By Gordon Fuller, Dalton Tarwater
|Tailored for a primary direction within the examine of analytic geometry, the textual content emphasizes the fundamental components of the topic and stresses the recommendations wanted in calculus. This new version used to be revised to give the topic in a contemporary, up to date demeanour. colour is used to spotlight thoughts. expertise is built-in with the textual content, with references to the Calculus Explorer and tips for utilizing graphing calculators. a number of new themes, together with curve becoming related to mathematical modeling have been extra. routines have been up-to-date. New and sundry purposes from medication to navigation to public healthiness have been added.|
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Extra info for Analytic Geometry
Hence the curve extends indefinitely to the The x-axis right, getting nearer and nearer to the z-axis, yet never touching it. Since there is symmetry with respect to the origin, is an asymptote of the curve. the graph consists of the two parts drawn in Fig. 1-8. FIGURE 1-8 ASYMPTOTES 1-9] EXAMPLE Draw 2. the graph of x*y 4y = 15 8. Solution. The i/-intercept is 2. But if we set y = 0, there is obviously no value of x which will satisfy the equation. Hence there is no z-intercept. The graph has symmetry with respect to the y-axis but not with respect to the x-axis.
3. 9. 9. and intercepts - y = 7. 3* - 4y = 14. = = 3 + 2y + 4 + 7y = 0. 5. 8. By inspection, give the slope tions 13-24. - 15. x +y+ 12. 18. 6* 14. 21. 7x 4. 24. - 3y by equa- 4 = - 10 + 3z/ + 3* + 3y = 6 0. = 0. = 0. 1. In each problem 25-36, write the equation of the line determined by the slope m and the ^-intercept 6. 25. m = 3; b = -4. 27. m = -4; b = 5. 29. m = 6 - -2. = 31. m 0; 6 = -6. 33. m = -J; 6 = -8. 35. m = 0; b = 0. ; 26. 28. 30. 32. 34. 36. = 2; 6 = 3. = -1;6 = 1. = $ 6 = -6. -5; 6 = 0.
If tjhe formula for this purpose. J and Pi(#i,2/i) ^2(^2,2/2) be the two given points, and indicate the m. slope by Then, referring to Fig. 2-8, we have Let m = tan & = FIGURE 2-8 PiR INCLINATION AND SLOPE OP A LINE 2-3] 23 Y x FIGURE 2-9 If the line slants to the left, as in Fig. 2-9, = ^lU. m = tanfl= _^LJ/? -" Xz Hence the the left or slope is determined in the to the right. THEOREM. P\(xi,yi) The slope and X\ X\ 2 same way for lines slanting either to m PZ(XZ,UZ) is of a line passing through two given points equal to the difference of the ordinates divided by same the difference of the abscissas taken in the order; that is mt This formula yields the slope if the two points determine a slant line.