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Mathematics

MAT137Y1

Anthony Lam

Fall

Description

Code:2876
DEPARTMENT OF MATHEMATICS
University of Toronto
MAT 135 H1F
Term-Test
Monday, October 24, 2011
Time allowed: 90 minutes
Please PRINTin INK or BALL-POINT PEN:
(Please PRINTull name and UNDERLINE surname):
NAME OF STUDENT:
STUDENT NO.:
SIGNATURE OF STUDENT:
TUTORIAL CODE(e.g.,M4A, R5D, etc.):
TUTORIAL TIME(e.g.,T4,R5,F3, etc.):
NAME OF YOUR TA:
NOTE: Before you start, check that this test has 13 pages. There are NO blank pages. This test has two
parts:
PART A [50 marks]: 10 multiple choice questions
PART B [50 marks]: 7 written questions
Answers to both PART A and PART B are to be given in this booklet. No computer
cards will be used. No aids allowed. No calculators!
DO NOT TEAR OUT ANY PAGES
FOR MARKERS ONLY
QUESTION MARK
PART A /50
B1 /7
B2 /8
B3 /8
B4 /6
B5 /6
B6 /7
B7 /8
Total /100
Page 1 of 13 Code:2876
PART A [50 marks]
Please read carefully:
PART A consists of 10 multiple-choice questions, each of which has exactly one correct answer. Indicate
your answer to each question by completely ▯lling in the appropriate circle with a dark pencil.
MARKING SCHEME: 5 marks for a correct answer, 0 for no answer or a wrong answer. You are
not required to justify your answers in PART A. Note that for PART A, only your ▯nal answers (as
indicated by the circles you darken) count; your computations and answers indicated elsewhere
will NOT count.
DO NOT TEAR OUT ANY PAGES
x ▯ 1
1. Find the value of lix!1 p x ▯ 1.
OA 1
OB 2
OC 3
OD 4
OE 5
x + x ▯ 12
2. Find the value of lim 2 .
x!3 x ▯ x ▯ 6
OA 1
OB 0
OC 3
4
7
OD 5
OE Does not exist.
Page 2 of 13 Code:2876
sin(2x)
3. Find the value of lim ▯ 4.
x!0 4x ▯ 3x
1
OA 2
2
OB ▯ 3
OC 0
OD +1
OE ▯1
4. Let f(x) = 5x ▯x +2: Find the horizontal asymptote for the graph of f.
3+x▯4x3
5
OA the line y = 3
1
OB the line y = ▯ 2
5
OC the line y = ▯ 4
2
OD the line y = 3
OE f has no horizontal asymptotes at all.
Page 3 of 13 Code:2876
5. Let 8 2
< 2x ▯ 1 if x < 2
f(x) = a if x = 2
: 3
x ▯ 2bx if x > 2
(where a and b are constants).
If f is continuous everywhere, ▯nd the value of the product ab.
3
OA 4
OB 7
5
OC 5
4
7
OD 4
7
OE 3
6. The line perpendicular to the curve y = x ▯3x+5 at the point (1;3) will intersect
the y-axis at the point
OA (0;0)
OB (0;2)
C
O (0;5)
OD (0;3)
OE (0;1)
Page 4 of 13 Code:2876
7. Let f(x) = ax + bx + c, where a;b and c are constants. Suppose that t

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