高等数学函数的极限与连续习题精选及答案

li

x 0

7、lim

x 0

1 2

x 1x 1

x 08、lim

x 1

lix 1x 1

lix 0

x 1

x 1

x 1

lix 1 1

x 0

x xx 1

lim

x 1

x 0

x xx 1

lim

x 1

x

x 1

x 1

1

9、lim

tanx sinx

x3

12x xsinx 1 cosx tanx sinx11 lim lim lim333x 0x 0x 0xxcosxxcosx2

12

x 0,1 cosx x(∵,sin x)

2

10、lim

x cos2x

x 0 0

解

x 0 0

lix co2sx

12

x) 2

lix 0 0

x12 2x 2

12

(∵x 0,1 cosx～

x

x 1

11、lim x x 1

1

1 x 1

x 1e1x lim lim 2 xx x 1ee x 1 解

1 x

12、limxln 1

x

x

1

x