Question

Find a power series expansion for the following function, and
determine its radius of con-

vergence. Please Show ALL steps

f(x) = x^2 arctan(3x)

Answer #1

Find a power series expansion for the function f(x)=1/x wither
center a=-3. What is its radius of convergence?

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)

Power Series (3 marks total) Find a power series representation
and the radius of convergence for the functions f(x) below where,
in each case, a is a non-zero constant. (a) f(x) = arctan(ax)
(b) f(x) = 1/(x−a)^2

Find the power series representation for the function: f(x) =
x2 / (1+2x)2 Determine the radius of
convergence.

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

Find a power series representation for the function.
f(x)=x^3/(x-8)^2
f(x)=SIGMA n=0 to infinity
Determine the radius of convergence
Use a Maclaurin series in this table to obtain the Maclaurin
series for the given function
f(x)=xcos(2x)

Find a power series representation and the radius of convergence
for functions f(x)= arctan(ax) where, in each case, a is a non-zero
constant.

Find a power series representation for the function:
?(?)=?^(2)arctan(?3)
?(?)=(?/(2−?))^3
Express the antiderivative as a power series;
∫?/(1+t^(3) ??
∫arctan(?)/(?)??

Find the power series expansion for the function g ( x ) = 2 x
/( 1 + 4 x ^2 )^ 2. Your answer should describe the process you
used to arrive at this answer.

Find a power series representation for f(x) = ln(x^7 + 2), and
find its radius of convergence.

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