Concept explainers
To graph: the first five members of the orbit of each initial value using iteration method.
Answer to Problem 43E
Explanation of Solution
Given:
Concept used:
Iteration:
An iterative sequence is one generated by the recurrence relation:
The starting value
In iterative method:
The order or the sequence of a function of preceding sequence or order.
Mathematically,
The graph of the iterative function can be drawn in Desmos graphing calculator.
Calculation:
First calculate the first five members of the orbit. Round the real and imaginary parts to the nearest hundredth.
First iteration:
Second iteration:
Third iteration:
Fourth iteration:
Fifth iteration:
The sketch of iterates in complex plane is:
Hence,
Chapter 9 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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