This is excerpted from George E. Hay's "Vector and Tensor Analysis". The author gives the statement that the limit is equal to 1 without any explanation, perhaps because he thinks it does not belong to the contents of vector analysis. I can see it intuitively, but I want a rigorous mathematical proof of this limit. So, do you know of any textbook that contains a rigorous mathematical proof of this limit? In particular, Is such a proof in Erwin Kreyszig's "Differential Geometry" or Michael Spivak's "Calculus on Manifolds" if you happen to have once read them? Thanks a lot.