Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series. 42. g ( x ) = 1 ( 1 − x ) 3 using f ( x ) = 1 1 − x
Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series. 42. g ( x ) = 1 ( 1 − x ) 3 using f ( x ) = 1 1 − x
Differentiating and integrating power seriesFind the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series.
42.
g
(
x
)
=
1
(
1
−
x
)
3
using
f
(
x
)
=
1
1
−
x
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Binomial seriesa. Find the first four nonzero terms of the binomial series centered at 0 for the given function.b. Use the first four terms of the series to approximate the given quantity.
Find the sum of the series
It will be a function of the variable x.
∞
x8n
x
Σ(-1)".
n=0
n!
20 (-3)*
B. Find the interval of convergence of the power series,
sum of the series as a function.
and find the
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