math100_L3_midterm_99

math100_L3_midterm_99 - (3) (25 marks) Find the tangent...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online