First of all, 1 raised to the power of infinity is not equal to e, but equal to 1.

The reason why such ambiguity arises is mainly because of the following two formulas:

At first glance, it seems to be equivalent substitution, and it is concluded that 1 raised to the infinite power is equal to e,

But——

Such equivalent substitution is not feasible in the limit calculation process,

because——

The calculation of limits is different from ordinary operations. Any formula with a limit is a whole and cannot be disassembled to calculate one part first and then the other part. This is because each part of the limit formula works synchronously on the overall convergence of the limit, rather than one part converging first and the other part later.

Take this question as an example:

When x tends to positive infinity, although 1/x is constantly decreasing, x as the index is constantly increasing,< /p>

The increase in exponent /p>

(For example: 1.0001 is very close to 1, but 1.0001^10000 is equal to 2.718145...far greater than 1)

So the following is the correct formula:

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Supplement——

Why does x increase? Can it exceed the reduction of 1/x?

See the picture below

As x increases, 1/x decreases more and more slowly, but the growth rate of x remains unchanged.

< p>In this way, the speed difference between the two sides will become larger and larger, eventually leading to the birth of extreme e~