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- 1.
- Use the
`Newton`command with the function*f*from the examples and the starting value*x*=1.1.- (a)
- Describe what happens when Newton's method is used with this
initial condition. You might want to use
`NewtonPlot`to help you understand what is going on. Start with just a few iterations, and then increase the number of iterations slowly. The maximum number of iterations you use should not exceed fifty. - (b)
- What value of
*n*is required to guarantee that for all ?

- 2.
- Use the
`Newton`command to find an approximation to the root near*x*=-2 of the equation - 3.
- Consider the function
*g*from the examples.- (a)
- Can you explain, using the graph of
*g*and perhaps the`NewtonPlot`command, why Newton's method fails to converge for the initial guess*x*=0? - (b)
- Find approximations to all of the roots of
*g*. How do you know that you have found all of the roots?

12/2/1997