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Math 133
HW 10
Be sure to show your work!
1. Find power series representations for the following functions by manipulating simpler known
power series representations. Make sure your power series are centered about x = 0.
23
(a) f(x)
xN+3
4n+1
4-3
n=0
.23
(b) f(x)
=
3" 22n+3
5n+1
5 - 3.02
n=0
(c) f(x) = x² arctan (3.c)
(-1)"32n+1,2n+3
2n +1
n=0
2
(d) f(x)
(4 + 2)2
n(–1)n-1,2n-1
4n+1
n=0
2. For each f(x), a, and k given below, find the degree-k Taylor polynomial Tk(x) of f(x)
centered at a:
22
(a) f(x) = esinx,
a = 0,
k= 2
T2(x) = 1 + x +
2
(b) f(x) = x In (2x – 1), a=1, k= 2
T2(x) = 2(x - 1)
(c) f(x) = tan (3x), a= 0, k= 2
T2(x) = 32
(d) f(x) = Vx2 +3,
x +1
k= 2
3(x + 1)2
a= -1,
T2(x) = 2 - +
2
16
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