Osgood, William F. (William Fogg), 1864-1943, Graustein, William C. (William Caspar), 1888-1941, joint author · New York : The Macmillan Company · leaf 174
CERTAIN GENERAL METHODS 155 Let the coordinates of P be(a^i, ?/i) ; those of P, {x, y),or (x^ -h h, ?/i 4- k). Then PQ = h, QP = k, and we have, for the slope ofthe secant PP, the expression: (2) tanr = h … where r = ^ QPP. The slope of the tangent line, T, at P is,then, (3) tan T = lim tan t = lim -, P=P h=^o Ji where t^^QPT. The sign = is used to mean approachesas its limit, and the expression: lim tanr, is read: the limit of tan r, as P approaches P. Suppose, for example, that P is the point (1,…
