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

1.利用 lim _(narrow infty )((1+dfrac {1)(n))}^n=e 求下列极限:-|||-(1) lim _(narrow inft

1.利用 lim _(narrow infty )((1+dfrac {1)(n))}^n=e 求下列极限:-|||-(1) lim _(narrow inft

求极限__-|||-lim _(narrow infty )dfrac (n)(ln n)(sqrt [n](n)-1).求极限.

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

(4) lim _(narrow infty )((1+dfrac {2)(n)+dfrac (2)({n)^2})}^n.

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

(3)收敛, lim _(narrow infty )(2+dfrac (1)({n)^2})=2 --|||-(4)收敛, lim _(narrow inft

16.-|||-□A、 (int )_(0)^1xdx=lim _(narrow infty )sum _(n=1)^infty dfrac (i)(n)cdo

(2)若 lim _(xarrow infty )((1+dfrac {k)(x))}^-3x=(e)^-1 ,则 k= __

__-|||-lim _(narrow infty )([ sin (dfrac {pi )(4)+dfrac (1)(n))] }^n=( )A.