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A Bug Problem

by Aaron Melman (Santa Clara University)

This article originally appeared in:
College Mathematics Journal
May, 2006

Subject classification(s): Differentiation | Single Variable Calculus | Calculus
Applicable Course(s): 3.4 Non-mainstream Calc I | 3.3 Mainstream Calculus III, IV | 3.1 Mainstream Calculus I

A bug is on the inside of a container that has the shape of a paraboloid \(y=x^2\) revolved about the \(y\)-axis. If a liquid is poured into the container at a constant rate, how fast does the bug have to crawl to stay dry?

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Capsule Course Topic(s):
One-Variable Calculus | Differentiation: Calculation Rules
Multivariable Calculus | Optimization
Multivariable Calculus | Properties of Curves
One-Variable Calculus | Integration: Applications
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