By using the Lagrange multiplier method to find the extreme values of multivariate function,the distance formulas from a point to a straight line,a point to a plan and between two nocoplanar straight lines were established.

IN the paper,I slolve the extreme problem of the dual function determined by the implicit function ,using Lagrange Multiplier Method and Dual Function extreme conditions exist to the full.

This paper has,from the Lagrange multiplier method,discussed the condition limit of a class quadratic form and brought out the main result,applying which to solve the condition limit of function of several variables.

By means of the Lagrange Multiplier, this paper points out the position of celestial bodies when their azimuth varies the slowest during diurnal motion, thus consummating the conclusion concerned.

An efficient iterative Lagrange multiplier approach is devel-oped to design the filter banks.

This article tries to present a proof to Lagrange multiplier in the condition of n functions with m additional conditions.

Furthermore, utilizing the Lagrange method of multipliers and the implicit theorem to work out the critical value which makes one of those inequality locally inverted.

This article mainly uses "Lagrangian multiplier method" wich is the important way of solving the Extremal Problem under the restraint condition to solve the distance question of space analytic geometry and proves some important conclusions.

Based on the ratio of middle to outside law design idea,the application target programming method is used to establish a simplification model and improvement model based on the most superior design of can shape and the size,and the simplification model is solved by the Lagrange multiplicator law.