6. L'H^pital's Rule o Everyone knows that 0/1 = 0. What do we mean when we say that 1/0 = or x is infinite or does not exist. We can't actually - , or "does not exist"? e.g., lim x1 x - 1 divide by zero; we mean something like the example above, that is,
5.
ABSOLUTE EXTREMA Definition, Existence & Calculation We assume that the definition of function is known and proceed to define "absolute mini-
mum". We also assume that the student is familiar with the terms "domain" and "range" of a function. Definitio
4. An Inventory Model In this section we shall construct a simple quantitative model to describe the cost of maintaining an inventory. Suppose you must meet an annual demand of V units of a certain product for which the rate of demand is constant througho
3. Profit Under a Monopoly Under a monopoly a producer has full control over how many units of a product will reach market. Since market demand and selling price are related by a demand relation, the monopolist can also control the price at which the comm
2. Bond Prices A bond is a security which offers semi-annual* interest payments, at a rate r , for a fixed period of time, followed by a return of capital. Suppose you purchase a $1,000 utility bond, freshly issued, which offers 16% interest per annum, pa
1. Mortgages Mortage loans are commonly quoted with a nominal rate compounded semi-annually; but the payments are monthly. To find the monthly payments in this case one finds the effective monthly rate of interest. Let r be the nominal rate compounded sem
FACULTY OF ARTS AND SCIENCE
University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2010
MAT 133Y1Y
Calculus and Linear Algebra for Commerce
PART A.
MULTIPLE CHOICE
1. [3 marks]
In any solution of the system
w 2x + 2y z = 8
2w 4x + 3y z = 13
we must have w =
FACULTY OF ARTS AND SCIENCE University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2009 MAT 133Y1Y
Calculus and Linear Algebra for Commerce
PART A.
MULTIPLE CHOICE
1. [3 marks] x If y is the solution of the system z x x then x =
A B C D E
+
y 2y
+ + -
3z z 3
FACULTY OF ARTS AND SCIENCE University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2008 MAT 133Y1Y
Calculus and Linear Algebra for Commerce
PART A.
1. [3 marks] The system
MULTIPLE CHOICE
x - 2y -x + 2y 2x - 4y has
A B C D E
- z + 5z - 6z
= 1 = -1 = 2
a uniq
FACULTY OF ARTS AND SCIENCE University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2007 MAT 133Y1Y
Calculus and Linear Algebra for Commerce
PART A.
1. [3 marks] The system of equations x + y y + +
MULTIPLE CHOICE
z z z
+ + +
u 2u u
+ +
v 2v
= = =
1 2 3
has
A
FACULTY OF ARTS AND SCIENCE University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2006 MAT 133Y1Y
Calculus and Linear Algebra for Commerce
PART A.
1. [3 marks]
MULTIPLE CHOICE
The derivative of x3 x2 + 1 is:
A
B C
D
3x2 2x x2 + 1 3x2 2x 1 3x2 x2 + 1 + x3 2
PG "
7 v v 7 0 4 A tgR 0 tG
F `'% d9yV
5 P P P P
81 q GEC3RRIqVGGcGPzIqqGs7PP7GGC@8 Pqz9 F D B A1 6 A D A 41 B 0 0 0 8 1 0 AF 4 8 0 D D 0 0 1 4 8 1 B 0 0 1 4 8 01 B F D 4 A 6 0 D D 0 0 0 A1 0 F D 4 1 6 A 4 6 4 P3GqqGC@zV(G R9cPPGqqGhGhR3cPD hP zG 7IP
FACULTY OF ARTS AND SCIENCE University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2004 MAT 133Y1Y
Calculus and Linear Algebra for Commerce
PART A.
MULTIPLE CHOICE
1. [3 marks] If f (x) = A. B. C. D. E. 0 1
10
(x2 + e2x )3 e-2x , then f (0) = (1 + x - x2 )2/
FACULTY OF ARTS AND SCIENCE University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2003 MAT 133Y1Y
Calculus and Linear Algebra for Commerce
PART A.
1. [3 marks]
MULTIPLE CHOICE
A $100,000 mortgage is to be repaid over 10 years by equal monthly payments made
FACULTY OF ARTS AND SCIENCE University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2002 MAT 133Y1Y
Calculus and Linear Algebra for Commerce
PART A.
1. [3 marks]
x-8- A B C
MULTIPLE CHOICE
lim
equals 1 equals 0 equals
x+8 |64 - x2 |
1 16
D E
1 16 does not exi
FACULTY OF ARTS AND SCIENCE University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2001 MAT 133Y1Y
Calculus and Linear Algebra for Commerce
PART A.
1. [3 marks]
MULTIPLE CHOICE
If Mr. Smith borrows $5000 from Ms. Jones and repays the loan 125 days later by g