1. Do Problem 67:1 (page 67, problem 1). Perform 6 iterations.

2. Do Problem 67:2

3. If we use the Bisection method to approximate a zero of a function on the interval [–2,3], what is the error bound after 12 iterations?

4. Write this Maple code for the Bisection Method. Then use it to do problem 67:1, and iterate until your approximation has converged to 5 digits.
   Write this code as soon as possble and save it, because you will use it as a template (model) for Programming Assignment 1.

5. Read and do the Maple example for approximating a zero of a function.
   Then use Maple's fsolve command to approximate the zeros in problem 67:1.

6. See the Bisection Method Algorithm (pseudocode).

   
   

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   10:15 class:   Do the problems below AFTER Wednesday's lecture in Week 2.

7. If we use interval halving to approximate a zero of a function on the interval [–2,3], how many iterations should be performed to obtain at least 12 decimal place accuracy in our approximation?
   Answer:   44 iterations guarantee at least 12 decimal place accuracy.

8. For the function

   f (x) = e^–x – cos x,

   use the Bisection method's error bound formula to determine the number of iterations required to guarantee that we would approximate a zero with an accuracy of at least 7 decimal places if we were to start on the interval [2,7].
   NOTE:   Use the error bound formula only — do NOT actually apply the Bisection method to answer the question.
   Answer:   27 iterations guarantee at least 7 decimal place accuracy.