lim(x趋于1)(x²–1/x–1)乘以e的1/x–1次方=
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简单分析一下，答案如图所示
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lim [(x²-1)/(x-1)]·e^[1/(x-1)]
x→1⁺
=lim [(x+1)(x-1)/(x-1)]·e^[1/(x-1)]
x→1⁺
=lim (x+1)·e^[1/(x-1)]
x→1⁺
=2·e^(+∞)
=+∞
lim [(x²-1)/(x-1)]·e^[1/(x-1)]
x→1⁻
=lim [(x+1)(x-1)/(x-1)]·e^[1/(x-1)]
x→1⁻
=lim (x+1)·e^[1/(x-1)]
x→1⁻
=2·e⁰
=2
[(x²-1)/(x-1)]·e^[1/(x-1)]在x=1处两侧极限不相等
lim [(x²-1)/(x-1)]·e^[1/(x-1)] 不存在
x→1
x→1⁺
=lim [(x+1)(x-1)/(x-1)]·e^[1/(x-1)]
x→1⁺
=lim (x+1)·e^[1/(x-1)]
x→1⁺
=2·e^(+∞)
=+∞
lim [(x²-1)/(x-1)]·e^[1/(x-1)]
x→1⁻
=lim [(x+1)(x-1)/(x-1)]·e^[1/(x-1)]
x→1⁻
=lim (x+1)·e^[1/(x-1)]
x→1⁻
=2·e⁰
=2
[(x²-1)/(x-1)]·e^[1/(x-1)]在x=1处两侧极限不相等
lim [(x²-1)/(x-1)]·e^[1/(x-1)] 不存在
x→1
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