设函数f(x)在点x0处可导,试求下列极值的值
limf(x0+h)-f(x0-h)\/2h=f'(x0)
设函数f(x)在点x0处可导,试求下列各极限的值.(1)lim△x→0f(x0?△...
原式=lim△x→0f(x0?△x)?f(x0)?(?△x)=-lim△x→0f(x0?△x)?f(x0)?△x=-f′（x0）（2）limh→0f(x0+h)?f(x0?h)2h=12limh→0 f(x0+h)?f(x0)+f(x0)?f(x0?h)h=12limh→0[f(x0+h)?f(x0)h?f(x0?h)?f(x0)?h]=12[f′（x0）+f′（x0...
设函数f(x)在点Xo处可导,求下列极限lim(ΔX→0)[F(X)-F(Xo-ΔX)]\/...
lim(ΔX→0)[F(X)-F(Xo-ΔX)]\/ΔX =lim(ΔX→0)[F(X)-F(Xo-ΔX)]\/【-ΔX*（-1）】=-f'(x0)
设f(x)在点x0处可导,计算极限
原式=lim[xf(x0)-xf(x)+xf(x)-x0f(x)]\/(x-x0)=lim[xf(x0)-xf(x)]\/(x-x0)+lim[xf(x)-x0f(x)]\/(x-x0)=limx[f(x0)-f(x)]\/(x-x0)+f(x0)=-x0f'(x0)+f(x0)=f(x0)-x0f'(x0)
设函数f(x)在点x0处可导,且f(x0)!=0,求极限lim[f(x0+1\/n)\/f(x0)]^...
先计算取对数后的极限 lim(n→∞)[lnf(x0+1\/n)-lnf(x0)]\/(1\/n)= f'(x0)\/f(x0),所以 lim(n→∞)[f(x0+1\/n)\/f(x0)]^n= e^lim(n→∞)[lnf(x0+1\/n)-lnf(x0)]\/(1\/n)= e^[f'(x0)\/f(x0)]...
设函数f(x)在点x0处可导,求lim(h→0)(f(x0+h)-f(x0-h))\/2h的值_百度...
设函数f(x)在点x0处可导，求lim(h→0)(f(x0+h)-f(x0-h))\/2h的值 lim(h→0)(f(x0+h)-f(x0-h))\/2h =lim(h→0)(f(x0+h)-f(x0)+f(x0)-f(x0-h))\/2h =lim(h→0)[f(x0+h)-f(x0)]\/2h+lim(h→0)[f(x0)-f(x0-h)]\/2h =1\/2 f'(x0)+1\/2f'(...
设函数f(x)在x0处可导,求下面极限
=lim a*[f(x0+ah)-f(x0)]\/ah - b*[f(x0+bh)-f(x0)]\/bh =a*f '(x0) - b*f '(x0)=(a-b)*f '(x0)
设函数f(x)在x=0处可导,且f(0)=0,求下列极限
答案是2*a*f‘(0)（f'(0)表示导数）
设函数f(x)在点x0处可导,且f(x0)!=0,求极限lim[f(x0+1\/n)\/f(x0)]^
先计算取对数后的极限 lim(n→∞)[lnf(x0+1\/n)-lnf(x0)]\/(1\/n)= f'(x0)\/f(x0)，所以 lim(n→∞)[f(x0+1\/n)\/f(x0)]^n = e^lim(n→∞)[lnf(x0+1\/n)-lnf(x0)]\/(1\/n)= e^[f'(x0)\/f(x0)]。
设函数f(x)在x=0处可导,且f(0)=0,求下列极限,其中a不等于0,为常数lim...
1)=a*lim [f(ax)-f(0)]\/(ax) + a*lim [f(0)-f(-ax)]\/(ax)=2af'(0)2)=lim x*[f(ax)-f(0)]\/(ax)=lim x * f'(0)=0
