数学中的极限思想及其应用

摘要：本文对数学极限思想在解题中的应用进行了诠释，详细介绍了数学极限思想在几类数学问题中的应用，如在数列中的应用、在立体几何中的应用、在函数中的应用、在三角函数中的应用、在不等式中的应用和在平面几何中的应用，并在例题中比较了数学极限思想与一般解法在解题中的不同。灵活地运用极限思想解题，可以避开抽象、复杂的运算，优化解题过程、降低解题难度。极限思想有利于培养学生从运动、变化的观点看待并解决问题。

：极限思想，应用关键词Abstract: In this paper, the application of in solving problems is the limit idea explained. What's more, the applications in several mathematic problems, such

as the application in series of numbers, the application in solid geometry, the

application in function, the application in trigonometric function, the application

in inequalities, the application in plane geometry are introduced in detail. The

mathematic limit idea is compared with a common solution in a example, showing their differences in solving a problem. Solving problem by applying the

limit idea can avoid abstract and complex operation, optimize the process of

solving problem and reduce difficulty of solving problem. Students will benefit

from the limit idea, treating and resolving problems from views of the movement and the change.

Keywords: application ，the limit idea

目录

1 绪论3..................................................................................................................................................... .1.1

研究意义3......................................................................................................................................

1.2国内外研究现状3........................................................................................................................ .1.3 本文解决的主要问题3...............................................................................................................

2数学极限思想的在解题中应用5..............................................................................................

2.1数学极限思想在数列中的应用5..............................................................................................

2.1.1利用极限思想处理无穷等比数列5 ...............................................................................

2.1.2利用极限思想简化运算过程，优化解题方案6 ....................................................... .

2.2数学极限思想在函数中的应用7..............................................................................................

2.2.1利用极限思想确定函数图像

7 ....................................................................................... .2.2.2利用极限思想确定函数定义域7...................................................................................

2.2.3利用极限思想求未知变量的取值范围8.....................................................................

2.3数学极限思想在三角函数中的应用9.....................................................................................

2.3.1通过求极端位置求三角函数的取值范围

9 ................................................................ .2.3.2通过假设极端状态推出角的取值范围

9 .....................................................................

2.4数学极限思想在不等式中的应用............................................. 错误！未定义书签。

2.4.1通过假设变量的极限求得答案错误！未定义书签。............................................

2.4.2利用极限思想解决不等式证明题错误！未定义书签。........................................