To find: The first four terms and the general term of the Taylor series.
Answer to Problem 58RE
The answer:
Explanation of Solution
Given information:
The equation is
The Taylor series generated by
Calculation:
The Maclaurin series, i.e. the Taylor series at
Based on this, the Taylor series generated by
According to the previous step, the first four terms and the general term of the Taylor series generated by
To find: The interval of convergence for the series found in part
Answer to Problem 58RE
The answer:
Explanation of Solution
Given information:
The equation is
Calculation:
Use the Ratio Test solely for series with non-negative terms; as a result, consider the series' absolute value of terms,
Based on the previous step, the series converges absolutely if
Based on part
which diverges according to the
Check to see if the series converges at
This diverges according to the
According to the examination above, the series converges if
Therefore, the required interval of convergence is
To find: The value of
Answer to Problem 58RE
The answer: six terms of the series to approximate
Explanation of Solution
Given information:
The equation is
Calculation:
By direct substitution, obtain that,
Approximate the value
To use,
Hence,
Since the truncation error is less than
In order for the approximation to be accurate to within one percent, the series must have at least six terms.
Chapter 9 Solutions
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