Exam 2 Spring11 - S = αw β h γ where h is the height w...

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MAC 2313-EXAM 2 NAME UF ID 1. Find the length of the curve whose vector valued function is r ( t ) = ± 2 t 3 / 2 , cos 2 t, sin 2 t ² 0 t 5 9 . 2. Write the formulas for the following important unit vectors. N ( t ) = T ( t ) = B ( t ) = 3. For the ideal gas law PV = mRT , where m is a fixed mass, P is pressure, V is volume, T is temperature and R a constant. Show that T ∂P ∂T ∂V ∂T = mR 4. Find and SKETCH the domain of the function f ( x,y ) = y - x 2 1 - x 2 . 5. Express the level curves of the function f ( x,y ) = e y/x in the form y = g ( x ) and state the restriction on the values of k . 1
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6. If f ( x,y ) L as ( x,y ) ( a,b ) along a path C 1 and f ( x,y ) L as ( x,y ) ( a,b ) along C 2 then lim ( x,y ) ( a,b ) f ( x,y ) = L a) TRUE b) FALSE 7. Find the limit, if it exists, or show that the limit does not exists. lim ( x,y ) (0 , 0) x 2 ye x 4 + 4 y 2 8. Find the indicated partial derivative if f ( x,y,z ) = p sin 2 x + sin 2 y + sin 2 z f z (0 , 0 ,π/ 4) = . 9. Find the linearization L ( x,y ) of the function f ( x,y ) = e - xy cos y at the point ( π, 0). 10. A model for the surface are of the human body is given by
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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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Exam 2 Spring11 - S = αw β h γ where h is the height w...

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