Example 11.1B Show sin r is continuous. Proof. Represent r as the arclength AP, so the point P is (cos x, sin x). Since the perpendicular PR is the shortest distance from P to the horizontal, we see that 0 x-x' X-X0 Po |PR| < \PPo], i.e., | sin r – sin rol < lx – xo] · A (3)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.