Find the first four nonzero terms in the Taylor polynomial approximation for the given initial value problem.
a.
b.
(a)
To find:
The first four nonzero terms in the Taylor polynomial approximation for the given initial value problem.
Answer to Problem 1RP
Solution:
The first four terms in the Taylor approximation is,
Explanation of Solution
Given:
The initial value problem is,
Approach:
The formula for the Taylor polynomial of any degree centered at
Calculation:
Consider the equation,
Substitute
Differentiate the equation
Substitute
Again differentiate equation
Substitute
Substitute
Therefore, the first four terms of the polynomial is,
Conclusion:
Hence, the first four terms in the Taylor approximation is,
(b)
To find:
The first four nonzero terms in the Taylor polynomial approximation for the given initial value problem.
Answer to Problem 1RP
Solution:
The first four terms in the Taylor approximation is,
Explanation of Solution
Given:
The initial value problem is,
Calculation:
Consider the equation,
Substitute
Differentiate the equation
Substitute
Again differentiate equation
Substitute
Substitute
Therefore, the first four terms of the polynomial is,
Conclusion:
Hence, the first four terms in the Taylor approximation is,
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