设函数z=f(x,y),f对y的二阶偏导数=2,且f(x,0)=1,fy'(x,0)=x,求f(x...答:∵ f''y=2 ∴ f'y=2y+s(x)∵ f'y(x,0)=s(x)=x ∴ f'y=2y+x 从f(x,y)=y^2+xy+t(x)∵ f(x,0)=t(x)=1 ∴f(x,y)=y^2+xy+1
二元函数z=f(x,y)在x0处存在偏导和一元函数f=(x,y0)在x0处可导互为充...答:两者一般不能等价,例:(x0, y0):(0,0),f(0, 0)=0,(x, y)≠(0, 0),f(x, y)=x*y^2/(x^2+y^4)|x^2+y^4|>=2|xy^2|,|f(x, y)|<=1/2 f(x, y0)=0*x/(x^2+0)=0, 对任意 x ,f'(x,y0)=0,而 f(x, y)=x*y^2/(x^2+y^...