Geometric Functions Worksheet Page 2
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5Calculus Maximus
WS 9.4: Pwr Series:Geom Series
4
x
6. Let f be the function given by
f t
( )
and G be the function given by
G x
( )
f t dt
( )
.
2
0
1
t
(a) Find the first four nonzero terms and the general term for the power series expansion of
f t
( )
t .
about
0
(b) Find the first four nonzero terms and the general term of the power series expansion of
G x
( )
x .
about
0
(c) Find the interval of convergence of the power series in part (b). Justify your answer.
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