Western University (Ontario)  Also known as University of Western Ontario
Introductory Calculus
MATH 0110A

Summer 2013
Mathematics 0110A
Test 2
Friday, November 13, 2009
Page 1
CODE 111
PART A  Multiple Choice (20 marks)
A1. [ 1
2
x
mark ] Find f (2) where f (x) = .
A: 32
B:
1
2
C: 0
D:
1
2
E: 1
2
4
= 2x1 , so f (x) = 2(x2 ) = 2x2 and f (x) = 2(2x3 ) = 4x3 = 3 .
x
x
4
1
Western University (Ontario)  Also known as University of Western Ontario
Introductory Calculus
MATH 0110A

Summer 2013
CHAPTER 1
EXERCISES 1.1, page 9
1. The statement is false because 3 is greater than 20. (See the number line that
follows).
2. The statement is true because 5 is equal to 5.
3. The statement is false because 2/3 [which is equal to (4/6)] is less than 5/6.
Western University (Ontario)  Also known as University of Western Ontario
Introductory Calculus
MATH 0110A

Summer 2013
CHAPTER 4
EXERCISES 4.1, page 209
1. a. C(x) is always increasing because as x, the number of units produced,
increases, the greater the amount of money that must be spent on production.
b. This occurs at x = 4, or a production level of 4000. You can see
Western University (Ontario)  Also known as University of Western Ontario
Introductory Calculus
MATH 0110A

Summer 2013
CHAPTER 3
EXERCISES 3.1, page 126
1.
4.
lim f ( x ) = 3.
lim f ( x ) = 2.
2.
x 2
lim f ( x ) = 3.
3.
x 1
x3
lim f ( x ) does not exist. If we consider any value of x to the right of x = 1, we
x 1
find that f(x) = 3. On the other hand, if we consider value
Western University (Ontario)  Also known as University of Western Ontario
Introductory Calculus
MATH 0110A

Summer 2013
CHAPTER 7
EXERCISES 7.1, page 350
1.
f is decreasing on (,0) and increasing on (0, ).
2.
f is decreasing on (,1), constant on (1,1), and increasing on (1,).
3.
f is increasing on (,1) (1,), and decreasing on (1,1).
4.
f is increasing on (,1) (1,) and decr
Western University (Ontario)  Also known as University of Western Ontario
Introductory Calculus
MATH 0110A

Summer 2013
1
Math 0110A Test 1, October 2011
Answers  Code 111
Part A
1.
A
6.
E
11. A
16. E
2.
7.
12.
17.
B
B
C
A
3.
8.
13.
18.
D
D
D
D
4.
9.
14.
19.
C
C
E
B
5.
10.
15.
20.
B
A
C
D
Part B
1
2
(b) 0
B2. (a) 3
(b) 2
B1. (a)
(c) No.
d) No.
B3. (a) f (x) = (2x + 3)(x3
Western University (Ontario)  Also known as University of Western Ontario
Introductory Calculus
MATH 0110A

Summer 2013
1
Math 0110A Test 2, November 2011
Answers  Code 111
Part A
1.
B
6.
C
11. C
16. B
2.
7.
12.
17.
C
D
B
D
3.
8.
13.
18.
D
C
C
D
4.
9.
14.
19.
A
C
C
B
5.
10.
15.
20.
A
D
D
D
Part B
B1. (a) f (x) = (6x + ex )(x3 x2 + ln x 1) + (3x2 + ex ) 3x2 2x +
(b) f (x)
Western University (Ontario)  Also known as University of Western Ontario
Introductory Calculus
MATH 0110A

Summer 2013
Mathematics 0110A
Test 1
Friday, October 16, 2009
Page 1
CODE 111
PART A  Multiple Choice (20 marks)
In the questions in Part A, if the quantity you are asked to nd is not dened or does not
exist, select DNE.
A1. [ 1
mark ] If f (x) =
A: 2
x2 + 1
nd f (3