f2sol-20C-sp2006

F2sol-20C-sp2006 - Print Name TA Name Math 20C Final Exam Section Number Section Time No calculators or any other devices are allowed on this exam

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Print Name: Section Number: TA Name: Section Time: Math 20C Final Exam. June 15, 2006 No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no credit will be given for illegible solutions. Read each question carefully. If any question is not clear, ask for clariFcation. Answer each question completely, and show all your work. 1. (10 points) Find the plane through the point P 0 = (2 , - 1 , 1) which is perpendicular to the planes 2 x - y - z = 3 and x + 2 y + z = 2. The plane is determined by its normal vector n and a point. We choose the point to be P 0 = (2 , - 1 , 1). The normal vector can be computed as n = n 1 × n 2 , n 1 = h 2 , - 1 , - 1 i , n 1 = h 1 , 2 , 1 i . where n 1 and n 2 are the normal vectors to the planes 2 x - y - z = 3 and x + 2 y + z = 2, respectively. Then, n = ¯ ¯ ¯ ¯ ¯ ¯ i j k 2 - 1 - 1 1 2 1 ¯ ¯ ¯ ¯ ¯ ¯ = h ( - 1 + 2) , - (2 + 1) , (4 + 1) i n = h 1 , - 3 , 5 i . Then, the equation of the plane is ( x - 2) - 3( y + 1) + 5( z - 1) = 0 x - 3 y + 5 z = 10 .
Background image of page 1

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

View Full DocumentRight Arrow Icon
2. (8 points) Decide whether the lim ( x,y ) (0 , 0) y 4 - x 2 y 4 + x 2 exists. Give reasons your answer. Consider the path given by the line
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/30/2008 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.

Page1 / 9

F2sol-20C-sp2006 - Print Name TA Name Math 20C Final Exam Section Number Section Time No calculators or any other devices are allowed on this exam

This preview shows document pages 1 - 3. Sign up to view the full document.

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