(a)
To calculate: The first four non-zero terms based on f(x) at x=0.
(a)
Answer to Problem 61RE
The general term of the series is given by
Explanation of Solution
Given information:
The given function is
Let
Formula used:
Maclaurin series is used.
Calculation:
Maclaurin series generated by function
Replacing x by -2x2
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
(b)
To calculate: The interval of convergence based on f(x) at x=0.
(b)
Answer to Problem 61RE
The series is always converges for interval
Explanation of Solution
Given information:
The given function is
Let
Formula used:
Ratio test is used.
Calculation:
For absolute convergence using ratio test.
Since,
Therefore the series is always absolutely for all real x.
Since,
Therefore, the series is always converges for interval
Conclusion:
The series is always converges for interval
(c)
To find: The value of
(c)
Answer to Problem 61RE
The error is less than
Explanation of Solution
Given information:
The given function is
Let
Formula used:
Calculation:
The function
Since,
The error is less than
Conclusion:
The error is less than
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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