求limx→0(根号2-根号(1+cosx))/(sin3x)^2的极限求详解
问题描述：
求limx→0(根号2-根号(1+cosx))/(sin3x)^2的极限
求详解
答
limx→0(√2-√(1+cosx))/(sin3x)^2=lim(1-cosx)/[(sin3x)^2(√2+√(1+cosx))]=lim(1-(1-2sin^2(x/2)))/[(sin3x)^2(√2+√(1+cosx))]=lim2sin^2(x/2)/[(sin3x)^2(√2+√(1+cosx))]=lim2sin^2(x/2)*1/4/(x/2)^2/[(sin...