7/23/2019 Lista de Ercicios mate III
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(a)∞n=1
arc tg(n)n2
(b)∞n=1
(n!)22n3
(c)∞n=1
12ln(n)
(d)∞n=1
ln(n)
n2 (e)
∞n=1
n2
3n (f )
∞n=2
ln(n)√ n
f (x) =∞k=0
akxk
∀x ∈ (−r, r) f a2k+1 = 0 ∀k ∈ N
f (x) =∞k=0
akxk
∀x ∈ (−r, r) f ak = 0 ∀k ∈ N
(a)∞n=0
n22n
3n (x + 1)n (b)
∞n=1
(−1)n (x + 8)n
n 6n (c)
∞n=1
n!
x + 1
n
n
(d)∞n=0
nn(3x − 5)n
(n + 3)! (e)
∞n=0
2n(n!)3x3n
(3n)! (f )
∞n=0
2n
3n(x − 3)n
x2 + x2
1 + x2 +
x2
(1 + x2)2 +
x2
(1 + x2)3 + · · ·
x ∈R
f (x) = ln(1 + x)
∞n=1
(−1)n
n5n = ln
56
f (x) = ex
∞n=0
22n+1
n!
7/23/2019 Lista de Ercicios mate III
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0,1 0
arctg(x)
x dx
10−6
1/2 0
1 − cos x
x2 dx
f (x) = (1 + x)1/2
√ 1, 02
f (x) = (1 + x)1/3
0,25 0
3
1 + x2 dx
10−3
Argsenh(x) =
x 0
dt√ 1 + t2
Argsenh(0, 25)
1
12 +
1
23 +
1
32 +
1
43 +
1
52 +
1
63 + · · ·
x senx x − x3
3!
3 · 10−4
f (x) = 3 − 2x
x2 − 3x + 2
|x| < 1 f (7)(0)
p(x) |(1 + x) ex− p(x)| < 1
106
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