Page:Calculus Made Easy.pdf/208

 {| style="border-style: none; margin-left: auto; margin-right: auto; width: 100%;" Now try to put the pieces together, setting each so that the middle of its base is the proper distance to the right, and so that they fit together at the corners; thus (Fig. 49). The result is, of course, not a smooth
 * When
 * $$x=0,$$
 * $$\frac{dy}{dx} = 0,$$
 * Calculus Made Easy - Fig 48a.png
 * $$x=1,$$
 * $$\frac{dy}{dx} = 0.2,$$
 * Calculus Made Easy - Fig 48b.png
 * $$x=2,$$
 * $$\frac{dy}{dx} = 0.4,$$
 * Calculus Made Easy - Fig 48c.png
 * $$x=3,$$
 * $$\frac{dy}{dx} = 0.6,$$
 * Calculus Made Easy - Fig 48d.png
 * $$x=4,$$
 * $$\frac{dy}{dx} = 0.8,$$
 * Calculus Made Easy - Fig 48e.png
 * $$x=5,$$
 * $$\frac{dy}{dx} = 1.0.$$
 * Calculus Made Easy - Fig 48f.png
 * }
 * $$x=4,$$
 * $$\frac{dy}{dx} = 0.8,$$
 * Calculus Made Easy - Fig 48e.png
 * $$x=5,$$
 * $$\frac{dy}{dx} = 1.0.$$
 * Calculus Made Easy - Fig 48f.png
 * }
 * $$x=5,$$
 * $$\frac{dy}{dx} = 1.0.$$
 * Calculus Made Easy - Fig 48f.png
 * }



curve: but it is an approximation to one. If we had taken bits half as long, and twice as numerous, like Fig. 50, we should have a better approximation. But