To find: The bound based on alternating series error bound.
Answer to Problem 22E
The error is less than
Explanation of Solution
Given information:
The approximation
Calculation:
Because the terms of the series meet all three of the characteristics indicated in Chapter 10—they alternate in sign, decrease in absolute value, and approach
The truncation error is therefore smaller than the absolute value of the term at
For all
the error this,
Therefore, the required error is less than
To find: The Lagrange error formula.
Answer to Problem 22E
The error is less than
Explanation of Solution
Given information:
The approximation
Calculation:
Since the fourth derivative of sine is zero at
And
But
thus
The
Based on this,
Since, the error
Therefore, the required error is less than
To find: The values that uses
Answer to Problem 22E
The answer is:
Explanation of Solution
Given information:
The approximation
Calculation:
If
underestimates this value. Based on these,
Summarizing,
Therefore, the required values that uses
Chapter 9 Solutions
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