Math 200 Problem Set III
1) A projectile falling under the inuence of gravity and slowed by air resistance proportional to
its speed has position satisfying
d2 r
dt2
= g k dr
dt
where is a positive constant. If r = r0 and
u(t) =
et dr (t)
dt
and substitut
Math 200 Problem Set IV
1) Show that the function z (x, y ) =
x+y
xy
obeys
z
z
x x + y y = 0
2) Let f be any dierentiable function of one variable. Dene z (x, y ) = f (x2 + y 2 ). Is
the equation
z
z
y x x y = 0
necessarily satised?
3) Four positive numbe
Math 200 Problem Set I
1) Find the equation of a sphere if one of its diameters has end points (2, 1, 4) and
(4, 3, 10).
2) Determine whether the given points are collinear (that is, lie on a common straight
line).
a) (1, 2, 3), (0, 3, 7), (3, 5, 11)
b) (
Math 200 Problem Set II
1) Find the equation of the sphere which has the two planes x + y + z = 3, x + y + z = 9
as tangent planes if the centre of the sphere is on the planes 2x y = 0, 3x z = 0.
2) Find the equation of the plane that passes through the p
December 20, 2005 MATH 200 Name Marks [10] 1.
Page 2 of 10 pages
One side of a right triangle is measured to be 3 with a maximum possible error of 0.1, and the other side is measured to be 4 with a maximum possible error of 0.2. Use the dierential or line
Math 200 - Final Exam - April 24th, 2008 Duration: 150 minutes Name: (1) (2) (3) (4) (5) (6) Student Number:
Do not open this test until instructed to do so! Please place your student ID (or another picture ID) on the desk. This exam should have 4 pages,
The University of British Columbia Final Examination - April 26, 2005 Mathematics 200 Instructors: Jim Bryan and Joseph Lo Closed book examination Time: 2.5 hours
Name Student Number
Signature
Special Instructions: - Be sure that this examination has 15 p
The University of British Columbia Final Examination - April 2007 Mathematics 200 Calculus III Closed book examination 9 A.M. Section 201 - Dale Peterson Last Name: Student Number: Section Number: Special Instructions: No books, notes, or calculators are
April 11, 2006 Marks [15] 1.
MATH 200
Name
Page 2 of 9 pages
If two resistors of resistance R1 and R2 are wired in parallel, then the resulting 1 1 1 resistance R satises the equation = + . Use the linear or dierential R R1 R2 approximation to estimate th
Math 200, Final Exam
December 2008 No calculators or notes of any kind are allowed. Time: 2.5 hours. 1. [11] A surface is given by z = x2 2xy + y 2 . (a) Find the equation of the tangent plane to the surface at x = a, y = 2a. (b) For what value of a is th
The University of British Columbia Final Examination - April 17, 2009 Mathematics 200 Instructors: Dr. Keqin Liu (Sec. 201) and Dr. Dale Peterson (Sec. 202) Closed book examination Last Name: Student Number Special Instructions: No books, notes or calcula
MATHEMATICS 200 December 2003 Final Exam Solutions
1) Consider a point P (5, 10, 2) and the triangle with vertices A(0, 1, 1), B (1, 0, 1) and C (1, 3, 0).
a) Compute the area of the triangle ABC .
b) Find the distance from the point P to the plane contai
The University of British Columbia
Final Examination - April 16, 2011
Mathematics 200
Closed book examination
Last Name:
Time: 2.5 hours
, First:
Signature
Student Number
Special Instructions:
- No books, notes or calculators are allowed.
Rules governing
The University of British Columbia
Final Examination - December 10, 2012
Mathematics 200
All Sections
Closed book examination
Last Name:
Time: 2.5 hours
, First:
Signature
Student Number
Special Instructions:
No books, notes or calculators are allowed.
Ru
The University of British Columbia
Final Examination - December, 2010
Mathematics 200
1. Let = ( ) = 222 .
+
(a) Sketch the level curves of ( )
(b) Find the tangent plane and normal line to the surface = ( ) at ( ) = (1 2).
(c) Find an approximate value f