By Robert Carl Yates
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1 Sec. 7 THE REAL NUMBER SYSTEM-GRAPHS 23 900 Fig. 27 Fig. 26 It is advisable to draw the unit circle with center 0 to help determine reciprocals of the numbers r1. (D) Consider the Rose r = sin 36 As 0 varies from 0 to 30° to 60°, r varies continuously from 0 to 1 to 0, and corresponding points form the "leaf" symmetric to the line B =30°. For 60° < B < 120°, r is negative and the leaf symmetric to the line 0 = 90° is formed. Repetition occurs for 0 > 180°. , make use of the techniques of addition of radii vectors and of reciprocal radii.
8) : x1/2 + yl2 = 1.
Definition. Formally, if y = f (x), the derivative is defined by either of the equivalent expressions Limit Ay Limit f (x or ox-> 0 Ox + ox) - f (x) AX -- o AX The derivative is a new function derived from y, and we shall represent it by the symbol Day, or f'(x). At times we may omit the subscript if there is no need to call particular attention to the independent variable. Note that the defining forms just given contain explicit directions for finding the derivative. The procedure, called the "delta process," consists of the following four steps: (1) Replace x, y by x + Ax, y + Ay, respectively.