These extra practice problems are for students who wish to have an extra set to practice. These problems do not have a posted solution so students should reflect on ways to determine whether their answer is correct. Feel free to discuss with peers to solve these problems.
Use incremental search to find the bounds (e.g., root1 is between x1 and x2) for the six different positive roots of the following equation. After the roots are found, graph the function to determine if these bounds were adequate.
Find the roots from the following equation when y = 2 and y = 3 using bisection method. Plug the roots back into the original equation to determine if it is correct.
Solve the following equation for the variable z for the positive root under the conditions found in the table below. Find the answer when |f(z)|<0.01.
Variable | Value |
---|---|
g | 3 |
a | 3.56 |
b | 2.154 |
c | 1.576 |
Use linear interpolation to solve the following problem until |f(x)| < 0.01.
Use modified linear interpolation to solve the following problem until |f(x)| < 0.01.
Using Ridder’s method, solve the following equation for all possible roots between 0 and 4.
Use all the methods discussed in this module to solve the following equation for one root to |f(x)|<0.001. Compare the number of iterations needed for each method using similar bounds.