lim{(x^2-1)/(x-1)×e^(1/(x-1))},当x→1时

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lim{(x^2-1)/(x-1)×e^(1/(x-1))},当x→1时lim{(x^2-1)/(x-1)×e^(1/(x-1))},当x→1时lim{(x^2-1)/(x-1)×e^(1/(x-1)

lim{(x^2-1)/(x-1)×e^(1/(x-1))},当x→1时
lim{(x^2-1)/(x-1)×e^(1/(x-1))},当x→1时

lim{(x^2-1)/(x-1)×e^(1/(x-1))},当x→1时
答案为2.
设X-1=t,原式=lim{(X+1)*e(1/X-1)}=lim{(t+2)/e^t}
当x趋向于1时,即t趋向于0时,极限为2.

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