QuesSol_2002

# QuesSol_2002 - FACULTY OF ARTS AND SCIENCE University of...

This preview shows pages 1–6. Sign up to view the full content.

FACULTY OF ARTS AND SCIENCE University of Toronto FINAL EXAMINATIONS, APRIL/MAY 2002 MAT 133Y1Y Calculus and Linear Algebra for Commerce PART A. MULTIPLE CHOICE 1. [3 marks] lim x →- 8 - x + 8 | 64 - x 2 | ± A equals 1 ± B equals 0 ± C equals 1 16 ± D equals - 1 16 ± E does not exist 2. [3 marks] The system of linear equations 2 x 1 - 4 x 2 - 6 x 3 = 2 x 1 - 2 x 2 - x 3 = 1 - x 1 + 2 x 2 + 5 x 3 = - 1 has ± A no solution ± B unique solution with x 3 = 0 ± C in±nitely many solutions with x 2 = 0 ± D in±nitely many solutions with x 3 = 0 ± E in±nitely many solutions with x 1 = 0 1

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

View Full Document
3. [3 marks] The equation ( xy ) 3 = 4 y - 3 defnes y implicitly as a Function oF x near the point x = 1 , y = 1 . At this point y 0 is ± A undefned ± B 3 ± C 0 ± D - 1 ± E - 3 4. [3 marks] IF f ( x ) = x x 2 + 1 , then ± A f has an absolute maximum and an absolute minimum ± B f has an absolute maximum but only a local minimum ± C f has an absolute minimum but only a local maximum ± D f has no absolute maximum and no absolute minimum, but only a local maximum and a local minimum ± E f has no absolute or local extrema at all 5. [3 marks] IF the total revenue Function is r ( q ) = 2500 q ln(10 q + 10) , where q is the number oF units oF some commodity, then the marginal revenue when q = 100 is closest to ± A 310 ± B 36 , 139 ± C 356 ± D 248 ± E 2 , 475 2
6. [3 marks] lim x 1 2 x - 2 ln x ± A = 2 ln 2 ± B = 2 ± C = 0 ± D = 1 2 ± E does not exist 7. [3 marks] y=ln x a x y b 1 x The area of the shaded region is given by: ± A Z a 0 ln y dy ± B Z b 0 ( a - ln x ) dx ± C Z a 0 e y dy ± D Z a 0 ( b - e y ) dy ± E Z b 0 ln x dx - Z b 1 ln x dx 3

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

View Full Document
8. [3 marks] If A and B are real numbers such that x + 9 x 2 - 9 = A x + 3 + B x - 3 (wherever both sides of the equality are deFned) then A = ± A - 2 ± B 0 ± C 1 ± D - 1 ± E 2 9. [3 marks] Z 1 0 xe 3 x dx = ± A 1 3 ± B 1 + 2 e 3 9 ± C - 1 + 4 e 3 9 ± D 1 + 2 e 3 3 ± E - 1 - 4 e 3 9 10. [3 marks] Z 2 dx x ± A equals 2 ± B diverges ± C equals 1 ± D equals 2 2 ± E equals 2 4
11. [3 marks] From time t = 0 until time t = 8 years, cash fows into an account which earns interest continuously at a rate o± 5% per year. I±, at time t years, the rate o± the cash fow is 1000 e . 3 t dollars per year, then the present value o± the total cash fow (to the nearest dollar) is ± A \$25 , 556 ± B \$27 , 038 ± C \$21 , 297 ± D \$18 , 254 ± E \$33 , 411 12. [3 marks] y is a ±unction o± x such that e y y 0 = 2 x and y = 1 when x = 0 , then when x = 1 , y = ± A 1 ± B 0 ± C ln(1 + e ) ± D ln 3 ± E - ln 2 13. [3 marks] f ( x, y ) = x y ±or x > 0 , y > 0 , then

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.

## This note was uploaded on 03/25/2010 for the course MATH MAT133 taught by Professor / during the Spring '09 term at University of Toronto.

### Page1 / 16

QuesSol_2002 - FACULTY OF ARTS AND SCIENCE University of...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online