Some Analyzer* Activities
(Thanks to Professor M. Readdy for many of the suggestions here.)
- Plot and on the domain
and then on the domain .
What do you conclude ?
- Using Analyzer*, find the approximate solution of the inequality
- 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 ?
- 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 ...)
- 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
- Compare the graphs of and .
- 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 ?
- 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
- 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.