Express the function as the sum of a power series by first using partial fractions. f(x) = 8/(x2 − 2x − 15) f(x) = sum n=0 to infinit Find the interval of convergence. (Enter your answer using interval notation.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Express the function as the sum of a power series by first using partial fractions.

f(x) = 8/(x2 − 2x − 15)

f(x) = sum n=0 to infinit

Find the interval of convergence. (Enter your answer using interval notation.)

 

(a) Use differentiation to find a power series representation for

f(x) = 1/(9 + x)2

f(x)= sum n=0 to infinit

What is the radius of convergence, R?
R = 

(b) Use part (a) to find a power series for

f(x) = 1/(9 + x)3

f(x) = sum n=0 to infinit

What is the radius of convergence, R?
R = 

(c) Use part (b) to find a power series for

f(x) = x^2/(9 + x)3

f(x) = sum n=0 to infinit

What is the radius of convergence, R?

Find a power series representation for the function.

f(x) = ln(3 − x)

f(x) = ln(3)- sum n=1 to infinit

Determine the radius of convergence, R.

 

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