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Use the Newton command with the function f from the examples and the starting value x=1.1.
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.
What value of n is required to guarantee that $\mid f(x_k)
\mid < 10^{-7}$ for all $k \geq n$?
Use the Newton command to find an approximation to the root near x=-2 of the equation

\sin(x) = \frac{x}{2} \end{displaymath}

Consider the function g from the examples.
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?
Find approximations to all of the roots of g. How do you know that you have found all of the roots?

William W. Farr