- Show that is an approximation of the nonzero root of the equation
using the cubic Taylor polynomial approximation to .
- Given that
prove that the number from part (a) satisfies
Determine if is positive or negative and prove the result.
- Proof. From a previous exercise (Section 7.8, Exercise #3) we know
So, to approximate the nonzero root of we have
- We know from the same previous exercise we used in part (a) that the error term for satisfies the inequality
Using the values for and given we have