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|- | When | ${\displaystyle x=0,}$ | ${\displaystyle {\frac {dy}{dx}}=0,}$ | |- | | ${\displaystyle x=1,}$ | ${\displaystyle {\frac {dy}{dx}}=0.2,}$ | |- | | ${\displaystyle x=2,}$ | ${\displaystyle {\frac {dy}{dx}}=0.4,}$ | |- | | ${\displaystyle x=3,}$ | ${\displaystyle {\frac {dy}{dx}}=0.6,}$ | |- | | ${\displaystyle x=4,}$ | ${\displaystyle {\frac {dy}{dx}}=0.8,}$ | |- | | ${\displaystyle x=5,}$ | ${\displaystyle {\frac {dy}{dx}}=1.0.}$ | |} 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

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