{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Winter 2008 - Cioaba's Class - Exam 2 (Version 2)

# Winter 2008 - Cioaba's Class - Exam 2 (Version 2) - Name...

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

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: Name: PID: Discussion Section- No: Time: TA’s name: Midterm 2, Math 20C - Winter 2008 Duration: 50 minutes Please close your books, turn off your calculators and phones and put them away. To get full credit you should explain your answers. 1. Let f ( x, y ) = x x 2 + y 2 . a.(2 points) Calculate all first order partial derivatives. Solution. f x = 1( x 2 + y 2 )- x (2 x + 0) ( x 2 + y 2 ) 2 = y 2- x 2 ( x 2 + y 2 ) 2 . f y = x- 2 y ( x 2 + y 2 ) 2 =- 2 xy ( x 2 + y 2 ) 2 . b.(3 points) Calculate all second order partial derivatives. Solution. f xx =- 2 x ( x 2 + y 2 ) 2- ( y 2- x 2 )4 x ( x 2 + y 2 ) ( x 2 + y 2 ) 4 = ( x 2 + y 2 )(- 2 x ( x 2 + y 2 )- 4 x ( y 2- x 2 )) ( x 2 + y 2 ) 4 = 2 x (- x 2- y 2- 2 y 2 + 2 x 2 ) ( x 2 + y 2 ) 3 = 2 x ( x 2- 3 y 2 ) ( x 2 + y 2 ) 3 . f yy = 2 x ( x 2 + y 2 )- 2 xy (0 + 2 y ) ( x 2 + y 2 ) 2 = 2 x 3- 2 xy 2 ( x 2 + y 2 ) 2 . f xy = f yx = 2 y ( x 2 + y 2 )- 2 xy (2 x + 0) ( x 2 + y 2 ) 2 = 2 y 3- 2 x 2 y ( x 2 + y 2 ) 2 . 2.a. (2 points) Let f ( x, y ) =- radicalbig 25- x 2- y 2 . Find the domain and the range of the function...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

Winter 2008 - Cioaba's Class - Exam 2 (Version 2) - Name...

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

View Full Document
Ask a homework question - tutors are online