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

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

lim(x→0)(cos2x-cos3x)/{[(1+x^2)^1/2]-1}
当x→0时,cos2x-cos3x=-2*sin[(5x)/2]*sin(-x/2),与5/2*x^2是等阶无穷小
[(1+x^2)^1/2]-1与1/2*x^2是等阶无穷小
lim(x→0)(cos2x-cos3x)/{[(1+x^2)^1/2]-1}=lim(x→0)(5/2*x^2)/(1/2*x^2)=5