Real Function Differentiability — Part II

The articles [18], [21], [2], [19], [6], [1], [3], [4], [10], [22], [8], [15], [5], [20], [12], [13], [17], [14], [16], [11], and [9] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: x0, r, r1, r2, g, p are real numbers, n, mare natural numbers,a, b, d are sequences of real numbers, h, h1, h2 are convergent to 0 sequences of real numbers,c is a constant sequence of real numbers, A i an open subset of R, and f , f1, f2 are partial functions fromR to R. Let us consider h. Observe that −h is convergent to 0. One can prove the following propositions: