To find: The power series.
Answer to Problem 63RE
The answer:
Explanation of Solution
Given information:
The integral is
Calculation:
Therefore, the required power series is
To find: The number of terms of the series.
Answer to Problem 63RE
The answer: At least two terms of the series.
Explanation of Solution
Given information:
The integral is
Calculation:
In part
in this case,
The error of the approximation for
If,
From which
because
Based on this, should use at least two terms of the series for the approximation with an error less than
Therefore, the required at least two terms of the series.
To find: The value of given integral.
Answer to Problem 63RE
The answer:
Explanation of Solution
Given information:
The integral is
Calculation:
From part
The first five partial sums of the series are:
Therefore, the required value of
To find: The difference between of the exact value and the approximation if use four terms of the series in part
Answer to Problem 63RE
The answer: The difference between of the exact value and the approximation is approximately
Explanation of Solution
Given information:
The integral is
Calculation:
The error of the approximation is less than the absolute value of the series'
Therefore, the required difference between of the exact value and the approximation is approximately
Chapter 9 Solutions
CALCULUS-W/XL ACCESS
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