高等数学(上册)习题答案_吴赣昌_人民大学出版社_高数_理工类(15)

高等数学(上册)习题答案_吴赣昌_人民大学出版社_高数_理工类

lim

1=0n→∞nk

ε

1

0<εnk

1

<n ε

lim

1k

1

k1 N=

ε

ε>0

n>N

1

0<εnk

1

=0n→∞nk

1

k1 ε

N

N

N

1+3n3

=

n→∞4n 14lim

ε

3n+137

=<ε4n 144(4n 1)

n>

7+4ε16ε 7+4ε N=

16ε

ε>0n>N

3n+13

<ε4n 14

1+3n3

=

n→∞4n 14

n+2

sinn=0lim2

n→∞n 2lim

n+2n+21

n <sin0=

n 2n2 2n2 2

ε

n+2

sinn 0<ε2

n 2

1

<εn 2

n>

1

ε

+2

n>2

1 N= +2

ε

ε>0

n>N

n+2

sinn 0<εn2 2

lim

n+2

sinn=0

n→∞n2 2

3

{xn}

xn=

1nπcosn2

limxn=?

n→∞

N

n>N

xn

ε

ε=0 001

N