ECON10071 Mid-Term Blackboard Exam 2015

ECON10071 Mid-Term Blackboard Exam 2015 - Each of these...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Each of these multiple-choice questions has exactly ONE correct answer. Complete this Assessment On—line via Blackboard 1. Consider the following two linear equations in x and y : 4x+3y = 2 3x+2y—5 = 0. Which of the following statements is correct? A. There is no solution. B. There is a unique solution. C. There are inﬁnitely many solutions. D. There are exactly two solutions. 2. Consider the following two equations in a: and y : y = 233+1 y = \$2—6JJ-l—3 Which of the following statements is correct? A. There is no solution. B. There is a unique solution. C. There are inﬁnitely many solutions. D. There are exactly two solutions. 3. Consider the following equation in x : e” 2 use + b where a and b are parameters. A suﬂicient condition for a solution to exist is: A.b>1 B C.a>0 D .b<1 4. Consider the following function What is its DOMAIN? A.x>0 B. 33<0 C. x2>0 D. 37%1 5. Consider the following function What is its RANGE? A. (1,00) B. (0,00) C. [0,00) D. [0,1) 33: . . 6. Let y = f(a:) = 1 +x’ 3: 2 0. What 1s the inverse of ﬂay)? A _ 9 9(9) — a, y 6 [03) B — y > 9(9) — E: y _ 0 _ y 1+y D g y = —, y 2 0 < > 3y LL‘ ,x > —1.Fi ure 2 lots 1+x g p 7. The Figure 1 is a graph of the function f (x) = f (x) and another function g(x), the “dashed—line”. Figure 1 Figure 2 The function g(x) is: 2 A. a: ,x>—1 1+x 2x B. >—12 1+2x’x / C. x ,x>—2 2+x a: D. —12 1+2\$,x> / 8. Let f (x) be a continuous function deﬁned on an interval D = [(1,1)], such that f (a) = f (b) = 0, say, and f’ (a) > 0 and f’ (b) > 0. Which of the following statements must necessarily be true? A. f(x) is a cubic B. The equation f (as) = c has only two roots in D, namely :0 = a and a: = b. C. There is a value 360 E (a, b) , such that ﬂew) = c. D. ﬂap) 2 c for all :0 E D. 9. Consider the following function: f(a:) = 3x4 — 2x2 + 6x + 4. What is its derivative? A. f’(w) = 9x3 — 45L“ + 6 B. fl(fL‘) = 33:3 — 2x —— 6 C. f’(x) = 4x3 — 4x —— 6 D. f’(x) = 12x3 — 4x + 6 10. Let f (as) = ln(a:) + 332, x > 0. What is the equation of the linear approximation to f(x) at x = 1? A. yzx—l B. y=3\$—2 C. y=3x—3 D. y—1=3a:—1 11. Let f (as) = ln(a:) + :52, a: > 0. What is the second derivative of f (x)? A. f”(x) = i + 2x B. f”(x) _ g + 2 C f”(m) — —% D f”(a:) = 2 — é LL‘ , x > 0. What is the second derivative of f (x)? 12. Let f(x) = 1 A. f”(rr) = “3—2). B. f”(m) = ﬂ C. f”(x) = —(1—2—x)2 D. f”(x) = % 13. The stationary points of f (x) = x3 — 6x2 + 12% + 18, can be characterised as: A. IL“ 2 2 is a point of inﬂection B. x = 2 is an upward turning point and x = 0 is a downward turning point C. x = 2 is an downward turning point and x = 0 is a upward turning point D. x = 2 can not be characterised because f” (2) = 0. 14. Consider the function f(:L') = 333 — 6352 +1235 + 18. Which of the following statements is correct? A. f x) is convex for x g 2 and concave for x Z 2. B. f :r) is convex for :r g 2 and concave for :r > 2. C. f x) is (globally) strictly increasing. D. f x) is globally convex. 15. What is the global maximum and what is the global minimum of the following function: f(a:) 2 3326—3”, 3: > 0 7 A. Minimum value of 0 at :r 2 00 and maximum value of 46—2 at x = 2. B. Minimum value of 0 at x = 0 and maximum value of 46—2 at :L' = 2. C. No maximum, but a minimum value of 0 at a: = 0. D. No minimum, but a maximum value of 46—2 at a: = 2. 5 16. Let y = y(x) be a differentiable function of as, satisfying x2 — 2953; + 3/2 = 4. What is y’(x) at the point (x, y) = (1, 2)? A. 0 B. 4 C. 2 D. 1 17. Given the difference equation xt+1 = gent — 6, x0 = 0, the particular solution is: A. 3-t — 3, t = 0, 1,2, B. 37*-2 — 9, t = 0, 1, 2, C. 3t—3, t=0,1,2,... D. 32—75 — 9, t = 0, 1, 2, 18. Suppose the proportion of people in the population who will have seen “2012” ( ) by the end of the ﬁrst week, following its release, is m > 0. Thereafter, the proportion of people in the population who will have seen it by the end of week t + 1, following its release, is given by nt+1 = omf, t = 1, 2, ..., where 0 < a < 1 and 0 < 6 < 1 are parameters. Taking natural logarithms we obtain a linear difference equation in xt = ln nt as xt+1 = lna + Bait, t = 1, 2, . Following a long run of the ﬁlm at the cinemas, approximately what proportion of the population will have seen it? A.a lna 31—5 19. Consider the following (2 X 1) vectors: 1 —2 1 —1 0 1(2),b:(1>,.=(0>,d:(_2).:(1> Which of the following statements is correct? A. a 85 b are orthogonal and c 85 e are orthogonal B. a 85 b are orthogonal, c 85 e are orthogonal and a 85 d are orthogonal C. a 85 d are orthogonal and c 85 e are orthogonal D. Just 0 85 e are orthogonal. 20. For the (2 X 1) vectors aTb calculate llall Nb“ 1 A. — x/E 4 B. — V65 1 C. — V65 4 D. — 65 THE END ...
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern