1. lim 2n - 1 n + 1 2. lim 5n + 1 7 - 9n 3. lim n2 + 1 n 4. lim n2 (n + 1

1. lim 2n - 1 n + 1 2. lim 5n + 1 7 - 9n 3. lim n2 + 1 n 4. lim n2 (n + 1

1.
2n − 1
n−→∞ n + 1
2.
5n + 1
n−→∞ 7 − 9n
3.
n2 + 1
n−→∞
n
4.
n2
n−→∞ (n + 1)2
5.
n+3
n−→∞ n2 − 2
6.
5n2 + 1
n−→∞ n − 3n2
7.
n+1
n−→∞ 2n3
8.
2n2 − 4
n−→∞ −n − 5
9.
3n2 − 7n + 1
n−→∞ 2 − 5n − 6n2
10.
(2n − 1)2
n−→∞ n2 + 3n − 1
11.
3n3 − 4n2 + 7
n−→∞
2n3 + 5n
12.
n3 − n
n−→∞ −2n4 + n − 5
lim
lim
lim
lim
lim
lim
lim
lim
lim
lim
lim
lim
13.
lim
n−→∞
2n − 1 1 + 2n3
−
5n + 7 2 + 5n3
n+2
n
n2
14.
15.
lim
n−→∞
n!
n→∞ (n + 1)! − n!
lim
16.
17.
lim
lim
1 + 3 + 5 + . . . + 2n − 1
n
n−→∞
n→∞
2
18.
lim
n→∞
1
2
n−1
+ 2 + ... +
2
n
n
n2
√
19.
20.
lim
n−→∞
n2 + 2n + n
n+2
lim √
3
n−→∞
√
3
21.
lim
n−→∞
√
3
22.
lim
n−→∞
√
4
23.
1 + 2 + ··· + n n
−
n+2
2
lim
n−→∞
n3
n
+1+n
n2 + 3n
n+4
n4 + 3n + 1
n−1
n3 + 3n + 1
n−1
24.
4n+1 + 1
n−→∞ 22n+1 − 1
25.
3n+1 − 7
n−→∞ 9n + 4
lim
lim
26.
4n−1 − 5
n→∞ 22n − 7
27.
(2n + 1) · (2n+2 − 4)
n−→∞
4n + 9
28.
4 · 3n+1 + 2 · 4n
n−→∞ 5 · 2n + 4n+2
29.
30.
31.
32.
33.
34.
35.
36.
lim
lim
lim
lim
√
n2 + 2 − n
lim
√
√ n2 + n − n
lim
√
√
n+1− n+2
lim
p
(n + 2) · (n + 8) − n
n−→∞
n−→∞
n−→∞
n−→∞
√
lim n 2n − 2n2 − 3
n→∞
lim
n−→∞
√ √
√ n
n+2− n
3
lim n 2
n−→∞
√
√
n3 + 1 − n3 − 2
q
q
√
√
lim
n− n− n+ n
n−→∞
37.
√
3n2 − n3 + 1
lim
n−→∞ n2 − 2n + 4
38.
lim n
n→∞
√
√
2n2 + 1 − 2n2 − 1
39.
lim n
n→∞
√
3
n3 + n − n
40.
(−1)n
n−→∞ 3n2 + n + 1
41.
−3n + (−1)n
n→∞ 4n − (−1)n
42.
lim
lim
lim
n−→∞
1 + 2 + ··· + n
· cos (n)
n3 + 1
43.
sin(2n) − 2n
n−→∞
3n + 5
44.
1
sin 2n
·√
lim
2
n→∞ 2n
4n + 3n − 2n
45.
√
n2 + 5 − n
1
lim √
cos √
n→∞
n
n2 + 2 − n
46.
lim
√
n
2n + en + π n
lim
p
n
π n + 4n + (2π)n
r
(−1)n
+ 3n
n
47.
48.
49.
lim
n→∞
n→∞
lim
n→∞
lim
n→∞
n
√
n
3n + sin n
50.
n
1
lim 1 +
n−→∞
3n
51.
n
4
lim 1 +
n−→∞
n
52.
53.
54.
55.
56.
57.
58.
59.
60.
n
n2 + 1 ( 2 )
n2
n2 + 1
3n2 + 2
n2 + 3
n2 + 2
n
n2 + 2
n2
−3n2
lim
n→∞
lim
n→∞
lim
n→∞
lim
n→∞
n2
lim n [ln(n + 3) − ln n]
n→∞
lim
n→∞
ln 1 +
2
n
1
n
lim (7n − 1) ln(2n2 + 3) − ln(2n2 + 5)
n→∞
lim n ln(n2 + 1) − ln n2
n→∞
lim (2n2 + 1) ln(n2 + 2) − ln n2
n→∞