 | Silvestre François Lacroix - Calculus - 1816 - 762 pages
...u'—u=ah\ and by dividing both sides of the equation by h, it becomes —7— =a ; that is to say, the ratio of the increment of the function to that of the variable, is independent of their particular values. Let us take a function a little more complicated,... | |
 | Jean-Louis Boucharlat - Calculus - 1828 - 480 pages
...each of them 0. The fraction — whicu appears in the equation (3), is a symbol which has expressed the ratio of the increment of the function to that of the variable : since this symbol retains no trace of that variable, we will represent it by -/- ; and then... | |
 | Baden Powell - Calculus - 1829 - 210 pages
...stand for a coefficient, but the symbol of an operation ; implying that we have taken the limit of the ratio of the increment of the function to that of the variable. The terms of this fraction are respectively called the differentials of y and of x. If we... | |
 | John Radford Young - 1831 - 300 pages
...be 3 x*h + 3 .,'A2 + If. We may, therefore, in each of these cases, readily find an expression for the ratio of the increment of the function to that of the variable, that ty' — y is to say, the value of the fraction " — — -. In the first case, * In... | |
 | John Radford Young - Calculus - 1833 - 288 pages
...function will be 3x2h + 3x№ We may, therefore, in each of these cases, readily find an expression for the ratio of the increment of the function to that of the varia/ ble, that is to say, the value of the fraction — 7_ -. In the first case, f , — 2mx + h.... | |
 | Charles Davies - Calculus - 1836 - 296 pages
...PTH, is independent of the increment h. When, therefore, we pass from equation (4) which expresses the ratio of the increment of the function to that of the variable, to equation (5) which expresses the limit of that ratio, the second member of equation (4)... | |
 | Charles Davies - Calculus - 1838 - 300 pages
...PTH, is independent of the increment h. When, therefore, we pass from equation (4) which expresses the ratio of the increment of the function to that of the variable, to equation (5) which expresses the limit of that ratio, the second member of equation (4)... | |
 | Augustus De Morgan - Calculus - 1842 - 878 pages
...let x be 100, we have C. log 100 = 2. If x be increased'by 2, this gives C. log 102 — 2-0086002, the ratio of the increment of the function to that of the variable being ihat of -0086002 lo 2, or '0043001. In passing from 1000 to 1003, we have the logarithms... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...•which expresses the ratio of the increment of the function to that of the variable. The value of the ratio of the increment of the function to that of the variable is composed of two parts, 2ax and ah. If now, we suppose h to diminish continually, the value... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...become --• equal when h—-Q. The part 2ax, which is independent of-A, 4. is therefore the limit of the ratio of the increment of the function to that of the variable. The term, limit of the ratio designates the ratio at the time h becomes equal to 0. This... | |
| |
If both members of the last equation be divided by h, we shall have u' — u •which expresses the ratio of the increment of the function to that of the variable. 
