1. A power series is a series of the form and cn's are where x is a 2. The power series can be considered a function of x resembling a(n) _polynomial. 3. The domain of a power series consists of those x's for which 4. A power series of the form E-o Cn (x – a)" is called a 5. For a given power series E-o Cn (x – a)", there are three cases for convergence. They are: 1). 2). 3) 6. The number R in Case 3 is called 7. In Case 1, R =, 8. In Case 2, R=, 9. True or False? The interval of convergence is the same as the domain of the power series. 10. There are 4 possibilities for the interval of convergence based on whether the endpoints are included or excluded. These possibilities are:
1. A power series is a series of the form and cn's are where x is a 2. The power series can be considered a function of x resembling a(n) _polynomial. 3. The domain of a power series consists of those x's for which 4. A power series of the form E-o Cn (x – a)" is called a 5. For a given power series E-o Cn (x – a)", there are three cases for convergence. They are: 1). 2). 3) 6. The number R in Case 3 is called 7. In Case 1, R =, 8. In Case 2, R=, 9. True or False? The interval of convergence is the same as the domain of the power series. 10. There are 4 possibilities for the interval of convergence based on whether the endpoints are included or excluded. These possibilities are:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:ICQ #13 (11.8)
1. A power series is a series of the form
and cn's are
where x is a
2. The power series can be considered a function of x resembling a(n)
_polynomial.
3. The domain of a power series consists of those x's for which
4. A power series of the form E-o Cn(x – a)" is called a
5. For a given power series En=0 Cn(x – a)™, there are three cases for convergence.
They are:
1)
2)
3)
6. The number R in Case 3 is called
7. In Case 1, R =,
8. In Case 2, R =.
9. True or False? The interval of convergence is the same as the domain of the power
series.
10. There are 4 possibilities for the interval of convergence based on whether the
endpoints are included or excluded. These possibilities are:
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