When x → ∞, the limit of (1+ 1/x) x is equal to e;

Or? When x → 0, the limit of (1+x) (1/x) is equal to e.

The second depends on the occasion. In the whole multiplication and division operation, the equivalent infinity can be replaced, but the addition and subtraction operation cannot be replaced. It is irreplaceable in the limit of power exponential function, because division becomes subtraction and multiplication becomes addition when logarithm is taken.

Extended data:

Let {xn} be a series of infinite real numbers. If there is a real number a, for any positive number ε (no matter how small), n >；; 0, such inequality | xn-a |

If the above condition n > is true, there is a positive number ε, and no matter what the positive integer n is, there is a certain n >; N, so that |xn-a|≥ε, that is to say, the sequence {xn} does not converge to a, and if {xn} does not converge to any constant, it is called {xn} divergence.

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