2008Final

2008Final - blue MATH 32A Final Exam LAST NAME FIRST NAME ID NO Your TA To receive credit you must write your answer in the space provided DO NOT

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: blue MATH 32A Final Exam March 17, 2008 LAST NAME FIRST NAME ID NO. Your TA: To receive credit, you must write your answer in the space provided . DO NOT WRITE BELOW THIS LINE 1 (20 pts) 5 (20 pts) 2 (20 pts) 6 (20 pts) 3 (20 pts) 7 (20 pts) 4 (20 pts) TOTAL 2 PROBLEM 1 (20 Points) Let function f ( x, y ) = x 4- x 2- y 2 . (A) Find all critical points of f ( x, y ) and classify each one as a maximum, minimum, or saddle point. Explain your work. Answer : (B) Find the absolute maximum and minimum of f ( x, y ) on the domain x 2 + y 2 ≤ 4. Explain your work. Answer : 3 PROBLEM 2 (20 Points) Suppose that f ( x, y ) is a function of x and y , and that x = u 2- v 2 , y = uv . Use the table of values ∂f ∂x and ∂f ∂y to compute ∂f ∂u ( u,v )=(1 , 1) and ∂f ∂v ( u,v )=(1 , 0) x y ∂f ∂x ( x, y ) ∂f ∂y ( x, y ) 2-3 1 5 1 1-1-4 1 1 3 2 Answer : ∂f ∂u ( u,v )=(1 , 1) Answer : ∂f ∂v ( u,v )=(1 , 0) 4 PROBLEM 3 (20 Points) Let r ( t ) = h cos 3 t, , sin 3 t i (A) Show that || r ( t ) || 2 = 9 cos 2 t sin 2 t (B) Find a formula for the curvature κ ( t ) at time t . Answer : 5 PROBLEM 4 (20 Points) Let P be the plane through the points P 1 = (1 , 2 , 0) , P 2 = (2 , , 1) , P 3 = (0 , , 2) (A) Find an equation for the plane P ....
View Full Document

This note was uploaded on 10/26/2011 for the course MATH 32A taught by Professor Gangliu during the Spring '08 term at UCLA.

Page1 / 15

2008Final - blue MATH 32A Final Exam LAST NAME FIRST NAME ID NO Your TA To receive credit you must write your answer in the space provided DO NOT

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online