a.
To write: The first four nonzero terms of the Taylor series for f about
a.
Answer to Problem 34E
The first four non-zero terms of the Taylor series for f about
Explanation of Solution
Given information:
Concept used:
Taylor series for f centered at
(Maclaurin series):
Compute the value of
Find the first derivative.
Compute the value of
Find the second derivative.
Compute the value of
Find the third derivative.
Compute the value of
Find the fourth derivative.
Compute the value of
Find the fifth derivative.
Compute the value of
Find the sixth derivative.
Compute the value of
Use the calculated values to get a polynomial.
Simplify.
The first four non-zero terms of the Taylor series for f about
b.
To find: The value of
b.
Answer to Problem 34E
The value of
Explanation of Solution
Given information:
Since
Substitute
Hence, the value of
c.
To show:
c.
Answer to Problem 34E
It is shown that
Explanation of Solution
Given information:
Let
The graph of
Concept used:
The partial sum
Lagrange error:
According to the definition of Lagrange error,
From the graph of
Thus,
Therefore,
Chapter 9 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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