EXAM 2 Review-solutions

EXAM 2 Review-solutions - Van Ligten (hlv63) – EXAM 2...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Van Ligten (hlv63) – EXAM 2 Review – Gilbert – (56650) 1 This print-out should have 27 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. Use this Review as part of your preparation for Exam 2. Remember that the Review will not count towards the Course Grade. JEG 001 10.0 points Find f x when f ( x, y ) = ln( radicalbig x 2 + y 2- x ) . 1. f x = x radicalbig x 2 + y 2 2. f x =- 1 radicalbig x 2- y 2 3. f x =- 1 radicalbig x 2 + y 2 correct 4. f x = 1 radicalbig x 2 + y 2 5. f x = 1 radicalbig x 2- y 2 6. f x = x radicalbig x 2- y 2 Explanation: Differentiating with respect to x keeping y fixed, we see that f x = x radicalbig x 2 + y 2- 1 radicalbig x 2 + y 2- x . But x radicalbig x 2 + y 2- 1 = x- radicalbig x 2 + y 2 radicalbig x 2 + y 2 . Consequently, f x =- 1 radicalbig x 2 + y 2 . 002 10.0 points Determine f xy when f ( x, y ) = (3 x + 2 y )ln( xy ) . 1. f xy = 3 x + 2 y xy correct 2. f xy = 3 x + 2 y y 3. f xy = 3 x- 2 y xy 4. f xy = 2 x + 3 y xy 5. f xy = 2 x- 3 y x 6. f xy = 2 x- 3 y xy Explanation: Since ln( xy ) = ln x + ln y , we see that f ( x, y ) = (3 x + 2 y )(ln x + ln y ) . Thus f x = 3(ln x + ln y ) + 3 x + 2 y x = 3(ln x + ln y ) + 3 + 2 y x . Consequently, after differentiating with re- spect to y we see that f xy = 3 y + 2 x = 3 x + 2 y xy . 003 10.0 points Evaluate the iterated integral I = integraldisplay 5 1 braceleftBig integraldisplay 5 1 parenleftBig x y + y x parenrightBig dy bracerightBig dx . 1. I = 24 ln5 correct Van Ligten (hlv63) – EXAM 2 Review – Gilbert – (56650) 2 2. I = 5 ln12 3. I = 24ln12 4. I = 12 ln5 5. I = 12 ln24 6. I = 5 ln24 Explanation: Integrating with respect to y keeping x fixed, we see that integraldisplay 5 1 parenleftbigg x y + y x parenrightbigg dy = bracketleftbigg x ln y + y 2 2 x bracketrightbigg 5 1 = (ln5) x + 12 parenleftbigg 1 x parenrightbigg . Thus I = integraldisplay 5 1 bracketleftbigg (ln5) x + 12 parenleftbigg 1 x parenrightbiggbracketrightbigg dx = bracketleftbiggparenleftbigg x 2 2 parenrightbigg ln5 + 12 ln x bracketrightbigg 5 1 . Consequently, I = 24 ln5 . 004 10.0 points Evaluate the double integral I = integraldisplay integraldisplay A xy 2 x 2 + 3 dxdy when A = braceleftBig ( x, y ) : 0 ≤ x ≤ 1 ,- 3 ≤ y ≤ 3 bracerightBig . 1. I = 9 2 ln parenleftbigg 4 3 parenrightbigg 2. I = 9 ln(2) 3. I = 9 2 ln(2) 4. I = 27 4 ln parenleftbigg 4 3 parenrightbigg 5. I = 27 4 ln(2) 6. I = 9 ln parenleftbigg 4 3 parenrightbigg correct Explanation: Since A = braceleftBig ( x, y ) : 0 ≤ x ≤ 1 ,- 3 ≤ y ≤ 3 bracerightBig is a rectangle with sides parallel to the coor- dinate axes, the double integal can be inter- preted as the iterated integral integraldisplay 3 − 3 parenleftbiggintegraldisplay 1 xy 2 x 2 + 3 dx parenrightbigg dy ....
View Full Document

This note was uploaded on 04/13/2010 for the course M 408L taught by Professor Radin during the Spring '08 term at University of Texas.

Page1 / 14

EXAM 2 Review-solutions - Van Ligten (hlv63) – EXAM 2...

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