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Midterm

Test1 - 2011.pdf

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Department
Mathematics
Course
MAT137Y1
Professor
Anthony Lam
Semester
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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