University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30
Winter 2012
Assignment #1
You are expected to work on this assignment prior to your tutorial in the week of
January 16, 2012. You may ask questions about this as

A30
FINAL EXAM
1. ( 20 points)
Sketch the graph of a) f (x) = x " arctan x . b) y = x 2 + 4 x
Carefully indicate domain, symmetry, points of X and Y intercepts, asymptotes,
critical points, points of inflection, concavity.
2. ( 6 points)
!
!
3. (8 points)

nﬂ'
FINAL EXAM REVIEW (part 111)
Section 5.2 The Deﬁnite Integral
This section deﬁnes the deﬁnite integral as a limitof sums like those discussed in
the previous section. Some properties of deﬁnite integrals (such as the integral of
the sum of two funct

FINAL EXAM REVIEW (part 1)
Section 2.5 Continuity
/
Suppose you could draw a graph of a function Without lifting your pencil as you
move from one end of an interval domain to the other; we would say that the
function is “continuous”——meaning that the grap

FINAL EXAM REVIEW (part II)
Section 4.1 Maximum and Minimum Values
Concepts to Master
Absolute maxima, minima, and extrema; the Extreme Value Theorem
Relative (or local) maxima, minima, and extrema
Critical Numbers; Fermat’s Theorem about local extrema‘

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MATA30: Calculus I - Midterm Test
Examiner: Sophie Chrysostomou
Date: Friday, November 25th, 2011
Duration: 110 minutes
DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED TO DO SO.
FA

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MATA30: Calculus I - Midterm Test
Examiners: Sophie Chrysostomou
Date: Wednesday, October 31, 2012
Duration: 110 minutes
DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED TO DO SO.
F

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MATA30: Calculus I - Solution Midterm Test
1. Let f (x) = 2ex + 3.
(a) [ 2 marks] Find the domain and range of f .
solution : Since ex is dened for all x R, then the domain o

University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MATA30: Calculus I - Solution Midterm Test
1. (a) [ 2 marks] Give the denition of the absolute value function f (x) = |x|.
solution :
x if x 0
f (x) = |x| =
.
x if x < 0
(b)

Quiz 8 (on Assignment 9)
TUT0001
Name: _
Student #: _
Marks: _/10
1. Express the integral as a limit of Riemann sum. Do not evaluate the limit.
[3 Marks]
6
xdx
1 x
2
2
2. Use Part I of Fundamental Theorem of Calculus to find the derivative of the functio

University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30
Assignment # 2
You are expected to work on this assignment prior to your tutorial in the week of
January 23, 2012. You may ask questions about this assignment in

University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30
Assignment #11
You are expected to work on this assignment prior to your tutorial in the week of
April 1, 2012. You may ask questions about this assignment in th

MATA30(TUT1)
Last Name:_ First Name:_
Student#:_
1. Is the function
one-to-one? Justify your answer.
2. Find a formula for the inverse of the function
3. a) Find the exact value of
b) Express as a single logarithm:
)
+ 8, where a,b and c are positive
cons

Quiz 9 (on Assignment 10)
Name: _
Student #: _
Marks: _/10
1. [2.5 Marks] Find the area between two curves.
y = x2
y = x,
2. [2.5 Marks] Evaluate the given integral using integration by parts.
2
! (ln x) dx
3. [2.5 Marks] Evaluate the integral.
5
" cos x

MATA30(TUT1)
Quiz 5 (Based on Assignment 5)
Last Name:_ First Name:_
Student#:_
1. [2] Use the definition of derivative to find the derivative the function
2. Without using the definition of derivative, differentiate the following function
a)[1]
b)[2]
c)[

University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30
2012
Assignment #9
You are expected to work on this assignment prior to your tutorial in the week of
March 19th, 2012. You may ask questions about this assignmen

University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30
2012
Assignment #10
You are expected to work on this assignment prior to your tutorial in the week of
March 26, 2012. You may ask questions about this assignment

University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30
2012
Assignment #7
You are expected to work on this assignment prior to your tutorial in the week of
March 5, 2012. You may ask questions about this assignment i

University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30
2012
Assignment #5
You are expected to work on this assignment prior to your tutorial in the week of
February 13, 2012. You may ask questions about this assignme

University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30
2012
Assignment #3
You are expected to work on this assignment prior to your tutorial in the week of
January 30, 2012. You may ask questions about this assignmen

University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30
2012
Assignment #6
You are expected to work on this assignment prior to your tutorial in the week of
February 27, 2012. You may ask questions about this assignme

A30 Final Exam
1. ( 5 points) Use logarithmic differentiation to find the derivative of the
x2 +1
function y = 5 2
x "1
$ x
1 '
2. ( 5points) Find the limit lim&
#
)
+
x "1 % x #1
ln x (
!
3. (10 points)
2