The knowledge points involved in limit calculation include the classification of continuous points and discontinuous points (the continuity problem of piecewise points of piecewise function), differentiability (the derivative is defined by functional limit), asymptote and double limit (multivariate differential calculus). Among them, double limit is more difficult.
Extreme indirect test or comprehensive test with other knowledge points accounts for a large proportion, and can also be taken directly, so there are many forms of test. Such as finding the parameters of known limit, the concept and comparison of infinitesimal, finding the type and number of discontinuous points, finding the number of asymptote equation or bars, finding the continuity and derivability at a certain point, finding the existence of limit of multivariate function at a certain point, finding the function expression with limit, finding the limit of known limit, etc.
The conventional methods for calculating the limit of function are mainly divided into four categories: equivalent infinitesimal substitution, Lobida rule, Taylor formula and derivative definition. There are four conventional methods involved in the limit of sequence: pinch theorem, definition of definite integral (mainly for partial sum limit), conversion to function limit (resolution principle) and monotone bounded discrimination.