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. 45. g ( x ) = ln (1 − 3 x ) using f ( x ) = 1 1 − 3 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. 45. g ( x ) = ln (1 − 3 x ) using f ( x ) = 1 1 − 3 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.
45.g(x) = ln (1 − 3x) using
f
(
x
)
=
1
1
−
3
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
use power series to represent a function
show steps
= cosx to find first four terms
Use the Maclaurin Series for w(x) = e*and q(x)
for nonzero
f (x) = w(x) · q(x)
Write down the first four terms in the binomial series for (1 + 5x)-4
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.
Chapter 9 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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