 | Silvestre François Lacroix - 1816 - 750 דפים
...APGMM'Q. This being premised, the differential coefficient — , relative to the variable x, expressing the limit of the ratio of the increment of the function to that of this variable, will be equal to the limit of the ratio of the segment Pm to the increment Pp of the... | |
 | Silvestre François Lacroix - 1816 - 762 דפים
...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, u=ax*;... | |
 | Jean-Louis Boucharlat - 1828 - 480 דפים
...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 — will... | |
 | Baden Powell - 1829 - 196 דפים
...Where d does not 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 had originally... | |
 | John Radford Young - 1831 - 300 דפים
...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 the second,... | |
 | John Radford Young - 1833 - 288 דפים
...function will be 3x2h + Sxh? 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 ' ble, that is to say, the value of the fraction —7 — -. In the first case, • L_Jf - 2^ + L In... | |
 | John Radford Young - 1833 - 288 דפים
...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 - 1836 - 296 דפים
...is du dx = 4 na?. 14. We have seen, in the preceding examples, that the differential coefficient, or limit of the ratio of the increment of the function to that of the variable, is entirely independent of the increment attributed to the variable. We now propose to show that the... | |
 | Charles Davies - 1838 - 298 דפים
...2ax, to which it will become equal when h~0. The part 2 ax, which is independent of h, 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 ratio is called... | |
 | Charles Davies - 1838 - 300 דפים
...have -=— = ax 14. We have seen, in the preceding examples, that the differential coefficient, or limit of the ratio of the increment of the function to that of the variable, is entirely independent of the increment attributed to the variable. Indeed, when the ratio is obtained... | |
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The part 2az, which is independent of h, is therefore the limit of the ratio of the increment of the function to that of the variable. 
