Workshop5Prob3Hint - 2011 Fall Calc. I Math. Phys. Sci....

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2011 Fall Calc. I Math. Phys. Sci. (Math 151) Sect. 01,02,03 1 Workshop 5 — Hint for Problem 3 Thursday October 13 Humberto can see two mathematically correct ways of solving this problem. Both rely on Fguring out a mathematical characterization of a circle that is ‘too big’ to be inside the parabola. Quite possibly there are other ways – perhaps better ways – of solving this problem correctly. Solution 1 hint. The key idea for this approach is to realize that a circle is too big if and only if it has points of intersection with the parabola, other than the origin. Take any positive number r . Write the equation of the circle that has radius r , that has its center on the positive y -axis and that is tangent to the x -axis. If you do not remember the equation of a circle, look it up in the book or in the internet. (You should know this equation by memory, or know how to derive it.) Armed with the equation of this circle of radius r , determine whether it has any points of intersection with the parabola other than the origin. After some work, you should be able to
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