(a)
To find: The first four non zero terms and general terms.
(a)
Answer to Problem 33E
The first four non-zero terms are
Explanation of Solution
Given:
The function is
Calculation:
Taylor series is a nthpolynomial series in which a function is expanded in a power series with an infinite number of terms.
The Taylor series can be written as:
The function given is:
This function can be written as:
Now, the Taylor series for this function is:
The first four non zero terms and general terms are calculated.
Conclusion:
The first four non-zero terms are
(b)
To find: The series converges at f (1) or not.
(b)
Answer to Problem 33E
The series does not converge at f (1).
Explanation of Solution
Given:
The function is
Calculation:
The Taylor series of the function can be written as:
Now, the ratio test can be done to find whether the series converge to zero or not when
So, for the series to converge
Now, when
Hence, when
Conclusion:
The series does not converge at f (1).
(c)
To find: The first four non-zero terms for the function
(c)
Answer to Problem 33E
The first four non-zero terms are
Explanation of Solution
Given:
The function is
Calculation:
Conclusion:
The first four non-zero terms are
(d)
To find: The rational number.
(d)
Answer to Problem 33E
The rational number satisfy the given equation.
Explanation of Solution
Given:
The function is
Calculation:
The Taylor series can be written as:
Now, this can be expanded in Taylor series as:
Now, let the value of A be:
As, the series is converging as well as alternating therefore, absolute values of the terms in series decreases to zero.
Conclusion:
The rational number satisfy the given equation.
Chapter 9 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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