QuesSol_2007

QuesSol_2007 - FACULTY OF ARTS AND SCIENCE University of...

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FACULTY OF ARTS AND SCIENCE University of Toronto FINAL EXAMINATIONS, APRIL/MAY 2007 MAT 133Y1Y Calculus and Linear Algebra for Commerce PART A. MULTIPLE CHOICE 1. [3 marks] The system of equations x + y + z + u + v = 1 y + z + 2 u = 2 z + u + 2 v = 3 has ± A no solutions ± B a unique solution ± C in±nitely many solutions with one parameter ± D in±nitely many solutions with two parameters ± E in±nitely many solutions with three parameters 2. [3 marks] Let h ( x ) = x 2 - 1 x - 1 for x 6 = 1 a - 2 for x = 1 Then h ( x ) is continuous everywhere for a equal to ± A 4 ± B 3 ± C 1 ± D 2 ± E - 2 1

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3. [3 marks] If f ( x ) = ( x + 1) 1 x + ln x , f 0 ( x ) = ± A ( x + 1 ) 1 x + ln x h ( - 1 x 2 + 1 x ) ln ( x + 1 ) + ± 1 x + ln x ² · 1 2( x + 1) i ± B e ( 1 x + ln x ) ln ( x + 1 ) h - ( 1 x 2 + 1 x ) ln ( x + 1 ) + ± 1 x + ln x ² · 1 2 x ( x + 1) i ± C ( x + 1 ) 1 x + ln x h ( - 1 x 2 + 1 x ) ln ( x + 1 ) + ± 1 x + ln x ² · 1 ( x + 1) i ± D e ( 1 x + ln x ) ln ( x + 1 ) h ( - 1 x 2 + 1 x ) ln ( x + 1 ) 2 x + ± 1 x + ln x ² · 1 2 x ( x + 1) i ± E ( x + 1 ) 1 x + ln x h ( - 1 x 2 + 1 x ) ln ( x + 1 ) + ± 1 x + ln x ² · 1 2 x ( x + 1) i 4. [3 marks] The slope of the tangent line to the curve x 3 + 3 y 2 = 4 at (1 , 1) is ± A undeFned ± B - 1 3 ± C 4 3 ± D 3 4 ± E - 1 2 2
5. [3 marks] On the interval ( 1 2 , 2 ) , the function f ( x ) = e - ( x 2 + x - 2 ) has ± A a local minimum but no local maximum ± B a local maximum but no local minimum ± C a local maximum and a local minimum ± D neither a local maximum nor a local minimum ± E two local minima and no local maximum 6. [3 marks] lim x →∞ ( x 2 + 1) 1 x 2 +2 ± A does not exist ± B = e 1 2 ± C = e ± D = 0 ± E = 1 7. [3 marks] When using the Trapezoidal Rule with the interval [ - 2 , 6] divided into n = 4 subintervals the approximate value of Z 6 - 2 p 1 + x 2 dx is closest to ± A 23 . 04 ± B 21 . 55 ± C 22 . 19 ± D 15 . 36 ± E 14 . 37 3

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8. [3 marks] Z 1 - 1 x 2 3 dx (2 + x 5 3 ) 3 = ± A - 1 3 ± B 3 5 ln 27 ± C - 64 27 ± D 1 5 ± E 4 15 9. [3 marks] Z e 1 x ln x dx = ± A e 2 - e + 1 2 ± B 1 2 ± C e 2 2 ± D e 2 + 1 4 ± E 0 4
10. [3 marks] Z 3 x - 4 ( x - 1)( x - 2) dx = ± A 3 ln | ( x - 1)( x - 2) | + C ± B 3 ln ± ± ± x - 2 x - 1 ± ± ± + C ± C 3 ln ± ± ± x - 1 x - 2 ± ± ± + C ± D ln ± ± ± ( x - 1)( x - 2) 2 ± ± ± + C ± E ln ± ± ± x - 1 ( x - 2) 2 ± ± ± + C 11. [3 marks] Z 8 1 3 x dx ± A diverges ± B = 6 ± C = - 6 ± D = 4 ± E = - 4 5

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12. [3 marks] If f ( x, y, z ) = x 2 y 3 z 4 , f xyz (2 , - 1 , - 2) = ± A - 3 8 ± B - 3 2 ± C - 1 4 ± D 3 2 ± E 3 8 13. [3 marks] If two products called A and B have the joint demand functions q A ( p A , p B
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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.

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QuesSol_2007 - FACULTY OF ARTS AND SCIENCE University of...

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