(x,y)neq (a,b)} 是否相同?-|||-3.证明:当且仅当存在各点互不相同的点列 {P)_(n)} CE _(n)neq (P)_(0), lim _(narrow infty )(P)_(n)=(P)_(0) 时,P0是E的聚点.-|||-4.证明:闭域必为闭集.举例说明反之不真.-|||-5.对任何点集SC R^2,导集S"亦为闭集.-|||-6.证明:点列(Pn(xn,yn))收敛于P0 (x0,y0)的充要条件是 lim (x)_(n)=(x)_(0) 和 lim (y)_(n)=(y)_(0)

证明:当且仅当存在各点互不相同的点列 {P)_(n)} CE _(n)neq (P)_(0), lim (P)_(n)=(P)_(0) 时,P0是E的聚点.

→(a)→∞-|||-lim _(narrow infty )(x)_(n)=+infty lim _(narrow infty )(y)_(n)=infty

6.证明:点列(Pn(xn,yn)收敛于P0 (x0,y0)的充要条件是 lim {x)_(n)=(x)_(0) 和 lim (y)_(n)=(y)_(0).

已知 lim _(narrow infty )(a)_(n)=2 lim _(narrow infty )(b)_(n)=3已知 lim _(narrow in

[题目]设曲线 y=f(x) 和 =(x)^2-x 在点(1,0)处有相同-|||-切线,则 lim _(narrow infty )nf(dfrac (n)(

2.按 -N 定义证明:-|||-(1) lim _(narrow infty )dfrac (n)(n+1)=1 ;-|||-(2) lim _(narrow

3.设随机变量X与Y的方差D(X)和D(Y)都存在,且 (X)neq 0 , (r)neq 0,-|||-(XY)=E(X)E(Y), 则( __ )。-|||

1.设(xk)为R^n中的点列, in (R)^n, lim _(karrow infty )(x)_(k)=a, 证明 lim _(karrow infty

没数列(xn)有界,又 lim _(narrow infty )(y)_(n)=0.没数列(xn)有界,又 lim _(narrow infty )(y)_(n

(B) lim f(x)=0.-|||-(C) lim _(xarrow 1)f(x)=infty . D)limf(x)不存在,且 lim _(xarrow