyzer*, estimate those points x where has the slope of its tangent line equal to -1, 0, or 1. Now check your estimates by graphing .
6. Compare the graphs of and .
7. Plot the graph of . For which initial values of x would one expect Newton's method to have difficulty at finding the roots of this function ?
8. Consider the graph of the function for constants a, b, and c. How does the graph look for different values of a, b, and c ? How does the sign of the discriminant affect the appearance of the graph ?
9. Consider numerical computation of the integral whose exact value is easy to compute. Some of the the numerical integration methods which Analyzer* supports include left-hand, midpoint, the trapezoid rule, and Simpson's rule. For each of these determine how many subdivisions you need to estimate the answer with no more than a 1% error.