计算limx→0[(sinx)^2+cos(x^2)]^(2/x^2)

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计算limx→0[(sinx)^2+cos(x^2)]^(2/x^2)计算limx→0[(sinx)^2+cos(x^2)]^(2/x^2)计算limx→0[(sinx)^2+cos(x^2)]^(2

计算limx→0[(sinx)^2+cos(x^2)]^(2/x^2)
计算limx→0[(sinx)^2+cos(x^2)]^(2/x^2)

计算limx→0[(sinx)^2+cos(x^2)]^(2/x^2)
limx→0[(sinx)^2+cos(x^2)]^(2/x^2)
=limx→0 e^ [(2/x^2)*ln((sinx)^2)+cosx^2)](用洛必达法则)
=limx→0 e^ 2[(sinx)^2+cosx^2-1]/x^2
因为 ln((sinx)^2)+cosx^2)~(sinx)^2+cosx^2-1
=limx→0 e^[(-2xsinx^2+2sinxcosx)/2x]
=limx→0 e^(2xcosx-2x*x^2)/x
=limx→0 e^(2cosx-2x^2)
=e^2