You should always perform 3 or 4 iterations of my classroom example(s) BEFORE attempting the homework.

1. Fill in the missing steps of the derivation of the formula for the x intercept x_m of the secant line. (See Slide 5 of the lecture notes.)

2. Click here to see an animated demo of false position.

3. What is the rate of convergence of the false position method? I.e., is it linear, quadratic, cubic?

4. The function f(x) = 2sin(x) – 1/4*exp(x) has two zeros near x = –5.
   1. Using a starting interval [–7, –5], apply 6 iterations of false position to approximate one the zeros.
   2. Using a starting interval [–5, –3], apply 6 iterations of regula falsi to approximate the other zero.

5. Change your Maple bisection code so that it uses false position to approximate a zero of a function f(x) on an interval [a,b]. Then use it to approximate the first positive zero of

   f (x) = e^–x – cos x,

   on interval [1,2] as we did in class.

   Make sure you use the printf command rather than the lprint command for printing ! !
   See the Maple tutorial entitled Formatted Printing and Plot Options.
   See these examples of Bad Tables.

   NOTE: It should be easy to take your program for the bisection method and make minor changes to turn it into false position.
   Click here for the False Position Algorithm (pseudocode). You should obtain these results.

6. Use your false position Maple program to do both parts of Problem 4 above.

7. What are the other names for the method of false position?

8. What stopping tests are appropropriate for false position?

9. Which statements are correct?
   False position –
   1. always gives 1-sided convergence toward zero z.
   2. generally gives 1-sided convergence toward zero z.
   3. always gives 2-sided convergence toward zero z.
   4. rarely gives 2-sided convergence toward zero z.

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