lim(1/(x^2-x))*sin(π/x)x趋向于0请详解

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/13 14:14:57
lim(1/(x^2-x))*sin(π/x)x趋向于0请详解
x)0"HBN< @vŋmO'L|//{|MR>z lȶ)35*M2 YAS_b\Ӎ@u yk)+mt}mc&[$N_ 3ΨBP3,68( dl @ 8

lim(1/(x^2-x))*sin(π/x)x趋向于0请详解
lim(1/(x^2-x))*sin(π/x)x趋向于0
请详解

lim(1/(x^2-x))*sin(π/x)x趋向于0请详解
答:
(x→0)lim[sin(x/π)/(x^2-x)] 属于0-0型,应用洛必达法则:
=(x→0)lim[(1/π)cos(x/π)/(2x-1)]
=(1/π)*(cos0°)/(-1)
=-1/π