当x趋于0,x^a与(sin^3)x^2为等价无穷小,则a等于?

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当x趋于0,x^a与(sin^3)x^2为等价无穷小,则a等于?当x趋于0,x^a与(sin^3)x^2为等价无穷小,则a等于?当x趋于0,x^a与(sin^3)x^2为等价无穷小,则a等于?您好,这

当x趋于0,x^a与(sin^3)x^2为等价无穷小,则a等于?
当x趋于0,x^a与(sin^3)x^2为等价无穷小,则a等于?

当x趋于0,x^a与(sin^3)x^2为等价无穷小,则a等于?

您好,这道题应该这么做。根据洛必达法则。两式同时求导。ax^(a-1)=3(sinx^2)*cos(x^2)*(2x),即ax^(a-1)=3sin(2x^2)*x,再同时求导,a*(a-1)x^(a-2)=3cos(2x^2)*4x^2+3sin(2x^2),趋进于0时,右边等于12x^2,所以a=4.