Can someone give a detailed reason why? - any why the letters d?....any historical/ etymological background info would be great too...
2007-08-29 03:31:37 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Δy/Δx is a true quotient: a finite change in "y" divided by a finite change in "x". If you graph a function and select two distinct points on it, Δy/Δx represents the slope of the line joining the two points. You can also think of this is as the _average_ rate at which the function changes between the two points.
dy/dx is not a true quotient (although informally you can think of it as an infinitessimally small change in y "divided by" an infinitessimally small change in x). If you graph a function and select a _single_ point on it, then dy/dx represents the slope of the line that is tangent to the function at that point. You can also think of this as the _instantaneous_ rate at which the function changes at that point. You can also think of it as the limit of Δy/Δx as the two distinct points get closer and closer until they're infinitessimally close.
"Infinitessimal" numbers don't follow all the same rules of arithmtetic as finite numbers do: So to underscore that difference, a different notation is used.
2007-08-29 04:09:43 · answer #1 · answered by RickB 7 · 0⤊ 0⤋
Δy/Δx denotes average rate of change in y over the interval of length Δx, while dy/dx stands for the instantaneous rate of change as Δx approaches zero.
The dy/dx notation is similar to that used by Leibniz, one of the founders of Calculus.
2007-08-29 03:43:39 · answer #2 · answered by Anonymous · 2⤊ 0⤋
DY/DXis the ratio of two smallquantitiesDY & DX
dy/dx is the limit of DY/DX when DX goes to zero. It is not a ratio.It is also written as y'.
2007-08-29 03:57:33 · answer #3 · answered by Anonymous · 0⤊ 0⤋
delta = Δ for uppercase and δ for lowercase in the Greek alphabet.
Both have a range of what they mean/represent based on focus of study, whether that is math, physics, etc.
2007-08-29 03:39:40 · answer #4 · answered by miggitymaggz 5 · 0⤊ 0⤋
Sounds interesting
2016-07-30 02:16:49 · answer #5 · answered by ? 3 · 0⤊ 0⤋
dy/dx = lim /\y / /\x as /\x ->0
Thus /\ denotes a change in y over change in x and dy/dx is the limit of this change as the change in x approaches 0
2007-08-29 03:43:42 · answer #6 · answered by swd 6 · 0⤊ 0⤋
delta as in relation to change. eg a change in time question deltat
2007-08-29 03:39:41 · answer #7 · answered by deburca98 4 · 0⤊ 0⤋
delta-D first letter and there is no difference
2007-08-29 03:39:51 · answer #8 · answered by Anonymous · 0⤊ 2⤋
I think it depends
2016-08-24 13:55:02 · answer #9 · answered by Anonymous · 0⤊ 0⤋