利用积分中值定理求极限

摘要

积分中值定理是定积分一个很重要的性质，在证明微积分基本定理、根和驻点的存在性、积分不等式和求极限等问题上作用明显。针对用积分中值定理计算积分的极限进行讨论，给出了含特殊点极限的求法，并结合实例分析由于中值点的不确定性导致的计算错误。%The mean value theorem in integral calculus is an important property for definite integral. It's widely applied in proving the basic theorem of calculus, the existence of roots, integral inequality and limit calculation. This paper discusses how to calculate the limit of integrals using the mean value theorem, presenting the calculation method for limits with special-points and analyzing the calculation errors caused by uncertain median points with examples.