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数分:函数极限存在的判别法及相关习题在此之前我们判别函数极限的存在性大多是直接通过定义进行验证，然而这样的判别方法在很多时候都比较繁琐，本节将介绍几种更加便捷的判别方法。值得注意的是迫敛性定理不仅能判别函数极限的收敛性，还能求出函数的极限；同时上述的两个重要极限在后续的极限运算中也起到重要作用。我们知道数列是一种特殊的函数，同时我们已经掌握了许多数列极限的判别法，于是我们考虑能否建立起函数极限与数列极限的关系，利用数列极限的判别方法来解决函数极限的问题。而Heine归结原理就将函数极限与数列极限架起了桥梁。事实上个人认为Heine归结原理可以理解为是数列与其子列关系的推广，我们知道数列｛an｝收敛等价于它的任何子列都收敛；而Heine归结原理中｛f(xn)｝可以理解为f(x)的一个子列，他们之间也有类似结论。而定理的推论也为我们判别函数极限发散提供了很好的办法。接下来我们将由数列的单调有界原理出发推导出函数的单调有界原理：
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