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
{xn}
M
n
xn≤M
xnyn≤Myn
limyn=0
n→∞
ε1
N
n>NN
yn<ε1
ε
ε1=ε
M
ε
M=ε
n>N
yn≤ε1=
ε
M
xnyn<M×
limxnyn=0
n→∞
6
{xn}
k→∞
limx2k 1=a
limx2k=a
k→∞
limxn=a
n→∞
ε>0
xn a<ε
n
ε>0
k→∞
limx2k 1=a
N1
2k-1>N1
x2k 1 a<ε
k→∞
limx2k=a
N2
2k>N2
x2k 1 a<ε
N=max{N1,N2}
n>N
n=2k 1
n=2k
xn a<ε
limxn=a
n→∞
1
f(x)
g(x)
f(x)g(x)
f(x)g(x)
f(x)=x
g(x)=sin
1x
limx=0
x→0
limg(x)
x→0
limxsin
x→0
1
=0x
2
2x+32
=
x→+∞3x3lim
x→+∞
lim
sinxx
=0
1lim=1x→2x 1
x2 1lim2=2x→1x x