{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

23 Sample Exam 2 - MATH 23 Sample Second Exam was April...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 23 Sample Second Exam was: April, 2003 NAME : Section (Last, First) 1. (10 points ) Sketch the level curves corresponding to the values -1, 0 and 2 for the function f ( x, y ) = y - 4 x 2 . 2. (10 points ) Let f ( x, y ) = ye xy . Find each of the following. (a) ∂f ∂x (b) ∂f ∂y (c) ∂f ∂y (0 , 2) 3. (10 points ) Find an equation of the tangent plane to the surface z = x 2 - 3 y 2 at the point ( - 3 , 2 , - 3) . 4. (15 points ) Let f be the function f ( x, y ) = cos(2 xy ) . (a) Find the directional derivative of f at the point (2 , π 8 ) in the direction of the vector a = < - 1 , 3 > = - i + 3 j. (b) Find the maximal rate of change of f at the point (2 , π 8 ) and the direction in which it occurs. 5. (15 points ) The function h ( x, y ) = xy - x 2 - y 2 + 3 y + 1 has only one critical point. Find the critical point and determine whether h has a local maximum, local minimum or saddle point. Give the value. 6. (10 points ) Use six squares with width 1 to find the estimate for the volume of the solid over the rectangle 0 x 3 , 0 y 2 that has height x 2 + y 2 at the point P ( x, y ) ,
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern