A33_exam_winter_2013.pdf

13 Pages
103 Views
Unlock Document

Department
Mathematics
Course
MATA33H3
Professor
Raymond Grinnell
Semester
Winter

Description
University of Toronto at Scarborough Department of Computer and Mathematical Sciences FINAL EXAMINATION ***** Solutions are not provided***** MATA33 - Calculus for Management II Examiners: R. Grinnell Date: April 19, 2013 E. Moore Time: 9:00 am Duration: 3 hours Last Name (PRINT): Given Name(s) (PRINT): Student Number (PRINT): Signature: Read these instructions: 1. It is your responsibility to ensure that all 13 pages of this examination are included. 2. Put your solutions and/or rough work in the answer spaces provided. If you need extra space, use the back of a page or blank page 13. Clearly indicate your continuing work. 3. Show all work and justify your answers. Full points are awarded for solutions that are correct, complete, and show appropriate concepts from MATA33. 4. You may use one standard calculator that does not perform any: graphing, matrix operations, numerical/symbolic differentiation or integration. Cell/smart phones, i-Pods/Pads, other elec- tronic transmission/receiving devices, extra paper, notes, textbooks, pencil/pen cases, food, drink boxes/bottles with labels, and backpacks are forbidden at your workspace. 5. You may write in pencil, pen, or other ink. Print letters for the Multiple Choice Questions in these boxes: 1 2 3 4 5 6 7 8 9 10 Do not write anything in these boxes A 1 2 3 4 5 6 7 8 TOTAL 30 17 14 15 16 16 11 15 16 150 1 Part A: Ten Multiple Choice Questions Print the letter of the answer you think is most correct in the boxes on the ▯rst page. Each right answer earns 3 points and no answer/wrong answers earn 0 points. ▯ 2 2 4 @z ▯ 83 1. If z = 8y ln(y − 3x) − then ▯ equals (A) (B) 257 (C) 79 y @y (1;2) 3 (D) 80 (E) 129 (F) none of (A) - (E) 2 2. If the y-intercept of a certain level curve of g(x;y) = xy + 3x − y is −1, then the equation of that level curve is y + 1 −y − 1 (A) x = y + 3 (B) x = y + 3 (C) x + y = −1 (D) none of (A) - (C) [ ] ( ) 3. If A is a 3 × 3 matrix such that det(A) = −2 then det det(A ) (2A) ▯1 equals (A) −4 (B) −2 (C) −1 (D) 1 (E) 2 (F) 4 2 4. Let M be an n×n matrix where n ≥ 2. Exactly how many of the following five mathematical properties imply that M is invertible ? 2 (i) det(M) > 0 (ii) MX = 0 has the trivial solution (iii) M ̸= 0 (iv) MX = B has a solution for any n × 1 matrix B (v) CM T = I for some 3 × 3 matrix C (A) 4 (B) 3 (C) 2 (D) 1 (E) 5 1 5. If R is the feasible region defined by the inequality 0 ≤ x ≤ y ≤ x + 1 then for what 2 values of the constant ▯ does the function Z = ▯x + y not have a maximum value on R ? −1 (A) −1 (B) (C) 0 (D) (A) and (B) (E) (B) and (C) (F) (A) and (C) 2 x + ey @z 6. If z = where x = rs + se r and y = 8r + r 2 then at (r;s) = (1;4) is y @s 2 + e 8 + e 8 + e 6 + e (A) (B) (C) (D) (E) none of (A) - (D) 9 4 9 9 7. If the equation z = 16x − 7y defines z implicitly as a function of independent variables x and y, then the value ofxx when x = 1; y = 0 and z = −4 is (A) −2 (B) −1 (C) 0 (D) 1 (E) a number not in (A) - (D) 3 ∫ 4∫ 1 ( √ ) 8. The value of 3 x + 2y dy dx is 0 0 16 26 (A) 20 (B) (C) 16 (D) (E) 12 (F) none of (A) - (E) 3 3 9. The critical points of f(x;y) = 3x+y+6 subject to the constraint x +y = 9 must satisfy the equation (A) x = y (B) x = 2y (C) x = −2y (D) x = 3y (E) y = 2x (F) x = −3y (G) none of (A) - (F) 10. For what values of the constant a will the function f(x;y) = ax −y + xy − x + y have a 2 relative minimum at the critical point (0;1) ? 1 −1 (A) a > 0 (B) a > (C) a < (D) a < 0 (E) (A) or (C) 2 2 (F) real values of a not precisely described by any of (A) - (E) (G) no values of a BE SURE YOU HAVE PUT YOUR ANSWERS IN THE 1-ST PAGE BOXES 4 Part B: Eight Full Solution Questions Full points are awarded only if your solutions are correct, complete, and sufficiently display appropriate concepts from MATA33. √ 9 − x − y 2 1 1. In all of this question let h(x;y) = y − 4 + xy (a) Give an accurate, labeled sketch of the domain D of h. Use light shading to clearly indicate D. Use solid lines for portions of the boundary included in D, and dashed lines or small circles for portions not included in D. [6 points] (b) Find h x2;1) and state your answer as a rational number, not a decimal. [5 points]
More Less

Related notes for MATA33H3

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit