 | Mineral industries - 1963 - 706 pages
...Proof. - The relation PF(AB) = Pp(A).PF(B) implies, as N -» °°, the further relation - P00(A)'P00(B), since the limit of a product is the product of the limits. Using the definitions of the operation and its inverse with the foregoing relations, ff -1{pF(A).PF... | |
 | Michael Spivak - Mathematics - 2006 - 682 pages
...Notice first that the sequence 1 = 1 j=l converges, since {an} and {bn} are absolutely convergent, and since the limit of a product is the product of the limits. So {PL} is a Cauchy sequence, which means that for any £ > 0, if L and L' are large enough, then L'... | |
 | 556 pages
...£-£•£-'»•/» ................ w For, if Bx, By, Bu be simultaneous increments, we have By _ By Su Bx Su' Bx' identically ; and therefore, since the limit of a...theory of rectilinear motion. Thus if, as in Art. 26, we denote by v and a the velocity and the acceleration, respectively, of a moving point, we have... | |
 | 558 pages
...symbols F,f denoting given functions, then For, if Sx, Sy, Su be simultaneous increments, we have = Sx~ Su' Sx' identically ; and therefore, since the...product is the product of the limits, dy _ dy du dx du' dot' A useful application of the formula (3) occurs in the theory of rectilinear motion. Thus if, as... | |
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Bx' identically ; and therefore, since the limit of a product is the product of the limits, dy _ dy du, dx du' dx' A useful application of the formula (3) occurs in the theory of rectilinear motion. 