One is that sinx/x =1when x tends to 0; The other is that when x tends to 0, (1+x) (1/x) = e.

Mathematical definition of limit: a variable in a function gradually approaches a certain value in the process of eternal change, and can never overlap, and is artificially defined as always approaching without stopping. Limit is a description of the state of change.

General concept of function limit: in a certain change process of independent variables, if the corresponding function value is infinitely close to a certain number, then this certain number is called the limit of function in this change process.

Function limit is one of the most basic concepts in higher mathematics, and the concepts such as derivative are all completed on the definition of function limit. Rational application of limit properties of functions. The common properties of function limit are uniqueness, local boundedness, order preservation, algorithm of function limit, composite function limit and so on.

Monotone bounded criterion: monotonically increasing (decreasing) a sequence with upper (lower) bounds must converge. When using the above two to find the function limit, we should pay special attention to the following points. First, we should prove the convergence by monotone bounded theorem, and then find the limit value. 2. The key to applying the pinch theorem is to find functions with the same limit value, and when they meet the limit value, they tend to the same direction, thus proving or finding the limit value of the function.