Concept explainers
In Problems 1 and 2, use the method of successive substitutions to approximate a solution of the given equation starting with the given value for
To find:
The approximate solution of the given equation
Answer to Problem 1RP
Solution:
The approximate solution of the given equation is
Explanation of Solution
Given:
The equation is,
The starting value is
Approach:
The procedure to determine the approximate solution for a function
a. Determine the recurrence relation as,
b. Start with the initial approximation
c. Continue the step (b) to obtain a sequence of approximations
This method is called successive substitution method.
Calculation:
The given equation is,
The recurrence relation for the given equation is,
The initial value is
Substitute
Substitute
Substitute
Substitute
Substitute
As both the values
Conclusion:
Hence, the approximate solution of the given equation is
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Chapter 13 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning