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
#13) Find the radius and interval of convergence of the power
series (Sigma∞ n=1) (−1)^n(x − 1)^n/n4^n by responding to the
following sequence of questions.
(a) Compute the limit L = lim n→∞ |an+1|/|an| .
(b) Given that the power series absolutely converges for L <
1 by the Ratio Test, compute the radius of convergence, where the
radius of convergence is the real number R such that the power
series converges for all |x| < R.
(c) Test whether...
find the power series representation of each of the following
functions and give an interval of convergence for each one. assume
that the center of each series is that a=0
a) xsin(x^2)
b) f(x)= e^(-x^10)
correction : a) f(x)=xsin (x^2)