1, Taylor formula is a formula that uses the information of a function at a certain point to describe the value near it.

2. If the continuous curve y=f(x) has a tangent that is not perpendicular to the X axis at every point between two points A(a, f(a)) and B(b, f(b)), then the curve has at least 1 points between A and B, so the tangent of the curve at point P is parallel to the secant AB.

3. L 'Bida Law (L'H? Pitard's Law) is a method to determine the uncertainty under certain conditions by taking the derivative and limit of the numerator and denominator respectively. It can solve the extended limit problems such as 0/0 infinitive limit and ∞ /∞ infinitive limit.

4. Discontinuities of functions: the first kind of discontinuity and the second kind of discontinuity. The first kind of discontinuity exists in both left and right limits, and the first kind of discontinuity has jump discontinuity and removable discontinuity. At least one discontinuity that does not exist in the left and right limits is the second discontinuity.

5. The essence of limit: local boundedness, uniqueness, local sign preservation, and inequality (order preservation).