大一高数极限Lim(n->∞)(1+1/3)(1+1/3^2)(1+1/3^4)…(1+1/3^(2^n))设f(x)在x=x0处可导,求极限lim(x->x0)(xf(x0)-x0f(x))/(x-x0)利用夹逼定理计算Lim(n->∞)(a^n+b^n)^(1/n),(a>0,b>0)

问题描述:

大一高数极限
Lim(n->∞)(1+1/3)(1+1/3^2)(1+1/3^4)…(1+1/3^(2^n))
设f(x)在x=x0处可导,求极限lim(x->x0)(xf(x0)-x0f(x))/(x-x0)
利用夹逼定理计算Lim(n->∞)(a^n+b^n)^(1/n),(a>0,b>0)

lim(x->x0)(xf(x0)-x0f(x))/(x-x0)
=lim(x->x0)(xf(x0)+x0f(x0)-x0f(x0)-x0f(x))/(x-x0)
=limf{(x0)(x-x0)-x0[f(x)-f(x0)]}/(x-x0)
=f(x0)-x0*f(x)的导数