Question

find the power series representation centered at a=0 of

a.) f(x) = x/(5+7x)

b.) f(x) = x^2 sin(3x)

Answer #1

Find a power series representation for the function. (Give your
power series representation centered at x = 0.)
f(x) = (x^2) / (x^4 +16 )
Determine the interval of convergence. (Enter your answer using
interval notation.)

Find a power series representation for the function. (Give your
power series representation centered at x = 0.)
f(x) =
8
3 −
x
f(x) =
∞
n = 0
Determine the interval of convergence. (Enter your answer using
interval notation.)

Find a power series representation for the function; find the
interval of convergence. (Give your power series representation
centered at x = 0.) f(x) = (x2 + 1)/ (2x − 1)

Find the power series expansion for f(x) = x^2 e^(x^2) centered
at a = 0 and centered at a=-3

Find a power series representation for the function.
f(x) = ln(5 − x)
f(x) = ln(5) +
∞
(−1)nn(x5)n
n = 0
Determine the radius of convergence, R.
R =

Find the Taylor series for f(x) centered at
the given value of a. [Assume that f has a power
series expansion. Do not show that
Rn(x) → 0.]
f(x) = sin(x), a = pi/2

Find a power series representation for the function; determine
the interval of convergence. f(X) = (3x^2)/(5x+1)

Find the maclaurin series for f(x), centered around 1. (n=1)
f(x) = ln(1-7x)

5. Power Series. Find a power series representation
and the radius of convergence for any the functions f(x) below
where, in each case, a is a non-zero constant.
(a) f(x) = arctan(ax)
(b) f(x) = ln(a − x^2)

find the power series representation for the function f(x) = x /
(1-x)^2

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