计算极限x→2,limx²-3x+2/x²-4,

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/22 13:50:34
计算极限x→2,limx²-3x+2/x²-4,计算极限x→2,limx²-3x+2/x²-4,计算极限x→2,limx²-3x+2/x²-

计算极限x→2,limx²-3x+2/x²-4,
计算极限x→2,limx²-3x+2/x²-4,

计算极限x→2,limx²-3x+2/x²-4,
(x²-3x+2)/(x²-4)
=(x-1)(x-2)/(x+2)(x-2)
=(x-1)/(x+2)
limx->2 (x-1)/(x+2)=1/4

运用洛必达法则可得:x→2,limx²-3x+2/x²-4=1/4

原式=x→2,lim(x-1)(x-2)/(x-2)(x+2)
=x→2,lim(x-1)/(x+2)
=(2-1)/(2+2)
=1/4