# A. C. Burdette (Auth.)'s An Introduction to Analytic Geometry and Calculus PDF

By A. C. Burdette (Auth.)

ISBN-10: 0121422526

ISBN-13: 9780121422523

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Extra resources for An Introduction to Analytic Geometry and Calculus

Example text

Example 3-12. Discuss and graph the equation 4x2 + 4y2 - \2x + 32y - 27 = 0. We divide both sides of this equation by 4 and obtain x2 + y2 27 3x + 8y - — = 0. This equation is of the form (3-3). We may say, then, that this is the equation of a circle with center at (3/2, —4). We find it convenient to reduce this equation to form (3-2) in order to obtain the radius. We have, completing the square, / 9\ 27 9 ί x2 - 3x + - 1 + (y2 + iy + 16) = — + - + 16 or (-if + (y + 4)2 = 25. Thus we reconfirm the fact that the center is at (3/2, —4) and discover that the radius is 5.

30 3. NONLINEAR EQUATIONS AND GRAPHS Example 3-11. Graph xy - 2y - 4 = 0. We have chosen this example to illustrate some points not covered by our discussion of intercepts, symmetry, and extent, but which occasionally are very useful. (a) Intercepts: If x = 0, y = — 2. If y = 0, the equation has no solution and consequently no x-intercept. (b) Symmetry: No symmetry to the coordinate axes or origin is indicated. (c) Extent : We solve for x and obtain x= 2y + 4 y . Any real value of y Φ 0 gives a real value for x; if y = 0, x is undefined.

Given: the sequences {rn} and {sn}9 the limits of which are both oo and {/„}, which has the finite limit / Φ 0; and the constant c Φ 0.