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

8.对于数列(xn),若 _(2k-1)arrow a(karrow infty ), _(2k)arrow a(karrow infty ), 证明: _(n

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

设 (x)=lim _(narrow infty )dfrac ({x)^n+2-(x)^-n}({x)^n+(x)^-n} 则函数(x)=lim _(narr

设函数(x)=lim _(narrow infty )dfrac ({x)^n+3}(sqrt {{3)^2n+(x)^2n}}(-infty lt xlt +

设(x)=lim _(narrow infty )dfrac ({x)^n+2}(sqrt {{2)^2n+(x)^2n}}，则(x)=lim _(narrow

设(x)=lim _(narrow infty )dfrac ({x)^2n-1+a(x)^2+bx}({x)^2n+1}-|||-+bx/，若(x)=lim

设 lim _(narrow infty )dfrac ({n)^99}({n)^k-((n-1))^k} 存在且不为零,则常数 k= __

1.利用数列极限的" -N 定义证明:-|||-(1) lim _(narrow infty )dfrac (1)({n)^2}=0;-|||-(2) lim

-|||-求 lim _(narrow infty )sum _(k=1)^ndfrac (k)({n)^2}ln (1+dfrac (k)(n))

设 f(x)=} lim_(n to infty) (x^n)/(1+x^n) & x geq 0 x & xA. $x=1$ 为跳跃间断点B. $x=0$