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

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

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