152sum2003MT2_2

152sum2003MT2_2 - Let f x,y be deﬁned as f x,y = sin x 3...

This preview shows pages 1–4. Sign up to view the full content.

Last Name Name Student No Department Section Signature : : : : : : : : : : : : : Code Acad. Year Semester Instructors Date Time Duration M E T U Department of Mathematics Calculus-II II. Midterm Math 152 2004 Summer A. ¨ O., M.K., B.K. 30.07.2004 19.00 90 minutes 4 Questions on 4 Pages Total 60 Points 1 2 3 4 Question 1 (12+6 pts.) (a) Find an equation of the plane passing through the points A = (0 , 0 , 0), B = (1 , 2 , 3) and C = ( - 1 , - 2 , 3). (b) Is the point (3 , 2 , 1) on the plane you found in part (a) ? Explain.

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

View Full Document
Question 2 (5+5+5 pts.) Evaluate the following limits if they exist. (a) lim ( x,y ) (0 , 0) yx 3 x 2 + y 4 (b) lim ( x,y ) (0 , 0) x 3 y x 6 + y 2 (c) lim ( x,y ) (1 , 0) xy x 2 + y 2
Question 3 (12 pts.)

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Let f ( x,y ) be deﬁned as f ( x,y ) = sin( x 3 + y ) x 2 + y 2 , ( x,y ) 6 = (0 , 0) , ( x,y ) = (0 , 0) . Find ∂f ∂x (0 , 0) and ∂f ∂y (0 , 0) if they exist. Question 4 (10+5 pts.) Let z = f ( x,y ) = g ( x 2 y, x-y, x 2 + y ). (a) Find ∂f ∂x and ∂f ∂y at ( x,y ) = (1 , 1), if g 1 (1 , , 2) =-2, g 2 (1 , , 2) = 3 and g 3 (1 , , 2) = 1. (b) Find the normal line to the graph of f ( x,y ) at (1 , 1), if g (1 , , 2) = 5 ....
View Full Document

This note was uploaded on 11/07/2010 for the course COMPUTER 223-231-25 taught by Professor Mcbulut during the Spring '10 term at A.T. Still University.

Page1 / 4

152sum2003MT2_2 - Let f x,y be deﬁned as f x,y = sin x 3...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online