高数上册答案

1 1

x lim 0

或 lim4x 2

x x 3x 1x 211 2 4

xx

2

2x (9)lim2 6x 8 x 4x 5x 4

2x 6x 8 lim(x 2)(x 4) limx 2 4 2 2

解 lim2

x 4x 5x 4x 4(x 1)(x 4)x 4x 14 13

(10)lim(1 12 1)

x xx2

1 lim(2 1) 1 2 2 解 lim(1 12 1) lim(1

x xx2x xx x2

(11)lim(1 1 1 1) nn 242

1 (1)n 1

解 lim(1 1 1 1) lim 2

n 242nn 1 2 (12)lim

1 2 3 (n 1)

n n2

(n 1)n1 2 3 (n 1) 1limn 1 1 解 lim limn n 2n n2n2n2

(n 1)(n 2)(n 3)

(13)lim

n 5n3

(n 1)(n 2)(n 3)1

(分子与分母的次数相同 极限为 解 lim3n 55n

最高次项系数之比)

(n 1)(n 2)(n 3)111 2)(1 3) 1 lim(1 或 lim n 5n nnn55n3

(14)lim1 33)

x 11 x1 x

2

131 x x 3 lim(1 x)(x 2) lim 解 limx 11 x1 x3x 1(1 x)(x 1(1 x)(1 x x2)1 x x2)

lix 22 1 x 11 x x