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Unformatted text preview: S = αw β h γ where h is the height, w is the weight, and α,β,γ are constants. Find the diﬀerential dS . 2 MAC 2313 — EXAM 2 Free Response NAME SECTION UF ID YOU MUST SHOW ALL OF YOUR WORK TO RECEIVE CREDIT!! 1. Let a,b > 0 be constants, given a space curve C with asssociated vector valued function r ( t ) = ± e at cos bt,e at sin bt,t ² Find the curvature κ at the point (1 , , 0), your answer should be in terms of a and b . 3 2. Verify that the function z = ln( e x + e y ) is a solution of the diﬀerential equations ∂z ∂x + ∂z ∂y = 1 and ∂ 2 z ∂x 2 ∂ 2 z ∂y 2± ∂ 2 z ∂x∂y ² 2 = 0 by computing the following ∂z ∂x = ∂z ∂y = ∂ 2 z ∂x 2 = ∂ 2 z ∂y 2 = ∂ 2 z ∂x∂y = 4...
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This note was uploaded on 12/15/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.
 Spring '08
 Keeran
 Calculus, Geometry, Vectors, Formulas

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