Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 6-10 із 100
Сторінка 68
... becomes u . = Let u = f ( x ) , then f ( x + h ) = 0 . But since u = f ( x ) , x = ƒ - 1 ( u ) , and if we call k the increment of u due to the increment h of x , 1 x + h = ƒ ̃1 ( u + k ) , or , expanding by Taylor's Theorem , x + h = x ...
... becomes u . = Let u = f ( x ) , then f ( x + h ) = 0 . But since u = f ( x ) , x = ƒ - 1 ( u ) , and if we call k the increment of u due to the increment h of x , 1 x + h = ƒ ̃1 ( u + k ) , or , expanding by Taylor's Theorem , x + h = x ...
Сторінка 81
... value when a = 1 , or when the series becomes that of the first order of figurate numbers . By two differentiations we find u = 0 0 n ( n + 1 ) = 2 ( 11 ) The sum of the series is u 6 EVALUATION OF INDETERMINATE FUNCTIONS . 81.
... value when a = 1 , or when the series becomes that of the first order of figurate numbers . By two differentiations we find u = 0 0 n ( n + 1 ) = 2 ( 11 ) The sum of the series is u 6 EVALUATION OF INDETERMINATE FUNCTIONS . 81.
Сторінка 82
... becomes indeterminate , we need only differentiate that factor so as to find its real value when a = 1 , and then multiply it by the value of the first factor when = 1. The real value of the fraction is ( 13 ) Let u = When u = n 2 p a ...
... becomes indeterminate , we need only differentiate that factor so as to find its real value when a = 1 , and then multiply it by the value of the first factor when = 1. The real value of the fraction is ( 13 ) Let u = When u = n 2 p a ...
Сторінка 87
... become inde- terminate for a particular value of the variable , but these may generally be reduced to the form 0 ... becomes for a , we assume P : = Q " so that P1 Q1 Q1 0 u = = when a 1 P1 0 Treating this as a vanishing fraction , u ...
... become inde- terminate for a particular value of the variable , but these may generally be reduced to the form 0 ... becomes for a , we assume P : = Q " so that P1 Q1 Q1 0 u = = when a 1 P1 0 Treating this as a vanishing fraction , u ...
Сторінка 88
... becomes can frequently be reduced to the form - when a ɑ , 1 0 for if P = and " P1 1 Q = 1 u = Q1- P1 P1Qi when x = a , and its value is to be found by the usual method . De Morgan's Differential Calculus , p . 172 . π ( 29 ) u = ( 1 ...
... becomes can frequently be reduced to the form - when a ɑ , 1 0 for if P = and " P1 1 Q = 1 u = Q1- P1 P1Qi when x = a , and its value is to be found by the usual method . De Morgan's Differential Calculus , p . 172 . π ( 29 ) u = ( 1 ...
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