limx^2(cos(1/x)+1/(sinx)^2)

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limx^2(cos(1/x)+1/(sinx)^2)limx^2(cos(1/x)+1/(sinx)^2)limx^2(cos(1/x)+1/(sinx)^2)(x->0时)limx^2(cos(1

limx^2(cos(1/x)+1/(sinx)^2)
limx^2(cos(1/x)+1/(sinx)^2)

limx^2(cos(1/x)+1/(sinx)^2)
(x->0时)
lim x^2(cos(1/x) +1/(sinx)^2)
= lim x^2 cos(1/x) + limx^2/(sinx)^2
因为 -x^2 < x^2 cos(1/x) < x^2,且 lim(-x^2) = lim(x^2) =0
所以 lim x^2 cos(1/x) =0
所以 = 0 + lim(x/sinx)^2 = 0+1 = 1