MATH 2450, QUIZ 7 (solutions), 11 JUNE, 2012
Refer to the function f (x, y) = x3 3x + y 3 3y in answering the following.
(1) Find all four critical points of f , and classify each as local maximum, lo
MATH 2450, EXAM 3, 01 JULY (solutions), 2011
(Each of the following ve problems is worth 12 points, with parts of problems weighted
equally. Be sure to show all work ; and, when in doubt, draw a pictu
MATH 2450, QUIZ 11 (solutions), 25 JUNE, 2012
(1) Find a potential (=primitive) function z = f (x, y) for the path-independent
vector eld F (x, y) = (x y) + (y 2 x). Use this function to evaluate
r
F
MATH 2450, QUIZ 1 (solutions), 23 MAY, 2012
(1) Find an equation for the sphere, centered at the point 1, 2, 3 and tangent to
the xz-plane.
(x 1)2 + (y 2)2 + (z + 3)2 = 4
(2) There is just one level c
MATH 2450, QUIZ 5 (solutions), 06 JUNE, 2011
Suppose z = xy, where x = u cos v and y = uv.
(1) Calculate z/v by rst eliminating the intermediate variables, and then calculating partial derivatives in
MATH 2450, QUIZ 3 (solutions), 29 MAY, 2012
(1) (a) (2 points) If = 3 and = + 5, nd 2 + 4 .
u
v
u
v
2 + 4 = 2(3 ) + 4( + 5) = 6 2 4 + 20 = 2 + 18.
u v
(b) (3 points) Find all vectors in the plan
MATH 2450, EXAM 2 (solutions), 17 JUNE, 2011
(Each of the following six problems is worth 10 points, with parts of problems weighted
equally. Be sure to show all work; and, when in doubt, DRAW A PICTU
MATH 2450, EXAM 2 (solutions), 15 JUNE, 2012
(Each of the following ten questions is worth 6 points. Be sure to show your work. And, when in doubt,
draw a picture.)
(1) Find the second-order Taylor po
MATH 2450, EXAM 1 (solutions), 01 JUNE, 2012
(Each of the following ten questions is worth 6 points. Be sure to show your work. And, when in doubt,
draw a picture.)
(1) Describe precisely the domain o
MATH 2450, QUIZ 9 (solutions), 19 JUNE, 2012
(1) Find parametric equations for the straight line that contains the points 1, 5, 2
and 5, 0, 1.
One possible parallel vector is = (1 5) + (5 0) + (2 (1)
MATH 2450, EXAM 1 (solutions), 03 JUNE, 2011
(Each of the following six problems is worth 10 points, with parts of problems weighted
equally. Be sure to show all work; and, when in doubt, DRAW A PICTU