A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 145
gn (a; and go are increasing functionsof each other). In a similar manner it is evident thatwhen the curve is convex upward, godecreases as x increases ; i. e.,ii x takesthe increment dx, the cortemporaneouschange in co is —dca. dy dx d tan go 2nd. P, dx^ doo d dx dx Bec2 GO—: Now, as sec go is… … cates that the curve is concave upward, andupward, q. e. d. Another Demonstration.—Let DD, and DD,Fig. 118, represent consecutive equal infinitesimalincrements of x, then PE and P E represent con-temporaneous infinitesimal increments of y. Eepre-sent them respectively by dyi and J?/2. The…
Geometry, Analytic · Calculus
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