MATH 230 Final: Final winter 2014 solutions
15 Feb 2019
School
Department
Course
Professor
Northwestern University NetID:
Math 230 Final Exam Solutions
Winter Quarter 2014
March 17, 2014
Instructions:
•Read each problem carefully.
•Write legibly.
•Show all your work on these sheets.
•Make sure that your final answer is clearly indicated. If two answers are
presented, the average of the points for each answer will be given.
•This exam has 16 pages and 9 problems. Before starting the exam, please
check that your copy contains all of them and obtain a new copy of the exam
immediately if it does not.
•You may not use books, notes, or calculators.
Good luck!
(2 points)
Mark your section and write your NetID in
the upper right corner of this page. Do NOT
write your name on this exam.
Sec. # Time Instructor
21 8:00 Zhu
31 9:00 Zhu
41 10:00 Broderick
51 11:00 Xia
61 12:00 Chau
63 12:00 Yang
71 1:00 Yang
81 2:00 Kahouadji
Prob. Points Score
possible
0 2
1 36
2 15
3 15
4 12
5 27
6 15
7 18
8 35
9 25
TOTAL 200
Math 230 Final Exam Solutions Winter Quarter 2014 Page 2 of 16
Question 1 (36 points, 3 points each).
PART A True or False? Circle the correct answer.
(a) The line x= 3 + 2t, y = 4 −t, z = 1 + 3tintersects the y-axis.
False
(b) The function f(x, y) = px2+y2is continuous on the entire xy-plane.
True
(c) Let g(x, y, z)be a continuous function of three variables. The level
surface g= 1 must not intersect the level surface g= 2.
True
(d) If z=h(x+y)for some differentiable function h(u), then ∂z
∂x and ∂z
∂y
must be equal for all values of xand y.
True
Math 230 Final Exam Solutions Winter Quarter 2014 Page 3 of 16
(e) Every ellipse has constant curvature.
False
(f) The point (x, y, z) = (√3,3,6) lies on the surface described in spherical
coordinates by φ=π/3.
False
(g) Let i,j, and kbe the unit vectors along the three-dimensional rectangu-
lar coordinate axes. The vectors iand ksatisfy (i×i)×k=i×(i×k).
False
(h) A curve represented by a vector-valued function r(t)lies entirely on a
surface. If r(0) = h1,2,3i, then the tangent vector r′(0) can be taken
as a normal vector for the tangent plane to the surface at (1,2,3).
False
Document Summary
Instructions: read each problem carefully, write legibly, show all your work on these sheets, make sure that your nal answer is clearly indicated. presented, the average of the points for each answer will be given. If two answers are: this exam has 16 pages and 9 problems. Before starting the exam, please check that your copy contains all of them and obtain a new copy of the exam immediately if it does not: you may not use books, notes, or calculators. Mark your section and write your netid in the upper right corner of this page. Do not write your name on this exam. Circle the correct answer. (a) the line x = 3 + 2t, y = 4 t, z = 1 + 3t intersects the y-axis. False (b) the function f (x, y) =px2 + y2 is continuous on the entire xy-plane. True (c) let g(x, y, z) be a continuous function of three variables.
