Practice exams
Errata: (corrected)
 October 29, 2009 4 PM, Exam 5: there are some problems which involve parametrization. While you should still
remember what a parametrized surface is for later parts of the course, this is not subject of this midterm.
Thanks to Christine Shrock for pointing this out.
 October 29, 2009, 9 PM, Exam 1: Problem TF 14, minimum should have been replaced by maximum in the explanation.
Thanks to Christina Guo for pointing this out!
 October 31, 2009, 9 AM, Exam 1: Problem 10, The formulas do not quite fit with the story. Without changing the
math, the story has been changed. Thanks to Phillip Yao for noticing this.
 October 31, 2009, 5 PM, Exam 1: problem 5: root(2), not root(3).
problem 6)a) the components of nabla(x,y,z) should be divided by 2. Thanks to Carl Daher for
these corrections. Nevin Raj for noticed the first mistake too.
Nolan Pollock corrected of the correction.
 October 31, 2009, 11 PM, Exam 3: TF 13, typo on solution. Should be "smaller" rather than larger.
Thanks to Christian Yoo.
 November 1, 2009, 9 AM, Exam 4: Problem 6: Typo in Lagrange equations: second equation 4x, not 4y.
Thanks to Insup Lee for pointing this out.
 November 1, 2009, 2 PM, Exam 2, TF 4: explanation not good. While it is true that the
directional derivative in the direction nabla f/nabla f is the length of the gradient, this
is irrelevant here. Thanks to Phillip Yao.
 November 1, 2009, 6 PM, Exam 2, Typo in TF 4 (the > then)
Thanks to Allen Shih.
 November 1, 2009, 9 PM, Exam 3, TF 20, x+y is a counter example, not xy. Thanks Phillip Gao.
for this correction.
 November 2, 2009, 8 AM, Exam 5, Problem 8, gradient at (1,0) not (1,1) and <3,0> instead of <2,0>.
End result not affected. Thanks to Sarvagna Patel.
 November 2, 2009, 5 PM, Exam 1, TF 15, f(x,y) should be f(x,y,z), thanks to Sam Himel.
 November 3, 2009, 3 PM, Exam 2, TF 4, answer key: directional derivative 1 not 1. Thanks to Eric Liao.
 November 3, 2009, 5 PM, Exam 3, r(0)=(0,0) not r(0,0)=0. Thanks to Christian Yoo.
