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Midterm

# Midterm 1 Oct 14th 2011

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School
Department
Mathematics
Course
Mathematics 0110A/B
Professor
Semester
Fall

Description
Mathematics 0110A CODE 111 Friday, October 14, 2011 Test 1 Page 1 PART A - Multiple Choice (20 marks) Circle your answer in each question below and mark it on the (scantron) answer sheet. Code as you go. Extra time will NOT be given for coding answers at the end of the exam. Be advised that ONLY THE SCANTRON CARD WILL BE MARKED IN THIS SECTION, but only this question paper will be returned to you. In the questions in Part A, if the quantity you are asked to ﬁnd is not deﬁned or does not exist, select DNE. Use the graph of y = f(x), provided below, to answer questions A1 to A5. 1 A1. Find the values of f(0) and f(2), in that order. mark A: 3 and −3 B: −3 and 3 C: 0 and −3 D: 0 and 0 E: 3 and 2 1 A2. Find lim f(x), if it exists. mark x→2+ A: −2 B: −3 C: 2 D: 0 E: DNE 1 A3. Find lim f(x), if it exists. mark x→−3− A: −2 B: −3 C: 0 D: 2 E: DNE 1 A4. Find lx→−3(x), if it exists. mark A: 0 B: −3 C: 2 D: −2 E: DNE 1 A5. Is f(x) continuous at x = −3? mark A: Yes B: No Mathematics 0110A CODE 111 Friday, October 14, 2011 Test 1 Page 2 x 1 A6. What is the domain of the function ? mark x(x + 2) A: All real numbers. B: All real numbers except 0. C: All real numbers except −2. D: All real numbers except 2. E: All real numbers except 0 and −2. Use the functions given below to answer questions A7 and A8. 2 f(x) = x + 1 and g(x) = x + x 1 A7. Find the function g − f. mark 2 2 2 A: x B: x − 1 C: x + 1 D: x + 1 E: x − 1 g mark A8. Find the function f, if it exists. 2 2 x x + x x + 1 x + x A: x + x B: x C: x D: x + 1 E: DNE Use the functions given below to answer questions A9 and A10. √ f(x) = x − 2 and g(x) = x 2+ 1 1 A9. Find the function f ◦ g. mark √ √ √ √ √ A: x − 2 B: x − 2 C: x − 1 D: x + 1 E: x + 2 1 A10. If h = f ◦ g, what is the value of h(1)? mark √ A: 0 B: 1 C: 2 D: 2 E: DNE x + 2x 1 A11. Evaluate lim , if it exists. mark x→0 x + 5 1 2 A: 0 B: 5 C: 2 D: 5 E: DNE x − 4 1 A12. Evaluate x→2 , if it exists. mark x − 2 A: 2 B: 3 C: 4 D: 5 E: DNE Mathematics 0110A CODE 111 Friday, October 14, 2011 Test 1 Page 3 3 2x + x − 1 mark A13. Evaluate lix→∞ 4x − x + 1 , if it exists. A: 2 B: 1 C: 0 D: 1 E: DNE 3 4 2 3 2 ′ 1 A14. If f(x) = x + 2x − 1, ﬁnd f (x). mark A: x + 2x 2 B: 3x + 2x C: 3x + 4x − 1 D: 3x + 4x + 1 E: 3x + 4x 1 A15. The following function values are known, for some functions f and g: mark f(0) = 0, f (0) = 1, g(0) = 2, g (0) = −1, ′ ′ f(2) = 0, f (2) = 3, g(2) = −2, g (2) = −3. If h = f ◦ g, ﬁnd h (0). A: 0 B: 3 C: −3 D: 1 E: −1 1 A16. If f(x) = √ x, ﬁnd the slope of the tangent line to the graph of y = f(x) at the point mark (1,1). 1 1 A: 1 B: 2 C: 0 D: − E: 2 2 2 ′ 1 A17. If f(x) = , what is f (x)? mark x 2
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