lim(x→0)(cos2x-cos3x)/{[(1+x^2)^1/2]-1}

问题描述:

lim(x→0)(cos2x-cos3x)/{[(1+x^2)^1/2]-1}

lim(x→0)(cos2x-cos3x)/{[(1+x^2)^1/2]-1}
=lim(x→0)[2sin(5x/2)sin(x/2)]/{[(1+x^2)^1/2]-1}
=lim(x→0)[5x^2/2*{[(1+x^2)^1/2]+1}/x^2
=5.