tan3 2x-tanx 2

利用等价无穷小,洛必达法则求解.(x->0)lim(1/x^2-1/arctan^2(x))=(x->0)lim(1/x^2-cos^2(x)/sin^2(x))=(x->0)lim[sin^2(x)

设函数f(x)=tanx/x,f'(x)=(xsec^2x-tanx)/x^2=g(x)/x^2g'(x)=sec^2x+2xsec^2xtanx-sec^2x=2xsec^2xtanx>0所以g(x