A Treatise on Infinitesimal Calculus ... |
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Page 30
Bartholomew Price. It will be observed that the coefficient of the second fraction corresponding to a pair of conjugate roots is deduced from that of the first by changing the sign of the impossible part . 21. ] Let two or more of the ...
Bartholomew Price. It will be observed that the coefficient of the second fraction corresponding to a pair of conjugate roots is deduced from that of the first by changing the sign of the impossible part . 21. ] Let two or more of the ...
Page 31
... observed that , equating the numerators in equation ( 35 ) , we have F ( x ) = ( x ) × ( x ) + Q ( x− a1 ) " ; F ( x ) .. ( x ) = φ ( 2 ) Q ( x - a1 ) TM φ ( α ) ( 39 ) ( 40 ) But as ( 38 ) involves y ( x ) and its derived functions up ...
... observed that , equating the numerators in equation ( 35 ) , we have F ( x ) = ( x ) × ( x ) + Q ( x− a1 ) " ; F ( x ) .. ( x ) = φ ( 2 ) Q ( x - a1 ) TM φ ( α ) ( 39 ) ( 40 ) But as ( 38 ) involves y ( x ) and its derived functions up ...
Page 44
... observed , failing when n = 1 . Ex . 1 . x2 dx ( x2 + a2 ) + x2 dx = : here m 2 , n = 4 . X 1 + √ ( x2 + a2 ) 3 dx 6 ( x2 + a2 ) 3 6 and the latter integral has been determined in Art . 27 , so that it is unnecessary to repeat it . Ex ...
... observed , failing when n = 1 . Ex . 1 . x2 dx ( x2 + a2 ) + x2 dx = : here m 2 , n = 4 . X 1 + √ ( x2 + a2 ) 3 dx 6 ( x2 + a2 ) 3 6 and the latter integral has been determined in Art . 27 , so that it is unnecessary to repeat it . Ex ...
Page 57
... observed , is always applicable when n is odd ; but if n is even , ultimately , when n = 0 , it becomes infi- nite , and fails to give a determinate result . Ex . 1 . S x3 dx ( a2 — x2 ) } x2 ( a2 — x2 ) 3 2 a2 + 3 3 J x dx x2 ( a2 — x2 ) ...
... observed , is always applicable when n is odd ; but if n is even , ultimately , when n = 0 , it becomes infi- nite , and fails to give a determinate result . Ex . 1 . S x3 dx ( a2 — x2 ) } x2 ( a2 — x2 ) 3 2 a2 + 3 3 J x dx x2 ( a2 — x2 ) ...
Page 93
... observed that the two members of ( 26 ) are not absolutely identical ; but that they differ by a quantity , △ say , which is an infinitesimal of an order which must be neglected ; so that we have where [ * ' v ' ( x ) dx = − [ " v ( x ) ...
... observed that the two members of ( 26 ) are not absolutely identical ; but that they differ by a quantity , △ say , which is an infinitesimal of an order which must be neglected ; so that we have where [ * ' v ' ( x ) dx = − [ " v ( x ) ...
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A Treatise On Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2018 |
Common terms and phrases
a₁ angle application axis Beta-function bx dx consequently convergent convergent series coordinates cosec cx² cycloid definite integral denoted determined double integral dx a² dx dx dx dy dx² dy dz dy² dz dy dx e-ax element-function ellipse equal evaluation examples expressed fraction function Gamma-function geodesic geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation length let us suppose limits of integration logr multiple integral plane curve preceding problem proper fraction quantity radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variables variation x-integration x₁ x2 dx x²)¹ x²)³