设函数f(x)与g(x)在点x_0连续, 证明函数 ϕ(x)=max(f(x), g(x)), ψ(x)=min(f(x), g(x))在点x_0也连续.

根据函数极限的定义证明1) lim _(xarrow 3)(3x-1)=8-|||-__1) lim _(xarrow 3)(3x-1)=8-|||-__

3.求下列极限:-|||-(1) lim _(xarrow 2)dfrac ({x)^2-3x-4}({x)^2-4} :-|||-(3) lim _(xarrow infty )dfrac (3{x)^2+5x+1}({x)^2+3x+4} :-|||-(5) lim _(xarrow infty )(1+dfrac (1)(x))(2-dfrac (1)({x)^2}) ;-|||-(7) lim _(xarrow 1)dfrac (sqrt {3-x)-sqrt (1+x)}({x)^2-1} ;-|||-(9) lim _(xarrow 1)dfrac ({x)^m-1}({x)^n-1} (m,n是正整数);-|||-(11) lim _(xarrow 0)dfrac ((1+x)(1+2x)(1+3x)-1)(x)-|||-(2) lim _(harrow 0)dfrac ({(x+h))^3-(x)^3}(h) ;-|||-(4) lim _(xarrow infty )dfrac ({(2x-3))^20((3x+2))^30}({(5x+1))^50}-|||-(6) lim _(xarrow infty )dfrac (2{x)^3+3x+1}(4{x)^5+2x+7} ;-|||-(8)lim _(xarrow 1)(dfrac (1)(1-x)-dfrac (3)(1-{x)^3});-|||-(10)lim √x-1-|||-(12) lim _(xarrow +infty )(sqrt ((x+2)(x-1))-x) .

利用极限存在准则证明数列. sqrt (2), sqrt (2+sqrt {2)} sqrt (2+sqrt {2+sqrt {2)}} 的极限存在,并求出该极限.

7.设-|||-._(1)=2 , _(n+1)=dfrac (1)(2)((x)_(n)+dfrac (2)({x)_(n)}) , n=1 ,2,3,...-|||-(1)证明limxn存在;-|||-(2)求limxn.-|||-n→∞

及函数f(x)在[a,b]上连续且 (x)gt 0, 则A、及函数f(x)在[a,b]上连续且 (x)gt 0, 则B、及函数f(x)在[a,b]上连续且 (x)gt 0, 则C、及函数f(x)在[a,b]上连续且 (x)gt 0, 则D、及函数f(x)在[a,b]上连续且 (x)gt 0, 则

AB=2A+B，AB=2A+B，则AB=2A+BA.AB=2A+BB.AB=2A+BC.AB=2A+BD.AB=2A+B

1.lim _(xarrow 0)dfrac (arctan x)(x)=

9.求曲面 ^2+2(y)^2+3(z)^2=21 的切平面,使它平行于平面 +4y+6z=0

9.求下列函数的极限-|||-(1) lim _(xarrow -1)dfrac ({x)^3-1}(x-1);-|||-(3) lim _(xarrow infty )dfrac ({x)^2-1}(3{x)^2-x-1}-|||-(5) lim _(xarrow 3)dfrac (sqrt {x+13)-2sqrt (x+1)}({x)^2-9} :-|||-(7) lim _(xarrow 1)(dfrac (1)(1-x)-dfrac (2)(1-{x)^2}) =-|||-(9) lim _(xarrow 1)(1-x)tan dfrac (pi )(2)x-|||-(11) lim _(xarrow 1)(x)^dfrac (2{1-x)} =-|||-(13) lim _(xarrow infty )((dfrac {x-1)(1+x))}^x-1 =-|||-(15) lim _(xarrow -1)dfrac (ln (2+x))(sqrt [3]{1+2x)+1} =-|||-(2.) lim _(xarrow 1)dfrac ({x)^2-1}(2{x)^2-x-1} =-|||-(4) lim _(xarrow 1)dfrac (2x-1)({x)^2-5x+4} =-|||-(6) lim _(xarrow +infty )dfrac (sqrt {{x)^2+1}-1}(x)-|||-(8) lim _(xarrow 0)dfrac (1-cos x)(xsin x) =-|||-(10) lim _(xarrow 0)dfrac (tan x-sin x)({x)^3} =-|||-(12) lim _(xarrow 0)((1-3x))^dfrac (1{x)} :-|||-(14) lim _(xarrow 0)dfrac (x+ln (1+x))(3x-ln (1+x)) :-|||-(16) lim _(xarrow infty )((dfrac {2x+3)(2x+1))}^x+1.