Calculus: Analytic Geometry and Calculus, with Vectors

6 Analytic geometry in two dimensions 148 < x < 152. This is a special instance illustrating the fact that if a and 8 (del ...

1.1 Real numbers 7 25 Iflx-5l <2,then 3 <x<7? 26 If lx-2l <0.01,then 1x2-4l <0.0401? 27 If lx- 31 <1,then lx2- ...

8 Analytic geometry in two dimensions 44 Let h be positive and let X (lambda) be greater than 1. Observe that Figure 1.191 shows ...

1.1 Real numbers 9 more elements of a sequence xi, x2, xs, of successively better approxima- tions. If we suppose that xn (where ...

14 Analytic geometry in two dimensions usual assumptions about them. We can hear many different and even contradic- tory tales a ...

1.2 Slopes and equations of lines 11 and the absolute values of the coordinates tell us how far we go. The quadrant (or subset) ...

12 Analytic geometry in two dimensions slope equation (or formula) (1.27) y - y1 = m(x - xi). Proof of this theorem is very simp ...

1.2 Slopes and equations of lines 13 2 Plot the points 1I(-7,-1), B(-5,O), C(-3,1), D(-1,2), and E(S,5). (These points all lie o ...

14 Analytic geometry in two dimensions slope m of L, to find the equation of L, and to determine xo algebraically. Do all this a ...

1.3 Lines and linear equations 15 the point (h,0) on the positive x axis as in Fig- ure 1.292. Supposing that the coordinates of ...

16 Analytic geometry in two dimensions the slope-intercept formula. The easiest way to find the slope m of the line having the e ...

1.3 Lines and linear equations 17 which employs the standard trigonometric for- mula for the tangent of the difference of two an ...

18 Analytic geometry in two dimensions two points. Then find in by putting the equation in the form y = mx + b Make the results ...

1.3 Lines and linear equations 19 10 Any given rectangle can be placed upon the x, y coordinate system in such a way that its ve ...

20 Analytic geometry in two dimensions (a) 2x + 3y = 12 (b) 2x - 3y = 12 (c) 2x - 3y = -12 (d) 2x + 3y = -12 (e) y=2x+3 (f) Y=0 ...

1.3 Lines and linear equations^21 of Ll is the first of the equations (1) (2) (3) (x3 - x2)x + (YS - y2)y = (xs - X2)XI + (y3 - ...

22 Analytic geometry in two dimensions center is called the circumcenter of thetriangle. The answer can be put in the forms yl(x ...

1.3 Lines and linear equations 23 and in other forms which look quite different. As we shall see in the next prob- lem, the circ ...

24 Analytic geometry in two dimensions Since the line segment R1M1 is a diameter of the circle, this implies that Q1 must be on ...

1.4 Distances, circles, and parabolas 25 and P2 lie on the same horizontal line and the formula reduces to the correct formula d ...