Question

whats the convergence set of this power series? (no derivatives
needed)

f(x)= 1/(2-x)

Answer #1

Find the interval of convergence of the power
series f ( x ) = ∑ n = 1 ∞ ( x + 3 ) n 2 n.

Find a power series representation for the function and
determine the radius of convergence.
1) f(x)=x^3/(x-2)^2
2) f(x)=arctan(x/3)

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

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

Suppose the power series for a function f(x) has the interval of
convergence I=(a,b]. Which of the following statement must be true
about the interval of convergence for the power series \int
f(x)dx?
I=[a,b)
I=(a,b)
I=(a,b]
I=[a,b]
Can't be determined.

find the maclaurin series for f and its radius of
convergence.
(1) f(x) = (1-x)^-5
(2) f(x) = ln(1+x^2)

Find a power series representation for the derivative of
x/(1+x^2). State its radius of convergence as well.

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)

Evaluate integral 1/1+x^9 dx as a power series. Give the
interval of convergence of the power series.

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

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