1 MATH 141B QUIZ#5 Solutions Date: Fri Feb 15, 2008 Instructor: Dr. M.Fabbri 1. i) False . V ( r, h ) = πr 2 h, whose graph is not a cylinder. An equation involving r, h and V whose graph in 3-space (with axes r, h and V ) is a cylinder is h 2 + r 2 = 1 . Note that for each ±xed V you get a circle. The potential confusion here is that the function V arose by taking the volume of a cylinder, but the graph of the function V ( r, h ) is not a cylinder. ii) False . Fixing r = r0 gives V = ( πr0 2 ) h, which is a straight line. iii) True . Fixing h = h0 gives V = ( πh0 ) r 2 h, which is a parabola. Therefore, D) is the answer. 2. ∂g ∂v = u cos( uv )-3 e 3 v and so, ∂g ∂v ( π, 0) = π-3 . Therefore, C) is the answer. 3. i) True . x · w t is the biomass of the trout (follow the units), and y · w b is the biomass of the bluegill. Therefore x · w t + y · w b is the total biomass (of the trout and the bluegill). ii)
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This note was uploaded on 03/30/2008 for the course MATH 141B taught by Professor Marcfabbri during the Spring '08 term at Pennsylvania State University, University Park.