calc exam2_review

# calc exam2_review - MATH 2300 Calculus III Fall 2010...

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

MATH 2300 - Calculus III Exam 2 Review Fall 2010 NAME: ................................................................... Student ID: ......................................... In order to receive full credit, SHOW ALL YOUR WORK. 1. (6 pts) Indicate whether the following statements are true (T) or false (F). (Circle one) T F (a) integraldisplay 1 0 integraldisplay 1 x f ( x, y ) dydx = integraldisplay 1 x integraldisplay 1 0 f ( x, y ) dxdy . T F (b) The maximum rate of change of z = f ( x, y ) is given by |∇ f | . T F (c) integraldisplay 2 1 integraldisplay 4 3 xydydx = x integraldisplay 2 1 integraldisplay 4 3 ydydx . 2. (12 points) Find the local maxima, minima, and saddle points of z = f ( x, y ) = xy 2 + x 2 2 xy , using the Second Derivatives Test. 1

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

View Full Document
3. (10 points) If w = xy + yz + xz , x = s cos t , y = cos( st ) and z = t , use the multivariate chain rule to find ∂w ∂s when s = 1 and t = π . 4. (10 points) Sketch the region of integration and rewrite the double integral with the order of integration reversed: integraldisplay 4 0 integraldisplay x x/ 2 f ( x, y ) dy dx 5. (12 points) A hiker is walking on a mountain path when it begins to rain. If the surface of the mountain is modeled by z = 1 3 x 2 5 y 2 , (where x , y and z are in miles) and the rain begins when the hiker is at the

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.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern