# 233-ex2-short-bysubject - Solutions to old Exam 2 problems...

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Solutions to old Exam 2 problems Hi students! Check for updates on the web site and note that the exam will cover material through section 15.3 on changing the order of integration. There will be no problems on the following material on Exam 2: 1 Lagrange multipliers; 2 projectile problems and related velocity, length and acceleration problems of particles or of curves. Problems on the above 2 topics will probably appear on the final exam. Enjoy!! Best, Bill Meeks PS. There are probably errors in the solutions presented here and for a few problems you need to complete them or simplify the answers; some questions are left to you the student. Also you might need to add more detailed explanations or justifications on the actual similar problems on your exam.
Problem 40 - Exam 1 Explain why the limit of f ( x , y ) = (3 x 2 y 2 ) / (2 x 4 + y 4 ) does not exist as ( x , y ) approaches (0 , 0).
Problem 40 - Exam 1 Explain why the limit of f ( x , y ) = (3 x 2 y 2 ) / (2 x 4 + y 4 ) does not exist as ( x , y ) approaches (0 , 0).
Problem 26(a) - Exam 1 - Fall 2006 Let g ( x , y ) = ye x . Estimate g (0 . 1 , 1 . 9) using the linear approximation L ( x , y ) of g ( x , y ) at ( x , y ) = (0 , 2).
Problem 26(a) - Exam 1 - Fall 2006 Let g ( x , y ) = ye x . Estimate g (0 . 1 , 1 . 9) using the linear approximation L ( x , y ) of g ( x , y ) at ( x , y ) = (0 , 2).
Problem 36 - Exam 1 Find an equation for the tangent plane to the graph of f ( x , y ) = y ln x at (1 , 4 , 0).
Problem 36 - Exam 1 Find an equation for the tangent plane to the graph of f ( x , y ) = y ln x at (1 , 4 , 0).
Problem 42(a) - Exam 1 Find all of the first order and second order partial derivatives of the function f ( x , y ) = x 3 - xy 2 + y .
Problem 42(a) - Exam 1 Find all of the first order and second order partial derivatives of the function f ( x , y ) = x 3 - xy 2 + y .
Problem 1 - Exam 2 - Fall 2008