求极限lim(x→0){(2x-sin2x)/xsin^2x}

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/10/06 22:34:19

lim(x→0){(2x-sin2x)/(x*sin^2x)}
= lim(x→0){(2x-sin2x)/(x*x^2*(sin^2x/x^2))}
= lim(x→0){(2x-sin2x)/(x*x^2) * lim(x→0){(sin^2x/x^2)}
= lim(x→0){(2-2cos2x)/(3x^2)
= lim(x→0){(4sin2x)/(6x)
= lim(x→0){(8cos2x)/(6)
= 4/3

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