lim x→0,[√(x^2+ x+ 1)-1]/tan2x
问题描述：
lim x→0,[√(x^2+ x+ 1)-1]/tan2x
答
设f(x)=√(x^2+x+1)-1.g(x)=tan2x.
lim[f(x)/x]
=lim{[f(x)-f(0)]/(x-0)}
=f'(0)
=1/2
lim[g(x)/x]
=lim{[g(x)-g(0)]/(x-0)}
=g'(0)
=2
原式=lim[f(x)/x]/lim[g(x)/x]=1/4