用数列极限定义证明:-|||-如果 lim (x)_(2k)=a, lim _(karrow infty )(x)_(2k+1)=a, 则 lim (x)_(n)=a.

(5) lim _(xarrow 0)((dfrac {{a)^x+(b)^x+(c)^x}(3))}^dfrac (1{x)}(agt 0,aneq 1;bgt 0 neq 1;cgt 0,cneq 1) ;

1.判断题排列24315是奇排列.(自然数从小到大为标准次序)A 对B 错

[题目]设 f(x)= ) 1,|x|lt 1 0,|x|=1 -1,|x|gt 1 .-|||-求f[g(x)]和g[f(x)],并作出这两个函数的图形。

1.利用 lim _(narrow infty )((1+dfrac {1)(n))}^n=e 求下列极限:-|||-(1) lim _(narrow infty )((1-dfrac {1)(n))}^n;-|||-(2) lim _(narrow infty )((1+dfrac {1)(n))}^n+1;-|||-(3) lim _(narrow infty )((1+dfrac {1)(n+1))}^n-|||-(4) lim _(narrow infty )((1+dfrac {1)(2n))}^n;-|||-(5) lim _(narrow infty )((1+dfrac {1)({n)^2})}^n

7.求证-|||-(1) (dfrac (OS)(OP))_(n)lt 0-|||-(2) (dfrac (OS)(OV))_(T)gt 0

3.设-1 1 2-|||-2 0 1-|||-0 1 3,-1 1 2-|||-2 0 1-|||-0 1 3的-1 1 2-|||-2 0 1-|||-0 1 3元的余子式记作-1 1 2-|||-2 0 1-|||-0 1 3,-1 1 2-|||-2 0 1-|||-0 1 3的-1 1 2-|||-2 0 1-|||-0 1 3元的代数余子式记作-1 1 2-|||-2 0 1-|||-0 1 3,则-1 1 2-|||-2 0 1-|||-0 1 3.A.9B.-15C.0D.-4

7.如果f(z)在区域D内解析,试证i (f(z)) 在区域D内也解析.

(2) lim _(xarrow 0)dfrac (sin ({x)^n)}({(sin x))^m} (n,m为正整数);

1.计算下列极限:-|||-(1) lim _(xarrow -1)dfrac ({x)^2+2x+1}(x-1) ;-|||-(3) lim _(xarrow 1)dfrac ({x)^2-3x+2}(x-1) =-|||-(5) lim _(xarrow 1)dfrac (sqrt {x)-1}({x)^2+5x-6} =-|||-(2) lim _(xarrow 2)dfrac (x-1)(sqrt {x+1)} ;-|||-(4) lim _(xarrow infty )dfrac ({x)^2+2x+1}({x)^4-3x+1} ;-|||-(6) lim _(harrow 0)dfrac ({(x+h))^2-(x)^2}(h) ;1.计算下列极限:-|||-(1) lim _(xarrow -1)dfrac ({x)^2+2x+1}(x-1) ;-|||-(3) lim _(xarrow 1)dfrac ({x)^2-3x+2}(x-1) =-|||-(5) lim _(xarrow 1)dfrac (sqrt {x)-1}({x)^2+5x-6} =-|||-(2) lim _(xarrow 2)dfrac (x-1)(sqrt {x+1)} ;-|||-(4) lim _(xarrow infty )dfrac ({x)^2+2x+1}({x)^4-3x+1} ;-|||-(6) lim _(harrow 0)dfrac ({(x+h))^2-(x)^2}(h) ;

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