注 类似地，设f(x,y)在区域D:0≤x≤1,0≤y≤1上可微，且f(0,0)=0.试求极限lim_(xto0^+)(int_(0)^x^(2)dtint_(x)^sqrt(t)f(t,u)du)/(1-e^-x^(4)).(-(1)/(4)f_(xy)(0,0))

1.设f(x,y)=e^sqrt(x^(2)+y^{4)},求f_(x)(0,0),f_(y)(0,0).1.设$f(x,y)=e^{\sqrt{x^{2}+y

设 F(x) = int_(0)^x tf(x^2-t^2) , dt, f(x) 在 x=0 某邻域内可导，且 f(0)=0, f(0)=1，则 lim_(x

4.设f(x),g(x)在x=0的某个邻域内连续,且lim_(xto0)(g(x))/(x)=-1,lim_(xto0)(f(x))/(g^2)(x)=2,则在

1 设lim_(xto0)(1+x+(f(x))/(x))^(1)/(x)=e^3,则lim_(xto0)(1+(f(x))/(x))^(1)/(x)=____

(3)设f(x)在[0,1]上连续，在(0,1)内二阶可导，lim_(xto0^+)(f(x))/(x)=1,lim_(xto1^-)(f(x))/(x-1)=

2【单选题】设f(x,y)=}(x^2+y^2)sin(1)/(sqrt(x^2)+y^(2)),(x,y)neq(0,0)0,(x,y)=(0,0)f(x,y

二、设函数y=y(x)由方程x=int_(1)^y-xe^-u^(2)du确定，试求lim_(xto0)(y-(1+e)x-1)/(x^2).二、(本题14分)

【0-19-0】设函数f(x,y)可微且满足df(x,y)=-2xe^-ydx+e^-y(x^2-y-1)dy,f(0,0)=2，求f(x,y)，并求f(x,y

3.(1915)求极限lim_(xto0)(int_(0)^x[ln(1+t)-t]dt)/(e^x^(3)-1).3.(1915)求极限$\lim_{x\to

已知函数f(x,y)在点(0,0)的某个邻域内连续，且lim_(x to 0 cdot y to 0) (f(x,y))/(1-cos(x^2)+y^(2))=