v = f(h) = 4/400 – h , 0 < h < 400 expresses the speed (in ft/sec) of a ball in terms of its hcight, measured in fcet. (a) Sketch an accurate graph of the function v = f(h). (b) Give numerical evidence that supports or refutes the claim that when the ball is 100 feet above the ground the change in its speed is approrimately proportional to a small change in its height. Compute enough difference quotients (at least six) to suggest or refute a progression toward a limit. Estimate the proportionality constant (if it erists) to three significant figures. What are its units? Include units in all steps of your computations.

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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.