(a)
The first four terms and general term of taylor series f(x) at x=3.
(a)
Answer to Problem 60RE
The first four non-zero terms of the series are
The general term of the series is given by
Explanation of Solution
Given information:
The given function is
Formula used:
Calculation:
To determine the first four terms of the series we need to evaluate f(x) its first three derivatives
at x = 3 f (3)=1
Therefore, series of a function f (x) is given by at x = 3
Therefore, the first four non-zero terms of the series are
The general term of the series is given by
Conclusion:
The first four non-zero terms of the series are
The general term of the series is given by
(b)
The first four terms and general term of taylor series at x=3.
(b)
Answer to Problem 60RE
The general term of the series is given by
Explanation of Solution
Given information:
Integrating term by term
Formula used:
Integration is used.
Calculation:
Therefore, the first four non-zero terms of the series are
The general term of the series is given by
Conclusion:
The general term of the series is given by
(c)
To determine: The value of
(c)
Answer to Problem 60RE
The value is
Explanation of Solution
Given information:
The function is
Formula used: Alternating Series Estimation Theorem is used.
Calculation:
Calculating the values of
By the Alternating Series Estimation Theorem,
Since the size of the third term is
Therefore first two terms will be sufficient
Therefore,
Conclusion:
The value is
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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