A Treatise on Infinitesimal Calculus ... |
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Page 142
... differences however between the true results and the approximate results thus determined will be less , according as the number of parts into which the range is divided is greater . [ ** r ' ′ ( x ) dæ express the area contained between ...
... differences however between the true results and the approximate results thus determined will be less , according as the number of parts into which the range is divided is greater . [ ** r ' ′ ( x ) dæ express the area contained between ...
Page 143
... difference is unity . If m = 1 , 1.2.3 ... n = ( 1 + n ) " + } e ̃ " . ( 207 ) Now the difference between the true value and the approximate value given in ( 206 ) of m ( m + 1 ) . . . ( m + n − 1 ) will become less , the larger n is ...
... difference is unity . If m = 1 , 1.2.3 ... n = ( 1 + n ) " + } e ̃ " . ( 207 ) Now the difference between the true value and the approximate value given in ( 206 ) of m ( m + 1 ) . . . ( m + n − 1 ) will become less , the larger n is ...
Page 144
... difference between F ( x + i ) and F ( x ) , which is generally finite , since i is finite , be denoted by AF ( x ) ; so that we have F ( x + i ) = F ( x ) + AF ( x ) ; ( 209 ) in reference to which it may be observed that △ becomes d ...
... difference between F ( x + i ) and F ( x ) , which is generally finite , since i is finite , be denoted by AF ( x ) ; so that we have F ( x + i ) = F ( x ) + AF ( x ) ; ( 209 ) in reference to which it may be observed that △ becomes d ...
Page 146
... differences of F ( x ) ; and in all cases to which the pre- ceding formula of approximation can be successfully applied , it is necessary that the values of these differences should rapidly decrease ; this circumstance may easily be ...
... differences of F ( x ) ; and in all cases to which the pre- ceding formula of approximation can be successfully applied , it is necessary that the values of these differences should rapidly decrease ; this circumstance may easily be ...
Page 158
... difference of two definite dn integrals , which are necessarily positive ; the former of which increases , and the latter decreases , as n increases ; therefore d.r ( n ) dn der ( n ) dn2 is positive , and r ( n ) has a minimum value ...
... difference of two definite dn integrals , which are necessarily positive ; the former of which increases , and the latter decreases , as n increases ; therefore d.r ( n ) dn der ( n ) dn2 is positive , and r ( n ) has a minimum value ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
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