(a)
The first three non-zero terms and the general term of the Taylor series by
(a)
Answer to Problem 57RE
The first three non-zero terms of the series are
Explanation of Solution
Given information:
The given function is
Formula used:
Calculation:
Replacing x by x/2 and multiplying whole series by 5
Therefore, the first three non-zero terms of the series are
The general term of the series is given by
Conclusion:
The first three non-zero terms of the series are
(b)
The interval of convergence
(b)
Answer to Problem 57RE
The series converges for all real values of x.
Explanation of Solution
Given information:
Since the series is,
Formula used:
Calculation:
By using ratio test,
Therefore, the series converges for all real values of x.
Conclusion:
The series converges for all real values of x.
(c)
The minimum number of terms for f(x) in the interval (-2,2)
(c)
Answer to Problem 57RE
The Maximum error is
Explanation of Solution
Given information:
The given function is
Formula used:
Calculation:
Therefore, all values of the function
Which gives
Therefore,
Maximum error is
So, to make this error less than 0.1, requires
So, two terms (up through degree four) are needed.
Conclusion:
The Maximum error is
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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