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- 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 graphing . - 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 graph ? - 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.