 | Silvestre François Lacroix - 1816 - 762 σελίδες
...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 σελίδες
...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 - 210 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...be increased by 2axh + h*. If both members of the last equation be divided by h, we shall have (I) which expresses the ratio of the increment of the function to that of the variable. 12. The value of the ratio of the increment of the function to that of the variable is composed of... | |
 | Charles Davies - 1838 - 300 σελίδες
...2axh + ah?. If both members of the last equation be divided by A, we shall have ^L = 2ax+ah, (1) h which expresses the ratio of the increment of the function to that of the variable. 12. The value of the ratio of the increment of the function to that of the variable is composed of... | |
 | Charles Davies - 1838 - 298 σελίδες
...-p- = dx 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... | |
 | Augustus De Morgan - 1842 - 878 σελίδες
...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 3 and... | |
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The value of the ratio of the increment of the function to that of the variable is composed of two parts, 2ax and ah. 
