midterm_04_L1_

midterm_04_L1_ - x ≥ 0, y ≥ 0 and z ≥ 0, that are...

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

View Full Document Right Arrow Icon
Math 100 (L1) Midterm Test 2004 Fall (1) (25 marks) Show that lim ( x,y ) (0 , 0) xy 2 x 2 + y 2 + x 2 y 2 = 0 , but lim ( x,y ) (0 , 0) xy 2 x 2 + y 4 + x 2 y 2 does not exist. (2) (25 marks) Assume that u ( x, t ) = t 1 / 2 y ( z ), with z = t - 1 / 2 x , satisfies the equation u t - Du xx = 0 , D = constant . Show that the function y = y ( z ) satisfies D d 2 y dz 2 + z 2 dy dz - 1 2 y = 0 . (3) (25 marks) Find the points on the surface xyz = 1, with
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ≥ 0, y ≥ 0 and z ≥ 0, that are closest to the origin. (4) (25 marks) Assume that ( x , y , z ) on the smooth surface z = f ( x, y ) is closes to the origin. Show that the normal line at ( x , y , z ) passes through the origin. 1...
View Full Document

This note was uploaded on 09/30/2010 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

Ask a homework question - tutors are online