求极限,x趋向于0,lim(x的平方/(sin(x/3)的平方))求极限,x趋向于0,lim(x^2/(sin(x/3)^2))

问题描述:

求极限,x趋向于0,lim(x的平方/(sin(x/3)的平方))
求极限,x趋向于0,lim(x^2/(sin(x/3)^2))

用三角不等式做:sinx

运用罗比达定理的 x^2 / (x/3)^2=9

利用等价无穷小 sin(x/3)^2 (x/3)^2
=lim(x^2/((x/3)^2))=9;