exam2sol_s07

# exam2sol_s07 - MATH 2400 CALCULUS 3 MIDTERM 2 I have...

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

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

View Full Document

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: MATH 2400: CALCULUS 3 March 14, 2007 MIDTERM 2 I have neither given nor received aid on this exam. Name: 001 E. Kim . . . . . . . . . . . . . . . . (9am) 002 E. Angel . . . . . . . . . . . . .(10am) 003 I. Mishev . . . . . . . . . . . . (11am) 004 J. Boisvert . . . . . . . . . . (12am) 005 A. Gorokhovsky . . . . . . (1pm) If you have a question raise your hand and remain seated. In order to receive full credit your answer must be complete , legible and correct . Show all of your work, and give adequate explanations. DO NOT WRITE IN THIS BOX! Problem Points Score 1 18 pts 2 16 pts 3 10 pts 4 16 pts 5 10 pts 6 10 pts 7 10 pts 8 10 pts TOTAL 160 pts 1. Consider lim ( x,y ) → (0 , 0) 2 x 2 y x 4 + y 2 . (a) (6 pts) Compute the limit along the line y = x . lim ( x,y ) → (0 , 0) Along y =0 2 x 2 y x 4 + y 2 = lim ( x,y ) → (0 , 0) x 4 = 0 (b) (6 pts) Compute the limit along the parabola y = x 2 . lim ( x,y ) → (0 , 0) Along y = x 2 2 x 2 y x 4 + y 2 = lim ( x,y ) → (0 , 0) 2 x 4 x 4 + x 4 = lim ( x,y ) → (0 , 0) 1 = 1 (c) (6 pts) Based on parts (a) and (b), what is lim ( x,y ) → (0 , 0) 2 x 2 y x 4 + y 2 ? The limit does not exist because the limits along different paths to (0 , 0) are different. 2. Given a function f ( x, y ) = y cos( x ) and a point P (0 , 0), (a) (8 pts) Find the local linear approximation L to the function f ( x, y ) at the point P ....
View Full Document

## This note was uploaded on 04/13/2008 for the course MATH 1012 taught by Professor N/a during the Fall '07 term at Colorado.

### Page1 / 6

exam2sol_s07 - MATH 2400 CALCULUS 3 MIDTERM 2 I have...

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

View Full Document
Ask a homework question - tutors are online