高等数学研究
高等數學研究
고등수학연구
STUDIES IN COLLEGE MATHEMATICS
2014年
4期
12-13
,共2页
导数%极限%连续性延拓%形式悖论%斜率通用函数
導數%極限%連續性延拓%形式悖論%斜率通用函數
도수%겁한%련속성연탁%형식패론%사솔통용함수
derivative%limit%extension of continuity%formal paradox%unified slope-function
形式悖论“Δx ≠0与Δx＝0”出现于蕴含点态连续性的导数极限等式，是合理的必然结果。差商函数的连续性延拓有分析意义和几何意义。
形式悖論“Δx ≠0與Δx＝0”齣現于蘊含點態連續性的導數極限等式，是閤理的必然結果。差商函數的連續性延拓有分析意義和幾何意義。
형식패론“Δx ≠0여Δx＝0”출현우온함점태련속성적도수겁한등식，시합리적필연결과。차상함수적련속성연탁유분석의의화궤하의의。
This expository note explains why the formal paradox “Δx ≠ 0 and Δx = 0” could be reasonably involved in an analytic equality that relates the derivative f′(x) of a differentiable function y = f(x) with the normalized limit of Δy/Δx as Δx → 0 ± ,etc .Also presented is a related geometrical interpretation .
