Solutions to Supplementary Questions for HP Chapter 12
1. 1)
2)
d
8
dx (x
d2
(x8
dx2
x8
x
ln x) = 8x7 ln x +
ln x) =
d
(8x7
dx
6
= 8x7 ln x + x7
ln x + x7 ) = 8 7x6 ln x +
8x7
x
+ 7x6
= 8 7x6 ln x + 8x + 7x6
Now note that the power of x in all terms are t
Solutions to Supplementary Questions for HP Chapter 11
1. The curve has derivative 3x2 . Let (x0 , x3 ) be any point on the curve. Then the tangent
0
2
line at this point has slope 3x0 , so if (1, 0) is on this line, then the line has equation
y = 3x2 (x
Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2
of the Supplementary Material
1. (a) Let P be the recommended retail price of the toy. Then the retailer may purchase
the toy at prices of 0.7P and 0.75P by cash and credit respect
Solutions to Supplementary Questions for HP Chapter 6
1. We have
1
2
3
4
ab
b+c
3d + c
2a 4d
=8
=1
=7
=6
Adding 1 and 2 , we get: 5 a + c = 9. By taking 5 3 , we get 6 a 3d = 2.
Now, 4 [2 6 ] gives us 7 2d = 2, or d = 1. Substituting back into 4 , we get
Department of Mathematics
University of Toronto
Tuesday, October 29, 2013, 6:108:00 PM
MAT 133Y TERM TEST #1
Calculus and Linear Algebra for Commerce
Duration: 1 hour 50 minutes
at
Aids Allowed: A nongraphing calculator, with empty memory, to be suppl
Math 133
Summer 2016
Instructor
Name
E-mail
Office
Office Hours
First Half
Craig Sinnamon
craig.sinnamon@utoronto.ca
HU 1029
None
Second Half
Charles Tsang
ck.tsang@utoronto.ca
BA 7256
TR: 21:00 22:00
Teaching Assistants.
Dmitri Chouchkov
dmitri.chouchkov
Supplementary Questions for HP Chapter 12
1. Find
d9 8
(x ln x).
dx9
2. Find
d
[ln(ln(ln(ln x)].
dx
3. Find
a
x
d (aa )
(x
+ a(x ) + a(a ) ) where a is a constant.
dx
4. (a) Let f (x) be a function such that f (x + z ) = f (x)f (z ) for all x and z , and
FACULTY OF ARTS AND SCIENCE
University of Toronto
FINAL EXAMINATIONS, APRIL 2011
MAT 133Y1Y
Calculus and Linear Algebra for Commerce
Duration: 3 hours
Examiners: A. Igelfeld
P. Kergin
J. Tate
O. Yacobi
LEAVE
Question
FAMILY NAME:
BLANK
Mark
MC/45
GIVEN NA
FACULTY OF ARTS AND SCIENCE
University of Toronto
FINAL EXAMINATIONS, APRIL 2013
MAT 133Y1Y
Calculus and Linear Algebra for Commerce
Duration:
3 hours
Examiners: A. Igelfeld
P. Kergin
J. Tate
P. Walls
LEAVE BLANK
Question
Mark
MC
/45
B1
/11
B2
/11
B3
/10
FACULTY OF ARTS AND SCIENCE
University of Toronto
FINAL EXAMINATIONS, APRIL/MAY 2014
MAT 133Y1Y
Calculus and Linear Algebra for Commerce
Duration:
3 hours
Examiners: A. Igelfeld
P. Kergin
L. Shorser
J. Tate
LEAVE BLANK
Question
Mark
MC/45
FAMILY NAME:
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FACULTY OF ARTS AND SCIENCE
University of Toronto
FINAL EXAMINATIONS, APRIL 2012
MAT 133Y1Y
Calculus and Linear Algebra for Commerce
Duration:
3 hours
Examiners: N. Francetic
A. Igelfeld
P. Kergin
J. Tate
LEAVE BLANK
Question
Mark
MC
/10
B4
/10
B5
SIGNATU
1. Accident Prevention, Rescue Response, Public Relations, and Administrations.
2. To the public, fellow lifeguards, employer and ones self.
3. - Deep, shallow, slope, and drop-off areas
- entry and exits points
- structures and equipment
- condition of t
Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the
Supplementary Material
1. The manufacturer of a certain toy sells to retailers on either of the following terms:
(i) Cash payment: 30% below recommended retail price
(ii) Six months cred
Supplementary Questions for HP Chapter 11
1. nd the two straight lines through the point (1, 0) that are tangent lines to the curve
y = x3 .
2. The normal line to a curve at a point on the curve is the straight line which passes
through that point and is
Supplementary Questions for HP Chapter 6
1. Solve the following matrix equation for a, b, c and d:
ab
3d + c
b+c
81
=
2a 4d
76
2. Two-Commodity Market Model
Consider a model in which only two commodities are related to each other.
For i equal to 1 or 2, l