+dfrac (1)({2)^n})-|||-1/2^n);(12)-|||-(13) lim _(narrow infty )dfrac ((n+1)(n+2)(n+3))(5{n)^2} ;-|||-(2) lim _(xarrow sqrt {3)}dfrac ({x)^2-3}({x)^2+1} ;-|||-(4) lim _(xarrow 0)dfrac (4{x)^3-2(x)^2+x}(3{x)^2+2x} =-|||-(6) lim _(xarrow infty )(2-dfrac (1)(x)+dfrac (1)({x)^2}) ;-|||-(8) lim _(xarrow infty )dfrac ({x)^2+x}({x)^4-3(x)^2+1} ;-|||-(10) lim _(xarrow infty )(1+dfrac (1)(x))(2-dfrac (1)({x)^2}) ;-|||-lim _(narrow infty )dfrac (1+2+3+... +(n-1))({1)^2} ;-|||-(14) lim _(xarrow 1)(dfrac (1)(1-x)-dfrac (3)(1-{x)^3}) -

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

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

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

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

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

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

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

[题目]-|||-(5) lim _(narrow infty )dfrac ({(-2))^n+(3)^n}({(-2))^n+1+(3)^n+1} ;

[题目]-|||-(5) lim _(narrow infty )dfrac ({(-2))^n+(3)^n}({(-2))^n+1+(3)^n+1} ;

【题文】lim _(narrow infty )dfrac ({2)^n+1+(3)^n+1}({2)^n+(3)^n}=________.【题文】______