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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. "
Elements of Analytic Geometry and of the Differential and Integral Calculus - Page 187
by Elias Loomis - 1859 - 277 pages
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An Elementary Treatise on the Differential and Integral Calculus

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, u=ax*;...
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An Elementary Treatise on the Differential and Integral Calculus

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 — will...
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A Short Treatise on the Principles of the Differential and ..., Volume 1

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 had originally...
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The elements of the differential calculus

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 the second,...
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The Elements of the Differential Calculus: Comprehending the General Theory ...

John Radford Young - Calculus - 1833 - 288 pages
...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...
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The Elements of the Differential Calculus: Comprehending the General Theory ...

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....
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Elements of the Differential and Integral Calculus

Charles Davies - Calculus - 1836 - 296 pages
...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...
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Elements of the Differential and Integral Calculus

Charles Davies - Calculus - 1838 - 300 pages
...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...
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Elements of the Differential and Integral Calculus

Charles Davies - Calculus - 1838 - 298 pages
...-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...
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The Differential and Integral Calculus: Containing Differentiation ...

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 3 and...
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