求lim sinx^2/(sinx)^2 x趋向0

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求lim sinx^2/(sinx)^2 x趋向0
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求lim sinx^2/(sinx)^2 x趋向0
求lim sinx^2/(sinx)^2 x趋向0

求lim sinx^2/(sinx)^2 x趋向0
当x趋向0时
sinx x 为等价无穷小
lim sinx^2/(sinx)^2
=lim x^2/(x)^2=1

lim(x→0)sinx^2/(sinx)^2 x=lim(x→0)(sinx^2)’/[(sinx)^2 x]'=lim(x→0)(2xcosx^2 )/ (2sinxcosx)=lim(x→0)xcosx/sinx=lim(x→0)(xcosx)'/(sinx)'= lim(x→0)(cosx-xsinx)/ (cosx)= 1 连续两次使用洛必达法则