Below are some of the major topics
covered in MATH 253.
1. Powerful integrating techniques including
A. By parts
B. Special Powers
C. Trigonometric substitutions
D. Quadratics
E. Partial fractions
F.
MATH 253, Fall 2013: Midterm
NAME:
Answer all of the following questions to the best of your ability. Full credit requires that all
work is shown clearly.
1.
(13) For each of the following statements,
Each problem should be solved without the use of a calculator!
1. Graph and find the area between the curves 2 y = 4 x and 2y = x .
2. Simplify the expression ( )
f( ) n
f n +1 for each function.
a) (
HOMEWORK ASSIGNMENT #1, Math 253
1. Sketch the curve r = 1 + cos , 0 2, and nd the area it encloses.
2. Find the dot product a b in the following cases:
(a) a =< 1, 0, 2 >, b =< 2, 0, 1 > . Are these
HOMEWORK ASSIGNMENT #2, Math 253
1. Find the equation of a sphere if one of its diameters has end points (1, 0, 5) and
(5, 4, 7).
2. Find vector, parametric, and symmetric equations of the following l
The University of British Columbia
MATH 253
Midterm 1
10 October 2012
Time: 50 minutes
FIRST NAME:
LAST NAME :
STUDENT #:
This Examination paper consists of 6 pages (including this one). Make sure you
COURSE OUTLINE
MATH 253 Section 103, Term 1 of 2005-06
Instructor: Denis Sjerve
Office: 107 Math Building. Office Hours: MW 1:00 to 2:30, or by appointment.
Office Phone: (604) 822-2714 Email: [email protected]
HOMEWORK ASSIGNMENT 3, Math 253
1. Calculate the following limits, or discuss why they do not exist:
y
(a) lim 2
(x,y)0 x + y 2
y3
(b) lim 2
[hint: |y 2| |x2 + y 2|]
(x,y)0 x + y 2
2. For each of the
HOMEWORK ASSIGNMENT #4, MATH 253
1. Prove that the following dierential equations are satised by the given functions:
2u 2u 2u
(a)
+ 2 + 2 = 0, where u = (x2 + y 2 + z 2 )1/2 .
2
x
y
z
w
w
w
(b) x
+y
Department of Mathematics
MATHS 253: Advancing Mathematics 3
Study Guide: Semester 1, 2013.
Welcome to MATHS 253, which is the standard sequel to MATHS 250, available
in semesters 1 and 2 on the City
This document includes three practice questions/examples
for Quiz 3/ midterm (to be held Nov. 8,
Oct
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2016, in-class).
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Full
of questions for midterm 2 (from Montgomery 8th ed.):