数列の極限，関数の極限
1 次の数列の極限を求めよ。
(1) lim
n→∞
(2n+ 1)2 n2+ 3n+ 1 (2) lim
n→∞
3n+ 1
√1 +n2
(3) lim
n→∞
2n−5
√1 +n2+n3
(4) lim
n→∞
√n3+ 1 n2 (5) lim
n→∞
√n3+ 1 nn (6) lim
n→∞
n2 2n (7) lim
n→∞
n5 2n (8) lim
n→∞
n!
(2n)!
(9) lim
n→∞
(n+ 1)!
2n!
(10) lim
n→∞
(n−1)!
2n!
(11) lim
n→∞
100n n!
(12) lim
n→∞(logn−log(n+ 1)) (13) lim
n→∞(log(3n2−2n+ 1)−log(n2+n−1)) (14) lim
n→∞
1 nsin1
n (15) lim
n→∞cos 3n n2+ 1 (16) lim
n→∞tan nπ 4n+ 2 (17) lim
n→∞(√
2n+ 5−√
2n−1)
(18) lim
n→∞
√2n2+ 2n+ 5−√
n2+n+ 2 n
1
2 次の関数の極限を求めよ。
(1) lim
x→2(x3−3x2+x−1) (2) lim
x→1
x2−3x+ 2 x3−1 (3) lim
x→−1
x2+ 5x+ 4 x3+ 1 (4) lim
x→∞
3x2−2x+ 1 x2−x+ 1 (5) lim
x→1+0
x2+ 3x−4
√x2−1
(6) lim
x→1
√2x2−x+ 4−√
x2+ 2x+ 2 x−1
(7) lim
x→0
sin 3x x (8) lim
x→0
cos 2x−1 x (9) lim
x→0
x ex−1 (10) lim
x→0
3x−2x x (11) lim
x→1
x−1 logx (12) lim
x→1+0(log(x2+ 4x−5)−log(x3−2x+ 1))
2
