MATH 1320 : Spring 2014
Lab 5
Lab Instructor : Kurt VanNess
Name:
Score:
Write all your solutions on a separate sheet of paper.
1. Give an example of power series with the following radius of convergence respectively:
(a) R = 0
(b) R = 1
(c) R = ∞
2. A function f is defined by
f (x) = 1 + 2x + x2 + 2x3 + x4 + · · ·
i.e. the coefficients are c2n = 1 and c2n+1 = 2 for n ≥ 0. Determine the interval of convergence of the
series and find an explicit formula for f (x) using geometric series.
3. (a) Show that the fucntion
∞
X
xn
g(x) =
n!
n=0
is a solution of the differential equation f 0 (x) = f (x).
(b) Find the general solution to the differential equation f 0 (x) = f (x). Find g(0). Can we conclude
g(x) = ex ?
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