Quiz 1
Math 126 E. 07/05/2011
Problem 1. [10 points] Find the plane that passes through the point P = (1, 0, 0) and the line
x = t, y = t, z = t 1.
Solution. We already have a point P on this plane; let us nd a normal vector n. To nd it,
let us nd the two
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Student Number:
Quiz 1
Math 126 E. 07/05/2011
Problem 1. [10 points] Find the plane that passes through the point P = (1, 0, 0) and the line
x = t, y = t, z = t 1.
Problem 2. [10 points] Consider the following three points:
A = (0, 0, 0), B = (2, 0,
Math 126 E
Quiz 2. 07/26/2011
Problem 1. [10 points] Find and classify all critical points of the function
f (x, y ) = 2x2 3xy + 2y 2 .
Solution. First, let us nd all critical points. Let us solve the system of two equations
fx = fy = 0. Since
fx = 4x 3y,
Math 126, Section C, Autumn 2012, Solutions to Midterm I
1. Answer the following question regarding the picture below
We know AC = 2, 6, 2, BD = 4, 0, 2 and A = (0, 2, 1).
(a) (4 points) Compute the two vectors u= AB = DC and v= AD = BC . From v+u= AC =<
Exam I Hints and Answers
Math 126 A & B Spring 2012
20
20
1. (a) (4 points) w = 3, 4, 2 or w = 3, 4, 2
29
29
1
(b) (4 points) = cos1
175
(c) (1 point) (3, 3 )
(d)
i. (1 point) circle
ii. (1 point) hyperbola
iii. (1 point) cone
2. x + 4y + z = 87
3. (a) (
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Student Number:
Math 126 E
Quiz 2. 07/26/2011
Problem 1. [10 points] Find and classify all critical points of the function
f (x, y ) = 2x2 3xy + 2y 2 .
Problem 2. [10 points] The n moles of any ideal gas obey the law
pV = nRT,
where R = 8.314JK 1 mo