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By F. H. C. Marriott (Auth.)

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Although the equation represents a parabola, it is perhaps better regarded as a linear relationship affected by a quadratic term which becomes important only when x is fairly large. These three curves are the only ones that can be represented by equation (2), or that correspond to the section of a cone by a plane. There are, however, certain "degenerate" cases. First, equation (2) can split into two factors, representing a pair of straight lines, when a section of the cone passes through the apex.

F(x)-l\ < *ifx> X. The second definition applies to a continuous variable x or to an integral variable n; in the latter case "all values greater than . . " of course means integral values, since n takes only these values. These definitions are a formal expression of the concept discussed in the last section. It is very important that they should be clearly understood. The cases of lim/(x) that have been discussed have been those x-+a for which f(a) is undefined. A continuous function has already been mentioned; it means, roughly, a function y =f{x) that is represented graphically by a continuous line.

To extend them to larger angles, further rules are needed, but it is easier to redefine the sine and cosine in a way that is valid for angles of all sizes. First of all, the angle 0 can be defined in terms of the arc PK. Since the circumference of the circle is 2π, the angle 0 in degrees is equal to the length of the arc PK x 360/2ττ. It is easier in many applications, however, to define the angle 0 as the length of the arc 43 44 MATHEMATICS FOR BIOLOGICAL AND SOCIAL SCIENCES PK. This gives the angle in radians.

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