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Taylor Series at a Nonzero Center
Worksheet
Grade Level
Calculus II
CAL2.144 Taylor Series at a Nonzero Center
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Suppose \(f
(n)
(-3)=2
n
n!\) for every \(n\ge 0\). Which Taylor series for \(f\) is centered at \(x=-3\)?
A
\(\sum_{n=0}
\infty
2
n
(x-3)
n
\)
B
\(\sum_{n=0}
\infty
2
n
(x+3)
n
\)
C
\(\sum_{n=0}
\infty
\frac{2
n
(x+3)
n
}{n!}\)
D
\(\sum_{n=0}
\infty
2
n
x
n
\)
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