I拉格朗日插值法及中值定理的应用摘要 本文运用拉格朗日插值和中值定理这两个原理，分别研究了数学计算中根号运算的算法，和在现实生活中汽车的测速问题,通过这两个例子来体现出这两个数学原理在日常生活中的重要作用.测速应用中，一般测速距离为 300 米，在 300 米中测定其中 1 秒的距离，利用拉格朗日中值定理测出在一秒内的速度.计算根号的应用中，利用公式和已知可以完全开方的数字（例如根号 4），用尽量多的已知条件来提高难以开根号的数字的精度，通过乘法除法等简单的数学运算来得到难以运算的根号运算的结果.由于计算量比较大，所以通过计算机软件 MATLAB 来实现.最后通过与现实例子的比较，得出两种模型可以实现测速和计算器计算，可以比较精确的达到提高精度的目的.关键词 拉格朗日中值定理 拉格朗日插值法 瞬时变化 极限 MATLABLagrange Interpolation and Application of Mean Value TheoremAbstract This article uses the two principles of Lagrange interpolation and median theorem to study the algorithm of the root operation in mathematical calculations and the speed measurement of cars in real life. These two examples show the two mathematical principles Important role in daily life.In the application of speed measurement, the general speed measurement distance is 300 meters, and the distance of 1 second is measured in 300 meters, and the speed within one second is measured by the Lagrange median theorem. In the application of calculating the root number, use formulas and numbers that are known to be easily rooted (for example, root number 4), use as many known conditions as possible to improve the accuracy of numbers that are difficult to root, simple by multiplication and division Mathematical operation to get the result of the difficult root operation. Because the calculation is relatively large, it is realized by the computer software MATLAB.Finally, through comparison with actual examples, it is concluded whether the two IIImo...
