160 求极限lim _(xarrow infty )(x)^2[ ln ((x)^2+1)-2ln x] = x]=

(5) lim _(xarrow -1)dfrac (sqrt {x+5)-2}(x+1):

([ varphi (x)] )^m+([ varphi (x)] )^n-([ varphi (x)] )^m (m,n为常数,且 gt mgt 0,-|||-[例27]试确定当 arrow 0 时,下列 __ 是关于x的三阶无穷小.-|||-A. sqrt [3]({x)^2}-sqrt [3](x) B. sqrt (1+{x)^3}-1 C. ^3+0.0002(x)^2 D. sqrt [3](sin {x)^3}-|||-解:根据三阶无穷小的定义,-|||-lim _(xarrow 0)dfrac (sqrt {1+{x)^3}-1}({x)^3}=lim _(xarrow 0)dfrac (dfrac {1)(2)(x)^3}({x)^3}=dfrac (1)(2) 因此,x→0时, sqrt (1+{x)^3}-1 是关于x的三阶无穷小.-|||-答案:B. ,与√2是等价无穷小 () .

设有向量组_(1)=((-1,2,1))^T (beta )_(2)=((1,0,b))^7可由向量组 _(1)=((-1,2,1))^T (beta )_(2)=((1,0,b))^7线性表示. ( 1 ) 求 _(1)=((-1,2,1))^T (beta )_(2)=((1,0,b))^7的值 ; ( 2 ) 写出_(1)=((-1,2,1))^T (beta )_(2)=((1,0,b))^7 由 _(1)=((-1,2,1))^T (beta )_(2)=((1,0,b))^7 表示的线性表示式.

lim _(xarrow {0)^-}(e)^dfrac (1{x)}=-|||-()

曲面 =(x)^2+(y)^2+1 在点 M(1,-1,3) 的切平面与曲面 =(x)^2+(y)^2 所围区域的体-|||-积为 __

(3)lim _(xarrow 1)dfrac (ln (2-x)arctan x)(sin ({x)^2-1)}

[题目]设函数f (x)在闭区间(0,1)上连续,在开区间-|||-(0,1)内可导,且 (0)=0, (1)=dfrac (1)(3),-|||-证明:存在 in (0,dfrac (1)(2)), in (dfrac (1)(2),1), 使得-|||-'(xi )+f(n)=(s)^2+(n)^2

(9)lim _(xarrow 0)dfrac (sqrt {1+5x)-sqrt (1-3x)}({x)^2+2x} .

[题目]-|||-lim _(xarrow infty )((dfrac {x+3)(x-1))}^x+1

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