It is proved that LIM (x approaches 1) x ^ 2-1 / x ^ 2-x = 2

It is proved that LIM (x approaches 1) x ^ 2-1 / x ^ 2-x = 2

Attention should be paid to the correct use of brackets to avoid misunderstanding
lim(x→1)［（x^2－1）/（x^2－x）］
＝lim(x→1)｛（x＋1）（x－1）/［x（x－1）］｝
＝lim(x→1)［（x＋1）/x］
＝2

LIM (1 x) / [1-e ^ (- x)] approaches 0

1-e ^ (- x) and SiNx are infinitesimals of the same order, and when x approaches 0, LIM (x) / [1-e ^ (- x)] = 1, and SiNx and X are infinitesimals of the same order, and when x approaches 0, Lim X / SiNx = 1; therefore, when x approaches 0, the above limit is 1

X tends to 0 LIM (x + e ^ x) ^ 1 / X

It can be done by ln method
Original formula = lime ^ [ln (x + e ^ x) ^ 1 / x]
=lime^[ln(x+e^x)/x]
The law of lobida
=lime^[(1+e^x)/(x+e^x)]
=e^2
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