Question: 37. The length (ell ), width ( w ), and height ( h ) of a box change with time. At a certain instant the
37. The length \(\ell \), width \( w \), and height \( h \) of a box change with time. At a certain instant the dimensions are \(\ell=1\mathrm{~m}\) and \( w=h=2\mathrm{~m}\), and \(\ell \) and \( w \) are increasing at a rate of \(2\mathrm{~m}/\mathrm{s}\) while \( h \) is decreasing at a rate of \(3\mathrm{~m}/\mathrm{s}\). At that instant find the rates at which the following quantities are changing. (a) The volume (b) The surface area (c) The length of a diagonal
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