A Treatise on Infinitesimal Calculus ... |
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Page xxii
... less or greater than unity 240 5 . 182. Σaƒ ( x ) is convergent or divergent according as [ ƒ ( x ) dx is finite or infinite .. 241 244 183. Examples of the criterion given in the preceding article 243 184. On comparable and ...
... less or greater than unity 240 5 . 182. Σaƒ ( x ) is convergent or divergent according as [ ƒ ( x ) dx is finite or infinite .. 241 244 183. Examples of the criterion given in the preceding article 243 184. On comparable and ...
Page 7
... less its value when x = x ; on this account it is fre- quently and conveniently expressed as follows [ ** v ( x ) de = [ x ( x ) ] " ; * = xo = F ( x ) F ( x ) . ( 11 ) 6. ] Perhaps it may be supposed that the value of the definite ...
... less its value when x = x ; on this account it is fre- quently and conveniently expressed as follows [ ** v ( x ) de = [ x ( x ) ] " ; * = xo = F ( x ) F ( x ) . ( 11 ) 6. ] Perhaps it may be supposed that the value of the definite ...
Page 41
... less than n . To determine m dx x " -1 The roots of the denominator are those given in Art . 23 ; and since X.m Xm + +1 Xm + +1 = = = nxn n F ( x ) f ( x ) nx2 - 1 we may determine without difficulty the coefficients of the several ...
... less than n . To determine m dx x " -1 The roots of the denominator are those given in Art . 23 ; and since X.m Xm + +1 Xm + +1 = = = nxn n F ( x ) f ( x ) nx2 - 1 we may determine without difficulty the coefficients of the several ...
Page 43
... less by unity , so may the same process be repeated successively until finally n = 1 , in which case the formula fails to give a determinate result : but the integral becomes and we have , see Art . 14 , dx + a2 , dx x2 1 X x2 + a2 a ...
... less by unity , so may the same process be repeated successively until finally n = 1 , in which case the formula fails to give a determinate result : but the integral becomes and we have , see Art . 14 , dx + a2 , dx x2 1 X x2 + a2 a ...
Page 69
... less than b , then ( 26 ) becomes dx La + b cos x dx a + b sin = ။ ။ = X 2 b + a b - a log ( b2 — a2 ) 1 ( b2 - a2 ) = f- = 2 log 2 Ꮖ d.tan 2 - ( tan ) ( b + a ) * + ( b − a ) 1 tan - 8122 ( 28 ) Ꮖ 2 ( b + a ) * — ( b− a ) 1 tan ...
... less than b , then ( 26 ) becomes dx La + b cos x dx a + b sin = ။ ။ = X 2 b + a b - a log ( b2 — a2 ) 1 ( b2 - a2 ) = f- = 2 log 2 Ꮖ d.tan 2 - ( tan ) ( b + a ) * + ( b − a ) 1 tan - 8122 ( 28 ) Ꮖ 2 ( b + a ) * — ( b− a ) 1 tan ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ a₂ angle application axis Beta-function bx dx consequently convergent series coordinates cosec cx² cycloid definite integral denoted determined differential double integral dx a² dx dx dx dy dx Ex dx² dy dx dy² e-ax element-function ellipse equal evaluation expressed find the area finite and continuous fraction function Gamma-function geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation involute left-hand member length let us suppose limits of integration multiple integrals plane curve polar coordinates preceding proper fraction radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variable x-integration x₁ x²)¹ x²)³ αξ πα