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设函数f(x)在x=0某邻域内有一阶连续导数,且f(0)≠0,f'(0)≠0,若af(h)+bf(2h)-f(0)在h→0时为比h高阶的无穷
设函数f(x)在x=0某邻域内有一阶连续导数,且f(0)≠0,f'(0)≠0,若af(h)+bf(2h)-f(0)在h→0时为比h高阶的无穷小,试确定a、b的值.
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设函数f(x)在x=0某邻域内有一阶连续导数,且f(0)≠0,f'(0)≠0,若af(h)+bf(2h)-f(0)在h→0时为比h高阶的无穷小,试确定a、b的值.
设函数f(x)在x=0的某邻域内具有二阶连续导数,且f(0)≠0,f'(0)≠0,f"(0)≠0,证明:存在唯一的一组实数λ1,λ2,λ3,使得当h→0时,λ1f(h)+λ2f(2h)+λ3f(3h)-f(0)是比h2高阶的无穷小
设二元函数f(x,y)在点(0,0)的某邻域内连续,且
证明:点(0,0)不是f(x,y)的极值点
设y=f(x)在x=x0的某邻域内具有三阶连续导数,如果f"(x0)=0,而f'"(x0)≠0,试问(x0,f(x0))是否为拐点?为什么?
设方程F(x2+y2,y2+z2,z2+x2)=0确定了函数z=z(x,y),其中F有连续一阶偏导数,求函数z = z(x,y)在点(1,0,-1)处的全微分dz,是xyz + (x2 + y2 + z2)^(1/2) =2^(1/2)
设函数f(x)在(-∞,+∞)内具有一阶连续导数,L是上半平面(y>0)内的有向分段光滑曲线,其始点为(a,b),终点为(c,d)。记
设函数f(x)在(-∞,+∞)内具有一阶连续导数,L是上半平面(y>0)内的有向分段光滑曲线,其起点为(a,b),终点为(c,d).记
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A.fx(x0,y0)=0,fy(x0,y0)=0
B.[fxy(x0,y0)]2-fxx(x0,y0)fyy(x0,y0)<0
C.fx(x0,y0)=0,fy(x0,y0)=0,[fxy(x0,y0)]2-fxx(x0,y0)fyy(x0,y0)<0,fxx(x0,y0)>0
D.fx(x0,y0)=0,fy(x0,y0)=0,[fxy(x0,y0)]2-fxx(x0,y0)fyy(x0,y0)<0,fxx(x0,y0)<0