1.求下列极限:-|||-(1) lim _(narrow infty )dfrac ({n)^3+3(n)^2+1}(4{n)^3+2n+3} =-|||-(3) lim _(narrow infty )dfrac ({(-2))^n+(3)^n}({(-2))^n+1+(3)^n+1} ;-|||-(2 lim _(narrow infty )dfrac (1+2n)({n)^2} =-|||-(4) lim _(narrow infty )(sqrt ({n)^2+n}-n) ;

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

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

求极限lim _(narrow infty )dfrac ({2)^n+(3)^n+(7)^n}({5)^n+(8)^n}lim _(narrow infty

lim _(narrow infty )dfrac ({2)^n+(3)^n}({2)^n+1+(3)^n+1}=________;________;

(2) lim _(narrow infty )dfrac (3n+1)(2n+1)=dfrac (3)(2) ;

1.计算下列极限:-|||-(13) lim _(narrow infty )dfrac ((n+1)(n+2)(n+3))(5{n)^3};

(3) lim _(narrow infty )dfrac (sqrt {{n)^2-3n}}(2n+1)

(5) lim _(narrow infty )dfrac ({(-2))^n+(3)^n}({(-2))^n+1+(3)^n+1} ,

根据数列极限定义证明：(1) lim _(narrow infty )dfrac (1)({n)^2}=0-|||-(2) lim _(narrow infty

数列极限lim _(narrow infty )(6(n)^2+2)sin dfrac (1)(3{n)^2+1}=( )A.B.C.2D.3数列极限