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Multivariable CalculusMediumPartial Derivatives & the Gradient

Partial Derivatives & the Gradient · Medium problem

A cylindrical can's volume V=πr2hV = \pi r^{2}h must stay within 5%5\% of its nominal value. If the radius is held to a relative error of at most 1%1\%, use differentials (dVV≈2drr+dhh\dfrac{dV}{V} \approx 2\dfrac{dr}{r} + \dfrac{dh}{h}) to find the largest allowable relative error in the height, as a percentage.