Original formula = lim (x→ 0) (1-x) (1/x)

=lim(x→0)( 1-x)^( 1/x)=( 1+(-x))^( 1/-x)×(- 1)

=lim(x→0)e^(- 1)

= 1/e

For example:

When x→0, the power of (1+x) is1/x = e.

Then "when (-x)→0, the power of (1+(-x)) is 1/(-x) =e"

The original formula =( 1+(-x)) to the power of1/x.

= 1/( 1+(-x)) to the power of 1/(-x)

= 1/e

Extended data:

1, there are at most n (finite) points outside the interval (a-ε, a+ε);

2. All other points xN+ 1, xN+2, ... (infinite) fall within this neighborhood. These two conditions are indispensable. If a series can meet these two requirements, then the series converges to a; If a sequence converges to a, then both conditions can be satisfied.

In other words, if we only know that {xn} has countless terms in the interval (a-ε, a+ε), we can't guarantee that there are only finite terms outside (a-ε, a+ε), so we can't come to the conclusion that {xn} converges to a, so we should pay special attention to this when doing judgment questions.

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