To find: The bound based on alternating series error bound.
Answer to Problem 21E
The bound for the maximum error is
Explanation of Solution
Given information:
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
Exercise
So,
The approximation by using
Therefore, the required bound for the maximum error is
To find: The Lagrange error formula.
Answer to Problem 21E
The bound for the maximum error is
Explanation of Solution
Given information:
Calculation:
From exercise
But
thus
And by using the formula the error at
If
for such
The approximation by using
Therefore, the required bound for the maximum error is
Chapter 9 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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