lim sinx/x = 1(x-& gt； 0) When x→0, the limit of sin/x is equal to 1.

Pay special attention to the fact that when x→∞, 1/x is infinite, the limit obtained from the property of infinitesimal is 0.

2. The second important limit formula:

Lim (1+ 1/x) x = e (x→∞) 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.

Other formulas:

The accurate calculation of 1 and ellipse circumference (L) requires integral summation or infinite series, which was first proposed by Bernoulli and developed by Euler. The discussion of this kind of problem leads to a (0-pi/2) integral of elliptic integral L = 4a * sqrt (1-e sin t), where A is the major axis of the ellipse.

2. Approximate calculation of definite integral, application of related formulas in definite integral, spatial analytic geometry and vector algebra, differential method of multivariate function and its application, application of differential method in geometry, directional derivative and gradient, extreme value of multivariate function and its solution, multiple integral and its application, cylindrical coordinate and spherical coordinate, curve integral, surface integral, Gaussian formula and Stokes formula are the relations between curve integral and surface integral.

3. Let {xn} be a series of source infinite real numbers 2 1 13. If there is a real number A of 526 1, it is n >； for any positive number ε of 4 102; 0, uniqueness If the limit of a sequence exists, the limit value is unique, and the limit of any of its subsequences is equal to the limit of the original sequence. Boundedness: If the convergence of a sequence is limited, then the sequence must be bounded.