a.
To state: The first four nonzero terms and the general term for a power series for
a.
Answer to Problem 72E
The first four terms are
Explanation of Solution
Given information:
It is given that
Consider the given function:
The sum of the infinite geometric series whose ratio is less than 1 is given by
On comparing the function
Therefore, the first terms are:
The general term is:
b.
To state: The first four nonzero terms and the general term for a power series for
b.
Answer to Problem 72E
The first four terms are
Explanation of Solution
Given information:
It is given that
Consider the given function:
From part (a), the series for the function
To find the power series
The series will become:
The first four terms are:
The general term is:
c.
To state: The interval of convergence of the power series in part (a).
c.
Answer to Problem 72E
The resultant interval is
Explanation of Solution
Given information:
The given statement says to find the interval of convergence of the power series in part (a).
Consider the given function:
From part (a), the series is
A geometric series converges when
The common ratio is
d.
To state: The two numbers if the interval of convergence of the power series in part (b) is almost the same as the interval in part (c), but it includes two more numbers.
d.
Answer to Problem 72E
The two numbers are
Explanation of Solution
Given information:
The given statement says to find the two numbers if the interval of convergence of the power series in part (b) is almost the same as the interval in part (c), but it includes two more numbers..
The two numbers are
which result in convergent series:
Substitute the values
Similarly,
Chapter 9 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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