To find: The first four non zero terms and the general term of the Taylor series.
Answer to Problem 61RE
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
Therefore, the required first four non zero terms and the general term of the Taylor series is:
To find: The interval of convergence for the series found in part
Answer to Problem 61RE
The answer: The interval of convergence is
Explanation of Solution
Given information:
The equation is
The Taylor series generated by
Calculation:
Use the Ratio Test solely for series with non-negative terms; as a result, consider the series' absolute value of terms,
Take the absolute value of the terms in the series since you can only use the Ratio Test for series with non-negative terms, and then look at the following limit:
Based on the previous step, the series converges absolutely, if the limit less than but for every , hence the series converges (absolutely) for all real i.e. the interval of convergence is
To prove: The statement
Explanation of Solution
Given information:
The equation is
The Taylor series generated by
Calculation:
The difference
Chapter 9 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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