Expand the function f(z) = (z − 1) / z^ 2 (z + 1)(z − 3) as a
Laurent series about the origin z = 0 in all annular regions whose
boundaries are the circles containing the singularities of this
function.
1. expand each function in a Taylor Series and determine radius
of convergence.
a) f(x) = 1/(1-x) at x0 = 0
b) f(x) = e^(-x) at x0 = ln(2)
c) f(x) = sqrt(1+x) at x0 = 0
Find a power series for the function, centered at
c.
f(x) =
3
2x − 1
, c = 2
f(x) =
∞
n = 0
Determine the interval of convergence. (Enter your answer using
interval notation.)
Expand in Fourier series:
Expand in fourier sine and fourier cosine series of: f(x) =
x(L-x), 0<x<L
Expand in fourier cosine series: f(x) = sinx, 0<x<pi
Expand in fourier series f(x) = 2pi*x-x^2, 0<x<2pi,
assuming that f is periodic of period 2pi, that is,
f(x+2pi)=f(x)
(a) Determine the Taylor Series centered at a = 1 for the
function f(x) = ln x.
(b) Determine the interval of convergence for this Taylor
Series.
(c) Determine the number n of terms required to estimate the
value of ln(2) to within Epsilon = 0.0001.
Can you please help me solve it step by step.