Math 202 Assignment #1 Solutions Spring 20181
Thomas 12.1-12.5, 14.1, 14.2
1. (Thomas 12.1) Describe the set of points in R3 that satisfy (x 1)2 + (y
1)2 + z 2 4. Use Julia to plot this set, include
Math 202 Assignment #1 - Spring 2017
Due on Thursday January 26th at the beginning of lecture
Each question is out of 7 marks, making the assignment out of 35 total.
Never leave your answer or work wi
Math 202 Assignment #2 - Spring 2017
Due on Thursday February 23rd at the beginning of lecture
Each question is out of 7 marks, making the assignment out of 35 total.
Never leave your answer or work w
Math 202 Assignment #1 - Spring 2017
Due on Thursday January 26th at the beginning of lecture
Each question is out of 7 marks, making the assignment out of 35 total.
Never leave your answer as a decim
Math 202 A01
Tutorial 9
1. Consider the initial value problem
y0
2
+ tan(x)y = ex ln(x3 ),
y +
ln x
00
with y
4
= 2 and y
0
4
= 6.
Determine the largest interval x (a, b) where we can gaurentee ex
Math 202 A01
Tutorial 8
1. Determine whether the differential equation
(3x2 y + ey )dx + (x3 + xey 2y)dy = 0
is exact. If it is exact, solve it.
2. Recall the logistic equation dP
= kP (c P ), where c
'Name: g 0/ (_/L l (0V1 e StudentNumber:
Math 202 A01
Midterm 1
February 15th, 2016
Version 1
This exam contains 5 pages and 5 problems. Please check that you have a complete exam.
NO textbooks, notes
Math 202
Dr. Ibrahim
Fall, 2016
Math 202 Tutorial III
Solutions
A1
Lines intersect planes unless they are parallel, that means that the direction vector
of the line is perpendicular to the normal vect
Math 202
Dr. Ibrahim
Fall, 2016
Math 202 Tutorial II
Solutions
A1
(1) Calculating
i
a b = 3
1
the cross-products:
j
k
2 1 = h2, 4, 2i
0 1
and
i j
k
b a = 1 0 1 = h2, 4, 2i = a b
3 2 1
This can be ob
Math 202
Dr. Ibrahim
Fall, 2016
Math 202 Tutorial IV
Solutions
A1
f
x
f
y
1
= z ln(y)
ln(x)2
z2
1
=
,
ln(y)
y
2
1
,
x
f
z
=
2z ln(y)
.
ln(x)
f
x
= 2 ex ey ex = 2e2x 2exy ,
f
y
= 2 ex ey ey = 2exy
Tutorial # 8
Higher-Order Differential Equations
Nov. 17, 2017
Sections: 4.4 - 4.5
.
Q1. Given the following auxillary equations write down the corresponding differential equation it represents. Do no
Tutorial # 5
First-Order Differential Equations
Oct. 20, 2017
Sections: 1.1 - 1.2, 2.1 - 2.2
.
Q1. Let a, b, k and C be nonzero constants. Show that y = a + Cek(1b)x is a solution to
the differential
Tutorial # 6
First-Order Differential Equations
Oct. 27, 2017
Sections: 2.3 - 2.5
.
Q1. Find the solution to the following initial value problem
xy 0 = y + x2 ,
y(1) = 2
Q2. Determine whether the foll
Tutorial # 7
Higher-Order Differential Equations
Nov. 3, 2017
Sections: 3.1 - 3.2, 4.1 - 4.3
.
Q1. When a vertical beam of light passes through a transparent medium, the rate at which
its intensity I(
Tutorial # 2
Vectors and the Geometry of Space
Sept. 22, 2017
Sections: 12.4 - 12.5
.
Q1: Let a = 3i 2j + k, b = i k, c = 3j and d = 6i + 4j 2k.
(a) Compute a b and b a. How are they related? Does thi
Partial Derivatives
Tutorial # 4
Oct. 13, 2017
Sections: 14.3 - 14.5
.
Q1: The surface f (x, y) = x3 3xy 2 is commonly referred to as the monkey saddle surface
(due to the fact that it has three depre
Tutorial # 1
Vectors and the Geometry of Space
Sept. 15, 2017
Sections: 12.1 - 12.2
.
Q1. Describe the set of points in R3 that satisfy the following:
(a) y = x2 and z = 2.
(b) Now just y = x2
(c) Wha
Partial Derivatives
Tutorial # 3
Sept. 29, 2017
Sections: 12.5, 14.1 - 14.2
.
Q1: Let L be the line through Q(0, 0, 0) with direction v = h1, 4, 2i, and let P be the plane
with equation 2x + z = 5. Do
Math202: Homework # 5
Due: December 1, 2017
.
Homework is due at the start of the lecture on Friday, December 1.
Present your solutions neatly and will all mathematical details. Marks will be deduct
Math 202
Dr. Ibrahim
Fall, 2016
Math 202 Tutorial I
Solutions
Thomas Section 12.1-12.3. Friday, September 16, 2016.
A1
1. x2 + z 2 = 4 along with y = 0 represents a circle of radius 2 in the xzplane.
Math 202
Dr. Ibrahim
Fall, 2016
Math 202 Tutorial V
Thomas Section 14.5, 14.6. Friday, October 14, 2016.
A1
You are racing in a hang-glider, and your nemesis Madame Vole-Vite is way ahead of you. You
Math 202
Dr. Ibrahim
Fall, 2016
Math 202 Tutorial IV
Thomas Section 14.3-14.4. Friday, October 7, 2016.
A1
Compute the first order partial derivatives for f (x, y, z) = z 2 logx (y).
A2
Compute the se
Math 202 A01
Tutorial 3
1. Suppose elevation above sea level is described by
z = f (x, y) = 150 30x2 20y 2 .
(a) If you are standing at the point P (1, 2), which direction would you walk to experience
Math 202 A01
Tutorial 5
1. Find the extreme values of f (x, y) = 3x y + 6 subject to the constraint x2 + y 2 = 4.
2. Your firm has been asked to design a storage tank for liquid petroleum gas. The cus
Math 202 A01
Tutorial 4
1. Find all the local maxima, local minima, and saddle points of the function f (x, y) = x3 +
y 3 + 3x2 3y 2 8. Do the absolute extrema exist?
2. Find all the local maxima, loc
Name :
Student Number:
Solutions to Math 202 A01
Midterm 2
This exam contains 5 pages and 5 problems. Please check that you have a complete exam.
NO textbooks, notes, formula sheets or cell phones dur
Math 202 A01
Tutorial 2
1. Decompose the vector ~v = h5, 1, 3i into components v| and v , where
~v = v| + v and v| is parallel to w
~ = h 2, 2, 1i, and v is perpendicular to w.
~
2. Find an equation o
Math 202 A01
Tutorial 1
1. Let ~a = h0, 2, 0i and vector ~b = h0, 0, 3i.
(a) Draw ~a, ~b, ~a + ~b and ~a ~b.
(b) Is ~a perpendicular to ~b? Why?
(c) The points P (~a), Q(~b) and R(~a + ~b) form a tria