Question

计算下列极限：1）lim(n→∞) 1/n3 2）lim(n→∞)4n+1/3n-1

1）lim(n→∞) 1/n3 2）lim(n→∞)4n+1/3n-1
3) lim(n→∞) (1/3)n

4)lim(n→∞)n3+2n-5/5n3-n 5) lim(n→∞)(1+1/2n)n

6) lim(n→∞)2x3-x2+1/3x2+2x-9 7) lim(x→0 )sin3x/sin7x

8) lim(x→∞)sinx/x 9)lim(x→0)tanx/x
10) lim(x→0)(1-x)1/x
我本科网络学员，答案详细点，谢谢

Answer 1

1）lim(n→∞) 1/n3 =0

2）lim(n→∞)（4n+1）/（3n-1）
=lim(n→∞)（4+1/n）/（3-1/n）
=(4+0)/(3-0)
=4/3

3) lim(n→∞) (1/3)n=∞

4)lim(n→∞)(n3+2n-5)/(5n3-n )
=lim(n→∞)(1+2/n²-5/n³)/(5-1/n² )
=(1+2*0-0)/(5-0)
=1/5

5) lim(n→∞)[1+1/(2n)]n
= lim(n→∞)(1/n+1/2)
=1/2

6) lim(x→∞)2x3-x2+1/(3x2+2x-9)
=∞

7) lim(x→0 )sin3x/sin7x
=lim(x-->0)3cos3x/(7cos7x)
=3/7

8) lim(x→∞)sinx/x
=0

9)lim(x→0)tanx/x
=1

10) lim(x→0)(1-x)1/x
= lim(x→0)(1/x-1)
=∞

Answer 2

1）lim(n→∞) 1/n3 0
2）lim(n→∞)4n+1/3n-1 ∞
3) lim(n→∞) (1/3)n ∞
4)lim(n→∞)n3+2n-5/5n3-n ∞
5) lim(n→∞)(1+1/2n)n ∞
6) lim(n→∞)2x3-x2+1/3x2+2x-9 ∞
7) lim(x→0 )sin3x/sin7x 1
8) lim(x→∞)sinx/x 0
9)lim(x→0)tanx/x 1
10) lim(x→0)(1-x)1/x ∞