{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2007Final

2007Final - blue MATH 32A FINAL EXAM LAST NAME FIRST NAME...

This preview shows pages 1–6. Sign up to view the full content.

blue MATH 32A FINAL EXAM December 13, 2007 LAST NAME FIRST NAME ID NO. Your TA: To receive credit, you must write your answer in the space provided . DO NOT WRITE BELOW THIS LINE 1 (20 pts) 4 (20 pts) 2 (20 pts) 5 (20 pts) 3 (20 pts) 6 (20 pts) TOTAL FOR WRITTEN PROBLEMS 1

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

View Full Document
2 PROBLEM 1 (20 Points) The temperature at position ( x, y, z ) in a room is f ( x, y, z ) = 18 + 2 z + xy o C A woman walks down a spiral staircase in the middle of the room. She holds a thermometer whose position at time t (seconds) is c ( t ) = ( cos t 3 , sin t 3 , 8 t 3 ) ( t in seconds). How fast is temperature reading on the thermometer changing at t = 6 π s.
3 PROBLEM 2 (20 Points) Find the maximum value of f ( x, y, z ) = xyz , subject to the constraint g ( x, y, z ) = 4 x 2 + y 2 + z 2 = 48

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

View Full Document
4 PROBLEM 3 (20 Points) Let f ( x, y ) = 2 xy 1 6 x 3 y 2 (A) Find the critical points of f ( x, y ). (B) Determine the nature of the critical points (min, max or saddle).
5 PROBLEM 4 (20 Points) The plane x + y 2 + z 3 = 1 intersects the x , y , and z axes in points P , Q , and R .

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