Chapter 2 - Section 2.1 - The Tangent and Velocity Problems - 2.1 Exercises - Page 82: 4

a) (i) $Q(0,1)$ $m=\frac{1-0}{0-0.5}=-2$ (ii) $Q(0.4,\cos(0.4\pi))$ $m=\frac{\cos(0.4\pi)-0}{0.4-0.5}=-3.09$ (iii) $Q(0.49,\cos(0.49\pi))$ $m=\frac{\cos(0.49\pi)-0}{0.49-0.5}=-3.14108$ (iv) $Q(0.499,\cos(0.499\pi))$ $m=\frac{\cos(0.499\pi)-0}{0.499-0.5}=-3.14159$ (v) $Q(1,\cos(\pi))$ $m=\frac{\cos(\pi)-0}{1-0.5}=-2$ (vi) $Q(0.6,\cos(0.6\pi))$ $m=\frac{\cos(0.6\pi)-0}{0.6-0.5}=-3.09017$ (vii) $Q(0.51,\cos(0.51\pi))$ $m=\frac{\cos(0.51\pi)-0}{0.51-0.5}=-3.14108$ (viii) $Q(0.501,\cos(0.501\pi))$ $m=\frac{\cos(0.501\pi)-0}{0.501-0.5}=-3.14159$ b) Slope from positive is approximately $-\pi$ c) $y=-\pi(x-0.5)$ d) See image

a) (i) $Q(0,1)$ $m=\frac{1-0}{0-0.5}=-2$ (ii) $Q(0.4,\cos(0.4\pi))$ $m=\frac{\cos(0.4\pi)-0}{0.4-0.5}=-3.09$ (iii) $Q(0.49,\cos(0.49\pi))$ $m=\frac{\cos(0.49\pi)-0}{0.49-0.5}=-3.14108$ (iv) $Q(0.499,\cos(0.499\pi))$ $m=\frac{\cos(0.499\pi)-0}{0.499-0.5}=-3.14159$ (v) $Q(1,\cos(\pi))$ $m=\frac{\cos(\pi)-0}{1-0.5}=-2$ (vi) $Q(0.6,\cos(0.6\pi))$ $m=\frac{\cos(0.6\pi)-0}{0.6-0.5}=-3.09017$ (vii) $Q(0.51,\cos(0.51\pi))$ $m=\frac{\cos(0.51\pi)-0}{0.51-0.5}=-3.14108$ (viii) $Q(0.501,\cos(0.501\pi))$ $m=\frac{\cos(0.501\pi)-0}{0.501-0.5}=-3.14159$ b) Slope from positive is approximately $-\pi$ c) $y=-\pi(x-0.5)$ d) See image