Elements of analysis as applied to the mechanics of engineering and machinery . a function or abscissaAM=x^ Figs. 9 and 10, of the corresponding curve be allowedto increase by an infinitesimal magnitude MN^ which we shall infuture designate by 9^, the corresponding dependent variable, orordinate MP = y passes into NQ^y^^ and increases by the infini-tesimal value B Q = NQ — MP, which is to be designated by dy. Both increments dx and dy of x and y are called differentials, orelements of the variables or co-ordinates x and y, and it is now ourchief task to find, for tlie most frequently recurring
Elements of analysis as applied to the mechanics of engineering and machinery . a function or abscissaAM=x^ Figs. 9 and 10, of the corresponding curve be allowedto increase by an infinitesimal magnitude MN^ which we shall infuture designate by 9^, the corresponding dependent variable, orordinate MP = y passes into NQ^y^^ and increases by the infini-tesimal value B Q = NQ — MP, which is to be designated by dy. Both increments dx and dy of x and y are called differentials, orelements of the variables or co-ordinates x and y, and it is now ourchief task to find, for tlie most frequently recurring functions, thedifferentials, or rather, the relations between the associated elementsof their variables x and y. If, in the function y=f(x), where xdesignates the abscissa A M, and y, the ordinate MP, we replace xhj x^dx = AM-^ MN= AN, we obtain, instead of ^Z, y -{-cy = MP -|- B Q ^ NQ; therefore: y + dy=f(x -{-dx); and if, from this we abstract the first value of y, there will remainthe differential of the variable y; i. e.: dy = df{x) =f(x + dx) -f{x). Fig. 9. Fig. M N X A
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