math100_L3_midterm_99

# math100_L3_midterm_99 - (3(25 marks Find the tangent plane...

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Math 100 L3 Introduction to Multivariable Calculus Mid-Term Test 1999 (1) (20 marks) Sketch the surface z = x 2 + 4 y 2 + 1. (2) (25 marks) Let λ 1 be the closed curve obtained by intersecting two surfaces x 2 + y 2 = 1 and x + y + z = 1; λ 2 be the closed curve obtained by x 2 + y 2 = 1 and x + y - z = 5. Show that both have the same arc length.
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Unformatted text preview: (3) (25 marks) Find the tangent plane to the surface sin( x + y ) + sin( y + x ) + sin( x + z ) = 0 at (0 , , 0). (4) (30 marks) Find all relative maxima, relative minima, and saddle points for the function f ( x, y ) = 3 x 2-2 xy + y 3 . 1...
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## This note was uploaded on 09/30/2010 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

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