MT2 w soln - Midterm 2 The exam starts at 4:10pm and lasts...

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

View Full Document Right Arrow Icon
Midterm 2 The exam starts at 4:10pm and lasts for 50 minutes. You turn in your work exactly at 5pm. You cannot use calculators, any books or other supplementary materials. However, you are allowed to have a formula sheet the size of which is a quarter of a regular sheet of paper. You can write on both sides of it. If you need to ask a question, please raise your hand and I will address your question. If cheating is noticed draconian measures will be taken. Please write legibly. Sketches should be done in a clear and neat way. The main features of graphs should be speciFed. Your explanations should be brief and clear. Please don’t forget to write your name above each of the problems. Good luck! 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Your Name Problem 1 The surface S is given in Cartesian coordinates by x 3 + y 3 + z 3 + 1 = ( x + y + z + 1) 3 . Find the equation of the tangent plane at the point (2 , - 2 , - 1). Solution Let F ( x, y, z ) = x 3 + y 3 + z 3 - ( x + y + z +1) 3 +1 then the surface S is given by F ( x, y, z ) = 0. We have at the point (2 , - 2 , - 1) F x = 3 x 2 - 3( x + y + z + 1) 2 = 12 , F y = 3 y 2 - 3( x + y + z + 1) 2 = 12 , F z = 3 z 2 - 3( x + y + z + 1) 2 = 3 . The equation of the tangent plane at the point (2
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 03/09/2010 for the course PHYSICS 7A taught by Professor Lanzara during the Fall '08 term at Berkeley.

Page1 / 6

MT2 w soln - Midterm 2 The exam starts at 4:10pm and lasts...

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