Question #90cf3
2 Answers
To find the roots of equations like
Explanation:
Let's do an example.
To use Newton's method, you write the equation in the form
Compute
Because the method requires that we do the same computation many times, until it converges, I recommend that you use an Excel spreadsheet; the rest of my answer will contain instructions on how to do this.
Enter a good guess for x into cell A1. For this equation, I will enter 2.
Enter the following into cell A2:
=A1-(EXP(A1) - A1^3)/(EXP(A1) - 3*A1^2)
Please notice that the above is Excel spreadsheet language for
Copy the contents of cell A2 into A3 through A10. After only 3 or 4 recursions, you can see that the method has converged on
We can use the Intermediate Value Theorem to see that each pair has at least one point of intersection.
Explanation:
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(Note that